text:
\section{Introduction}
The conduction of ions in nanochannels forms the basis of electrical signalling in biology ~\cite{hille2001ion, eisenberg1996computing, doyle1998structure, catterall2000ionic, sakmann2013single, Maffeo2012} and of promising technologies in desalination ~\cite{shannon2010science, goh2016nano}, ionic separations \cite{lu2020efficient, li2020strong}, and nanofluidic transistors ~\cite{karnik2007rectification, karnik2005electrostatic, daiguji2010ion}. As ions become confined to nanopores, they experience strong chemical and electrostatic interactions with the pore walls, leading to membrane selectivity based on charge or chemical interactions. Nanoporous membranes can even enter the regime where the double layers emanating from each charged surface begin to overlap, leading to strong electrokinetic coupling of fluid flow, electric field, and ionic fluxes ~\cite{gross1968membrane, peters2016analysis, biesheuvel2016analysis, alizadeh2017multiscale, qiao2005scaling, qiao2005surface}. Understanding the electrostatics of charges in confinement is crucial to determining the flux, selectivity, and driving force relationship for engineering applications ~\cite{elimelech2011future,faucher2019critical} and for understanding biological pore systems ~\cite{Branton2008,HAQUE201356, gillespie2002coupling, chen1997permeation}.

The unique physics of ionic screening in one dimensional confinement leads to the phenomenon of electroneutrality breakdown, where the number of counter-charges within a pore does not perfectly counterbalance the number of fixed charges on the pore walls ~\cite{levy2020breakdown}. One dimensional (1D) confinement refers to confinement onto a line, for example, in a cylindrical nanopore connecting two reservoirs of fixed concentration. In essence, electroneutrality breakdown signifies that a fraction of the electric field must escape through the pore walls into the dielectric matrix constituting the membrane. The screening charge does not exist locally within the pore, but rather is distributed over the membrane surface in the reservoirs, outside of the membrane domain. Uniquely, in 1D confinement, the loss of electroneutrality can extend to macroscopic scales (beyond length $L=10$ $\mu$m), since for strong confinement $\kappa_D R\rightarrow 0$ the system only approaches electroneutrality as $\log(L/R)\rightarrow \infty$, where $L$ is the length of a pore, $R$ is its radius, and $\kappa_D$ is the inverse Debye length. The long-range breakdown of local electroneutrality in 1D confinement is surprising, and many models of electrokinetic phenomena have assumed pore-wide electroneutrality, even in the limit of strong double layer overlap ~\cite{peters2016analysis, secchi2016scaling, biesheuvel2016analysis}.

Here, we perform continuum simulations of 1D nanopores using COMSOL Multiphysics, to confirm the occurrence of electroneutrality breakdown. We show that the results for the screening charge within an isolated 1D pore can be captured quantitatively with analytical formulas. Furthermore, we perform simulations of a periodic array of channels, a multipore membrane, with varying spacing between the channels. There, we find how the interactions of closely-spaced channels can lead to the return of electroneutrality in the system. In the limit of strongly interacting channels, the variations in potential in the axial direction dominate the distribution of ionic charges within the membrane. Effectively, when channels are too close to each other, the electric field lines cannot emanate through the membrane domain.

The continuum simulation results show the ensemble interactions of the channels with each other play a role in ionic conduction through nanochannels. In membrane applications, the interactions mean that the greatest ionic selectivity and per-channel-conductivity can be achieved when channels are close together for the regime of strong double layer overlap.  Further, the results point to ensemble interactions between 1D-confined channels, and the importance of electric field spilling into the dielectric matrix when channels are isolated. The competition between channel interactions and electroneutrality breakdown ultimately affects the conductance and slectivity behavior of arrays of nanochannels in the low concentration limit.

\begin{figure*}[!htbp] \label{fig:fig1}
\includegraphics[width=1\linewidth]{Figure1.png}
\caption{The simulation configuration in COMSOL (a) with the membrane, pore, and electrolyte (b) for an isolated pore that does not feel its periodic neighbors and (c) a periodic arrangement of pores on a square lattice. (d) A cross-section of the system through the center of the cylindrical pore is shown to describe the domains and equations applied in the simulations. (e) A sample of continuum simulation results showing the progress from non-interacting to interacting channels for small charge densities. For all channels, the channel radius is 1 nm and the length is 100 nm. The membrane dielectric constant is $\epsilon_m=10\epsilon_0$ and the electrolyte dielectric constant is $\epsilon_w=80\epsilon_0$. The salt concentration is 1 mM. In order from left to right, the spacing between the channel centers $\ell$ is 129 nm, 77 nm, 46 nm, 28 nm, and 17 nm. Also in order, the amount of charge within the pore versus on the channel walls, $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ is: 12\%,13\%, 17\%, 26\%, and 43\%. As the channels become closer together and more interacting, the system returns closer to electroneutrality, which is evidenced by the higher $\phi$ values within the pore. }
\end{figure*}

\section{Theoretical framework}
\subsection{Outline of equations}
As explained in more detail in Appendix A, the ionic flux and selectivity out of equilibrium can be assumed to be related to the solution of the Poisson-Boltzmann (PB) equation in equilibrium, assuming that both reservoirs on each side of the membrane have the same concentration of electrolyte and fluid flow is neglected ~\cite{gross1968membrane, peters2016analysis}. As emphasized in Fig. 1, the simulation is composed of a square membrane domain, $\Omega_m$, with side length $\ell$, through which a cylindrical pore of radius $R$ and length $L$ connects two reservoirs of fixed concentration. The reservoirs and pore constitute the electrolyte domain, signified as $\Omega_w$, where $w$ is chosen to signify water.

As exhibited in Fig. 1(a-d), the system of equations being solved in the electrolyte domain $\Omega_w$ is:
\begin{equation}
    \epsilon_w\nabla^2\phi=-\rho_e
\end{equation}
with dielectric constant $\epsilon_w$, electrostatic potential $\phi$, and charge density $\rho_e$ where the ionic concentrations are Boltzmann-distributed:
\begin{equation}
    \rho_e=\sum_i z_i e c_{i,b}\exp\left(-\frac{z_ie\phi }{k_B T}\right),
\end{equation}
where $z_i$ are the ion valencies, $e$ is the elementary charge, $c_{i,b}$ is the bulk reservoir concentration for ion $i$, $k_B$ is the Boltzmann constant, and $T$ is the absolute temperature. Here we neglect any packing ~\cite{bazant2009towards}, correlation ~\cite{Bazant2011}, or charge regulation ~\cite{trefalt2016charge} effects in our model.
We assume a 1:1 solution of salt with concentration $c_0$ in units of number density, such that the PB equation is reduced to:
\begin{equation}
    \epsilon_w\nabla^2\phi=2 e c_0 \sinh\left(\frac{e\phi }{k_B T}\right)
\end{equation}

In the membrane domain, we solve the Laplace equation:
\begin{equation}
    \epsilon_m\nabla^2\phi=0
\end{equation}
assuming that the membrane is a perfect dielectric material with dielectric constant $\epsilon_m$.

At the membrane/electrolyte domain interface, Maxwell's equation is enforced:
\begin{equation}
\mathbf{\hat{n}}\cdot\left[-\epsilon_m\nabla\phi+\epsilon_w\nabla \phi\right]\Bigg\rvert_s=q_s
\end{equation}
where $\mathbf{\hat{n}}$ is the unit normal pointing from the electrolyte to the membrane domain and $q_s$ is the surface charge density. To isolate the electrostatic potential variations due to fixed charge on the channel walls, $q_s$ is assumed to be zero on the membrane/electrolyte reservoir interfaces, but is nonzero at the pore walls.

At the lateral boundaries of each cell, symmetry conditions are applied; namely, the electric field at the boundary is zero $\mathrm{\hat{n}}\cdot \nabla \phi=0$. The boundary conditions are identical to assuming a periodic array of channels with regular spacing, consisting of unit cells identical to the simulation box, as illustrated in Fig. 1(c). At the top and bottom boundaries of the simulation box, Dirichlet conditions are applied $\phi=0$. A useful check to ensure that the simulation box is large enough is to ensure that all the integrated charges in the electrolyte domain are equal and opposite to the integrated amount of fixed charges on the pore walls. For this study, a reservoir height of 20 $\lambda_D$ is sufficient to meet this criterion, where the Debye length, $\lambda_D$ is given by:
\begin{equation}
    \lambda_D={\kappa_D}^{-1}=\sqrt{\frac{\epsilon_w k_B T}{2 e^2 c_0}}
\end{equation}

\begin{figure*}[!htbp] \label{fig:fig2}
\includegraphics[width=1\linewidth]{Figure2.png}
\caption{The results for an isolated pore with overlapping and non-overlapping double layers within the pore.  (a) plot of the potential profile for overlapping double layers at $c_0=1 $ mM ($\kappa_DR\approx0.1$) (a) versus less overlapping double layers at $c_0=100$ mM ($\kappa_DR\approx1$)(b). The same parameters are used as in Fig. 1(e), except the center to center distance between pores is 500 nm such that the periodic channels are not interacting. For (a) 12\% of the charge is contained within the pore, whereas for (b) 91\% of the charge is contained within the pore.(c) The charge within the pore versus on the pore walls as a function of $\kappa_D R$ for the same channel in parts (a) and (b). Electroneutrality breakdown occurs in the region of strong double layer overlap $\kappa_D R\rightarrow 0$. For (c) the markers are the COMSOL simulations, whereas the line is the application of the approximate formula in equation \ref{eq:eq1DMLR}. (d-e) The integrated ionic charge as a function of the lateral position for $c_0=$ 1 mM and 100 mM. The charge is distributed over a wide area $O(L)$ extending beyond the pore mouth when electroneutrality is broken ($c_0$=1 mM), but is more localized when electroneutrality is maintained ($c_0$=100 mM) . (e) Quantification of end effects for two different concentrations. The electrostatic potential is plotted as a function of the $z$ coordinate, evaluated at the center axis of the channel. End effects are not significant for isolated channels.     }
\end{figure*}

\subsection{Approximate formulas}
While we compute the full results of the PB equation in 3D, we compare the results to mathematical simplified formulas. As outlined in more detail in Appendices B and C, we can reduce our partial differential equation system of the 3D PB and Laplace equations into ordinary differential equations with appropriate boundary conditions. For small potentials, we then linearize the equations and get simple analytical formulas for the number of ionic charges within the membrane. In order to quantify the extent of electroneutrality breakdown, we take the ratio for the integrated amount of charge within the pore and the integrated amount of charge on the pore walls: $\mid Q_\mathrm{in}/Q_\mathrm{out} \mid$. In the limit of electroneutrality, we get  $\mid Q_\mathrm{in}/Q_\mathrm{out} \mid\rightarrow 1$, whereas in the limit of complete electroneutrality breakdown, we get $\mid Q_\mathrm{in}/Q_\mathrm{out} \mid\rightarrow 0$.
\begin{figure*}[!htbp] \label{fig:fig3}
\includegraphics[width=1\linewidth]{Figure3.png}
\caption{Extent of electroneutrality breakdown for channels of different center-to-center separation distances on a lattice.
 (a) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\kappa_D R$ for $\ell/L=5$, $\ell/L=1$, $\ell/L=0.1$. (c) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\ell/L$ for $c_0=0.01, 1,100$ mM for $\ell/L=0.02$ to $\ell/L=0.5$. For both (a) and (c), the markers are the COMSOL simulations, whereas the solid lines are the application of the approximate formula in equation \ref{eq:eq1DMLR} and the dotted lines are the application of the approximate formula in equation \ref{eq:eqEndEffects}. (b) The integrated ionic charge as a function of the lateral position for $\ell/L=$ 5 and 0.05, with $c_0=$ 1 mM. The charge is distributed over a wide area when channels are isolated, but is localized when the channels are closely spaced and strongly interacting. (d) Quantification of end effects for two different lattice spacings with $c_0=$ 1 mM. The electrostatic potential is plotted as a function of the $z$ coordinate, evaluated at the center axis of the channel. End effects are significant when the channels are interacting.      }
\end{figure*}

\textbf{No end effects:} Ignoring end effects, the inner potential can be solved for in terms of only the radial coordinate:
\begin{equation}
    \frac{\epsilon_w}{r}\frac{d}{dr}\left(r\frac{d \phi}{dr}\right)=2ec_0 \sinh\left(\frac{e\phi}{k_B T}\right)
\end{equation}
with boundary conditions given by:
\begin{equation} \label{eq:eqBCMLR}
    \frac{d\phi}{dr}(r=R)=\frac{q_s}{\epsilon_w}-\frac{\epsilon_m}{\epsilon_w}\frac{\phi(r=R)}{R M_{L/R}}, \quad \frac{d\phi}{dr}\left(r=\frac{\ell}{2}\right)=0
\end{equation}
where the constant $M_{L/R}$ is:
\begin{equation}\label{eq:eqMLR}
    M_{L/R}=\log \left(\frac{2L}{\pi R}\right)-\gamma+\frac{\mathrm{K}_1(\frac{\pi\ell}{2L})}{\mathrm{I}_1(\frac{\pi\ell}{2L})}.
\end{equation}
with $\gamma=0.577$ signifying the Euler-Mascheroni constant. Here, we assume circular shape of a unit cell for analytical simplicity, and the derivation is presented in Appendix B. Linearizing the equations and solving, we find the folllowing relationship for the amount of charge inside versus the amount of charge fixed on the pore walls:
\begin{equation}\label{eq:eq1DMLR}
    \left\rvert \frac{Q_\mathrm{in}}{Q_\mathrm{out}}\right\rvert=\frac{1}{1+\frac{\epsilon_m}{\epsilon_w}\frac{2}{{\kappa_D}^2 R^2 M_{L/R}}}
\end{equation}

\begin{figure*}[!htbp] \label{fig:fig4}
\includegraphics[width=1\linewidth]{Figure4.png}
\caption{Role of dielectric mismatch on extent of electroneutrality breakdown. (a)Results for isolated pore with same properties as in Fig. 1 (e), but with $\epsilon_m=\epsilon_0$, $\epsilon_m=10\epsilon_0$, and $\epsilon_m=100\epsilon_0$. (b) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\kappa_D R$ for varying $\epsilon_m$. (b) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\ell/L$ with $c_0=1$ mM for varying $\epsilon_m$.For both (b) and (c), the markers are the COMSOL simulations, whereas the solid lines are the application of the approximate formula in equation \ref{eq:eq1DMLR}  and the dotted lines are the application of the approximate formula in equation \ref{eq:eqEndEffects}.   }
\end{figure*}

Looking at the form of the above equation, one recognizes that electroneutrality breakdown is promoted as $\kappa_D R\rightarrow 0$. Furthermore, the effect has a weak dependence on the length of non-interacting nanopores, since the length appears logarithmically in $M_{L/R}$. However, the electrostatic interactions of the cylinders with each other can cause a return to electroneutrality as $\ell/L\rightarrow 0$. Furthermore, the amount of charge within the pore is strongly controlled by the dielectric constant of the membrane (and not necessarily the inner pore dielectric constant).

\textbf{No radial variations:} On the other hand, when channels become strongly interacting ($\ell/L\rightarrow 0$), the potential variations happen principally in the axial direction along the pore, governed by the dimensionless ratio $\lambda_D/L$. In order to capture the end effects of the channel, which become important on the scale of the Debye length, we write down a homogenized equation for the potential in linear response, which neglects radial variations in the potential by integrating over the lateral dimensions of a unit cell:
\begin{equation}\label{eq:eqAvgPois}
    \bar{\epsilon}\frac{d^2\phi}{dz^2}=-\frac{2 q_s}{R}+2ec_0\sinh\left(\frac{\phi e}{k_B T}\right)
\end{equation}
\begin{equation}\label{eq:eqAvgPoisPerm}
    \bar{\epsilon}=\epsilon_w-\epsilon_m+\epsilon_m\left(\frac{\ell}{\pi R}\right)^2
\end{equation}
The linear response boundary conditions are given by:
\begin{equation} \label{eq:eqAvgPoisBC}
    \frac{d\phi}{dz}\left(z=0,L\right)=\pm\frac{\epsilon_w}{\bar{\epsilon}}\frac{\ell^2}{\pi R^2}\frac{\phi\left(z=0,L\right)}{\lambda_D}.
\end{equation}
Solving the set of equations, we get the following fraction of charge inside the pore.
\begin{equation} \label{eq:eqEndEffects}
    \left\rvert \frac{Q_\mathrm{in}}{Q_\mathrm{out}}\right\rvert=\frac{1-(\gamma-p)\tanh(1/\gamma)}{1+p\tanh(1/\gamma)}
\end{equation}
with constants
\begin{equation}
    \gamma=2\sqrt{\frac{\bar{\epsilon}}{\epsilon_w}}\frac{\lambda_D}{L}, \quad p=\left(\frac{\bar{\epsilon}}{\epsilon_w}\frac{\pi R^2}{\ell^2}\frac{\pi R^2}{(\ell^2-\pi R^2)}\right)^{1/2}
\end{equation}

For strongly interacting channels, the electroneutrality condition is controlled by the ratio of $\lambda_D/L$. As $\lambda_D/L\rightarrow 0$, the system returns to overall electroneutrality within the pore.

Following the theoretical argument, a comprehensive set of numerical simulations is presented to validate the above formulas in their regime of validity, focusing on the linear regime with small but finite surface charge, $q_s\rightarrow 0$. The standard conditions chosen for the simulations, unless otherwise stated, are a pore length of 100 nm, a pore radius of 1 nm, a membrane permittivity of $\epsilon_m=10\epsilon_0$, an electrolyte permittivity of $\epsilon_w=80\epsilon_0$. Finally, a comparison is also made to the nonlinear solution of the full 3D equations.

The results are presented with a number of dimensionless numbers, so a reader can easily interpret the plots. First, the dimensionless number $\kappa_D R$ indicates the extent of double layer overlap within the channel. $\kappa_D R\rightarrow0$ indicates strong double layer overlap while $\kappa_D R\rightarrow\infty$ indicates thin double layers relative to the pore radius. $\ell/L$ is the ratio of the center to center spacing between channels to the length of the channels. In plotting, the potential is normalized by the charge per unit length of a cylinder:
\begin{equation}\label{eq:eqDimPot}
    \tilde{\phi}=\frac{\phi \epsilon_w R}{2 q_s \lambda_D^2}
\end{equation}
One can roughly interpret these graphs as $\tilde\phi\approx 1$ means local electroneutrality in a give cross section of the pore, and $\tilde\phi\approx 0$ as local electroneutrality within the pore. Further, the depth-integrated charge density is plotted as a function of lateral position, to illustrate the extent of screening charges at the membrane/reservoir interfaces:
\begin{equation}
    \bar{\rho}_e(x,y)=\frac{\int \rho_e(x,y,z) dz}{L}.
\end{equation}

\section{Results and Discussion}
First, Fig. 1(e) summarizes the main trends seen in the simulations, where the potential is plotted as a function of position around the pore, as the spacing between pores is modified. When channels are isolated ($\ell=129$ nm), the potential within the channel is fairly constant. The variations in the potential in the radial direction are dominant. For the parameters chosen ($\kappa_D R=0.1$, $c_0=$ 1 mM), the amount of charge within the channel is only 12\% of the charge on the pore walls. However, as the size of a unit cell is reduced ($\ell=17$ nm) the variations in the potential become dominant in the axial direction, and edge effects become more pronounced. Furthermore, the potential does not vary significantly in the radial direction from the channel center axis.  The close channel spacing also limits the amount of field that can escape out of the pore, meaning that more charges are present within the channel, 43\%.

\begin{figure*}[!htbp] \label{fig:fig5}
\includegraphics[width=1\linewidth]{Figure5.png}
\caption{Role of aspect ratio on extent of electroneutrality breakdown. (a)Results for isolated pore with same properties as in Fig. 1 (e), but with $L=10$ nm, $L=100$ nm, and $L=1000$ nm, also with $c_0=$ 1 mM. (b) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\kappa_D R$ for varying $L$, with $\ell/L=5$. (b) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\ell/L$ with $c_0=1$ mM for varying $L$. For both (b) and (c), the markers are the COMSOL simulations, whereas the solid lines are the application of the approximate formula in equation \ref{eq:eq1DMLR} and the dotted lines are the application of the approximate formula in equation \ref{eq:eqEndEffects}.   }
\end{figure*}

The trends in the potential profiles as a function of the salt concentration are shown in Fig. 2. Fig. 2(a) corresponds to $\kappa_D R=0.1$ or $c_0$=1 mM, and 2(b) corresponds to $\kappa_D R=1$ of $c_0=$ 100 mM, illustrating that electroneutrality is restored as the concentration is increased. The solid line in Fig. 2(c) given by equation \ref{eq:eq1DMLR} coincides quite closely with the results of the continuum simulations for the isolated channels. For these cases, neglecting end effects is a reasonable approximation for determining the number of charges within the pore, which is confirmed via the plot of the potential as a function of position along the center axis of the pore in Fig. 2(f). In Fig. 2(d-e), the depth-integrated charge density, $\bar{\rho}_e$, is plotted as a function of the $x$ and $y$ coordinate. When electroneutrality is broken within the pore, the screening charge is distributed over the membrane surface over a distance that is on the order of the channel length, $L$. However, if electroneutrality is maintained, the screening charge is localized within the channel, and does not extend very far beyond the pore mouth.

\begin{figure*}[!htbp] \label{fig:fig6}
\includegraphics[width=0.9\linewidth]{Figure6.png}
\caption{Role of dimensionality of confinement by inspecting a slit pore geometry. (a)Results for isolated pore with same properties as in Fig. 1 (e), but for a slit pore. (b) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\kappa_D R$ for varying $\ell/L$. (c) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\ell/L$ for varying $c_0$. (d-e) The same as (b-c) but with $L=1000$ nm.  For (b), (c), (d), and (e), the markers are the COMSOL simulations, whereas the solid lines are the application of the approximate formula in equation \ref{eq:eq2DMLR} and the dotted lines are equation \ref{eq:eqEndEffects} with constants given by equations \ref{eq:eq2Dconst1} and \ref{eq:eq2Dconst2}.   }
\end{figure*}

Next, we isolate the influence of channels interacting through the membrane domain, via modifying the ratio $\ell/L$ in Fig. 3. As channels are closer together, $\ell/L\rightarrow 0$, the amount of charge within the channel is increased closer towards electroneutrality. We also see a clear difference between the predictions neglecting end effects (equation \ref{eq:eq1DMLR}) in solid lines and the predictions neglecting radial variations (equation \ref{eq:eqEndEffects}) in dotted lines. As $\ell/L\ll1$, the predictions of the model neglecting radial variations become superior. However, when $\ell/L$ is 1 or greater, the predictions of the model that neglects end effects are superior. Such a result is expected, given the illustrative example in Fig. 1(e), where the importance of end effects are visible on the plot when channels are close together. For further confirmation, the magnitude of the electric field is plotted as a function of position for varying channel spacings in Fig. S2, exhibiting the importance of end effects for closely spaced channels. In Fig. 3(d), the potential plotted as a function of position on the center axis of the nanopore shows significant end effects for closely spaced channels ($\ell/L$=0.05). Also, the closely spaced channels localize the screening charge near the pore mouth, as evidenced by the depth-averaged charge density in Fig. 3(b).

\begin{figure*}[!htbp] \label{fig:fig7}
\includegraphics[width=1\linewidth]{Figure7.png}
\caption{Role of nonlinearity on extent of electroneutrality breakdown. (a)Results for isolated pore with same properties as in Fig. 1 (e), but with $q_s\rightarrow 0$, $q_s=0.001$ C/m$^2$, and $q_s=0.01$ C/m$^2$ with $c_0=$ 1 mM. (b) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\kappa_D R$ for varying $q_s$. (b) $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid$ versus $\ell/L$ with $c_0=1$ mM for varying $q_s$. For both (b) and (c), the markers are the COMSOL simulations, whereas the solid line is the application of the approximate formula in equation \ref{eq:eq1DMLR} and the dotted line is the application of the approximate formula in equation \ref{eq:eqEndEffects}.   }
\end{figure*}

The interactions of channels has a profound impact on the selectivity of a multipore dielectric membrane. The ensemble interactions can lead to a return to electroneutrality in strongly confined systems, leading to more charge selectivity and higher channel conductance. The extent of electrokinetic couplings are also maximized when the amount of ionic charge within the pore is higher ~\cite{peters2016analysis, VanderHeyden2006}. Such a design principle could be used to promote higher electrokinetic conversion efficiencies in ``blue energy'' harvesting of salinity gradients ~\cite{POST2007218, He2017}.

Another important design parameter is the dielectric constant of the membrane matrix. In Figure 4, we examine the influence of the membrane dielectric constant on the extent of electroneutrality breakdown. As the membrane dielectric constant decreases, the system moves closer towards electroneutrality in the pore. Again, the predictions from equations \ref{eq:eq1DMLR} and \ref{eq:eqEndEffects} seem to describe the data quite well within their respective realms of validity.

A critical question remains to understand the influence of the aspect ratio on the extent of electroneutrality breakdown, the subject of Figure 5. Again observing equation \ref{eq:eq1DMLR}, for an isolated channel, the electroneutrality is enforced as $\log(L/R)\rightarrow\infty$. Therefore, the electroneutrality breakdown is only weakly affected by the length of the channel. As shown in Figure 5(b), we see only small shifts in the extent of electroneutrality breakdown with increasing channel length, $L$. Furthermore, the channels exhibit similar behavior with varying channel spacing, $\ell$. Such results arise from the exponentially long screening length in one dimensional confinement~\cite{levy2020breakdown}.

As a point of comparison, it is instructive to perform the same analysis for two dimensional confinement, or slit pore geometry. Here, we perform analogous continuum simulations to the 1D confinement case. In Figure 6, we have simulated a slit pore with width $2R$ and length $L$, with channel center to channel center distances of $\ell$. We compare the simulation results to two analytical formulas, one where we have neglected end effects, and one where we have neglected radial variations in the potential, similar to the analysis for 1D confinement, as outlined below.

The extent of electroneutrality breakdown in 2D confinement, \textbf{ignoring edge effects}, is:
\begin{equation} \label{eq:eq2DMLR}
    \left\rvert \frac{Q_\mathrm{in}}{Q_\mathrm{out}}\right\rvert=\frac{1}{1+\frac{\epsilon_m}{\epsilon_w}\frac{1}{{\kappa_D}^2 R^2 M_{L/R}}}
\end{equation}
with modified constant $M_{L/R}$ given by:
\begin{equation}
    M_{L/R}=\frac{L}{\pi R}\coth\left(\frac{\pi}{L}(\ell/2-R)\right)
\end{equation}
Observing the form of the 2D $M_{L/R}$ in this scenario, it is apparent that electroneutrality is enforced as $L/R\rightarrow\infty$. This means that electroneutrality will be much more strongly upheld in 2D confinement compared to 1D confinement.

When $\ell/L$ becomes smaller, the potential variations in the axial direction of the 2D slit pore become dominant, similar to 1D confinement. The extent of electroneutrality breakdown \textbf{neglecting radial variations} is given identically by equation \ref{eq:eqEndEffects}, but with constants
\begin{equation}\label{eq:eq2Dconst1}
    \gamma=2\sqrt{\frac{\bar{\epsilon}}{\epsilon_w}}\frac{\lambda_D}{L}, \quad p=\left(\frac{\bar{\epsilon}}{\epsilon_w}\frac{4 R^2}{\ell^2}\right)^{1/2}
\end{equation}
where
\begin{equation}\label{eq:eq2Dconst2}
    \bar{\epsilon}=\epsilon_w-\epsilon_m+\epsilon_m\left(\frac{\ell}{2 R}\right).
\end{equation}
The progression towards electroneutrality breakdown for 2D confinement is similar to 1D confinement when the channel spacing is close together.

In Fig. 6(b-e), we see that the propensity towards electroneutrality is much stronger in 2D confinement than in 1D confinement. We find that, similar to 1D confinement, electroneutrality is promoted when channels are strongly interacting. We also find that the extent of electroneutrality breakdown is extremely sensitive the to the length of the channel domain, especially as compared to 1D confinement, as emphasized by comparing Fig. 6(d-e) to Fig. 6(b-c). Note that the normalization of the potential in Fig. 6(a) is adjusted from the definition in equation \ref{eq:eqDimPot} due to the difference in geometry.

So far, we have examined the linear regime with small but finite values of $q_s$. Evidently, the nonlinearity in the equations will affect the validity of our approximations in equations \ref{eq:eq1DMLR} and \ref{eq:eqEndEffects}. In Fig. 7, we show that as the charge density is increased into the nonlinear regime, the system moves closer towards electroneutrality. The approximations we derived earlier are insufficient to describe the extent of electroneutrality breakdown in the nonlinear limit.  It is particularly difficult to derive analytical approximations in the nonlinear limit, so we do not explore such approximations here. Even so, for isolated channels, the electroneutrality breakdown emerges as a function of the ratio of the Gouy-Chapman length to the pore radius in this limit~\cite{levy2020breakdown}.

Finally, we preview the possible manifestations of electroneutrality breakdown that could be observed in experiments: single channel conductance and transference number, using the simplified formulas in equation \ref{eq:eq1DMLR} and equation \ref{eq:eqEndEffects}. We assume a KCl solution with fixed and equal mobilites, equal to the bulk value of $D=D_+=D_-=2\times10^{-9}$ m$^2$/s. For an uncharged pore, the fraction of current carried by each ion would be 50\%. However, in this case, we assume that the pore walls are negatively charged with a value of $q_s=-0.001$ C/m$^2$. Therefore, we approximate the anion and cation concentrations within the channel as:
\begin{equation}
    c_+=c_0+\frac{2 \mid q_s\mid}{e R}\frac{\mid Q_\mathrm{in}\mid}{\mid Q_\mathrm{out}\mid}, \quad c_-=c_0
\end{equation}
We approximate the overall channel conductance as:
\begin{equation}
    G= \frac{2 \pi D R^2  e^2 c_0}{k_B T L}+\frac{2  \pi D R e \mid q_s\mid}{ k_B T L}\frac{\mid Q_\mathrm{in}\mid}{\mid Q_\mathrm{out}\mid}
\end{equation}
which can be rendered dimensionless:
\begin{equation}
    \tilde{G}= G/\left(\frac{2 \pi D R^2  e^2 c_\mathrm{ref}}{k_B T L}\right)=\frac{c_0}{c_\mathrm{ref}}+\frac{ \mid q_s\mid}{ R e c_\mathrm{ref}}\frac{\mid Q_\mathrm{in}\mid}{\mid Q_\mathrm{out}\mid}
\end{equation}
where $c_\mathrm{ref}$ is arbitrarily chosen to be 1 mM.
The corresponding cation transference number, or fraction of current carried by the cation, is:
\begin{equation}
    t_+= \left(c_0+\frac{2 \mid q_s\mid}{e R}\frac{\mid Q_\mathrm{in}\mid}{\mid Q_\mathrm{out}\mid}\right)/\left(2 c_0+\frac{2 \mid q_s\mid}{e R}\frac{\mid Q_\mathrm{in}\mid}{\mid Q_\mathrm{out}\mid}\right).
\end{equation}
The dimensionless conductance and cation transference number are shown in Fig. 8, for a channel with the sample parameters: $L=$ 100 nm, $R=$ 1 nm, $\epsilon_m=10\epsilon_0$,  $\epsilon_w=80\epsilon_0$, and $T=$ 300 K. The plateau in conductance does not occur when electroneutrality breakdown is present. The decrease in conductance at low concentration has been experimentally observed in Refs. ~\cite{secchi2016scaling} and ~\cite{yao2019strong}, but the effects were ascribed to surface reactions and electrokinetic coupling, respectively. However, as channels become closely spaced or strongly interacting, their behavior returns to the plateau behavior. Furthermore, electroneutrality breakdown at low concentrations leads to a cation transference number that does not saturate at $t_+=1$. Another practically significant quantity is the capacitance of a conducting nanotube embedded in a membrane dielectric medium, which is explored in the Supplemental Information. Electroneutrality breakdown can be used to increase the effective capacitance per unit pore area at low ionic concentrations. However, the capacitance per total membrane area and per total membrane volume do not benefit from electroneutrality breakdown, since the dense channel spacing reduces the effectiveness of electroneutrality breakdown.

\begin{figure}[b] \label{fig:fig8}
\includegraphics[width=1\linewidth]{Figure8.png}
\caption{ The dimensionless conductance (a) and cation transference number  (b) through a negatively charged nanochannel for varying channel separation distances. The solid lines are the predictions using equation \ref{eq:eq1DMLR} and the dotted lines are the predictions using equation \ref{eq:eqEndEffects}. The dotted lines are good predictors of the extent of electroneutrality breakdown at small $\ell/L$, but fail at large $\ell/L$, e.g. the blue dotted lines.  The plateau in conductance at low concentration is only apparent when $\mid Q_\mathrm{in}/Q_\mathrm{out}\mid=1$. As the ratio $\ell/L$ decreases, the system moves closer to electroneutrality.  When electroneutrality is broken, the cation transference number does not saturate to 1 at low concentration.}
\end{figure}

Nanoconfined domains are most ubiquitous in biological membranes, where protein channels selectively conduct specific ions. The selectivity filter in ion channels are at the molecular scale, with a radii on the order of single angstroms ~\cite{malasics2009protein}. In our model thus far, the radius of the channel signifies the accessible area for the \textit{ion centers}, which becomes negligible in true molecular confinement, $R\rightarrow 0$.   Therefore, we expect electroneutrality breakdown to be critical in describing the conduction of ions through protein channels. In the absence of an electroneutrality constraint, molecular separation in the selectivity filter would instead rely on specific chemical interactions or energy barriers to enter the pore ~\cite{EPSZTEIN2019316}. Closely spaced channels on the order of the membrane thickness $\sim 10$ nm could interact electrostatically with each other, leading to ensemble gating and ion conduction events.

The electrokinetic coupling and electrokinetic conversion from salinity gradients or pressure gradients are most effective and efficient in the regime of strong double layer overlap. Electroneutrality breakdown can adversely impact the expected performance of such a process. A large density of channels is not only desired for higher flux membranes, but to eliminate the possibility of electroneutrality breakdown at low concentration.

In unstructured charged nanoporous media, such as porous rock or polymer membranes, a large network of charged pores are connected and interact strongly with each other. Applications include desalination, ionic separations, and oil recovery~\cite{Dydek2013, deng2015water, schlumpberger2015scalable, alkhadra2019continuous, conforti2020continuous, alkhadra2020small}. In an interconnected porous medium consisting of closely spaced pores, a similar homogenized model to equation \ref{eq:eqEndEffects} should be pursued ~\cite{schmuck2015homogenization}. If the medium length scale is large relative to the Debye length, then electroneutrality will be maintained.

With our emphasis on the physics of electroneutrality breakdown, we have neglected other chemical mechanisms, such as charge regulation~\cite{trefalt2016charge, behrens2001charge, lin2019modulation, lin2019electrodiffusioosmosis}. Charge regulation, or reactions to form or neutralize surface charge, is certainly occurring at the pore walls-- after all, the origin of surface charge is a result of charge adsorption to the interface. Even if charge regulation is present, the effect of electroneutrality breakdown should still be important. In order to delineate from a chemical mechanism, one convincing evidence of electric field escape from a channel would be to observe differences in measureable quantities as a function of the spacing between channels. Only measurements that determine single channel conductance, transference number, or capacitance, as a function of the density of channels in a membrane could distinguish the electroneutrality breakdown mechanism from other competing chemical mechanisms. Furthermore, in Single Digit Nanopores channels, we can expect energy barriers associated with ions' dehydration to enter the channel. Energy barriers in the pore domain can be easily added to the model explored here, by changing the effective chemical potential for ions within the pore~\cite{levy2020breakdown}. Non-ideal effects ~\cite{bazant2009towards} such as packing effects ~\cite{kilic2007steric, Kornyshev2007} or electrostatic correlations~\cite{Bazant2011, storey2012effects,de2020continuum},are also not considered in this work.
\section{Conclusions}
The electroneutrality breakdown phenomenon is studied with an extensive set of continuum simulations. The results are shown to agree with simplifying analytical formulas within their regime of validity. Furthermore, the practical influence of electroneutrality breakdown on channel conductance and selectivity is discussed.

The experimental validation of screening in lower dimensions presents multiple competing mechanisms which can obscure the presence of electroneutrality breakdown. Even so, the set of simulation results presented here can guide researchers to isolate electroneutrality breakdown for multipore systems. One can expect wide variations of properties as a function of channel number density per area when electric fields enter into the membrane domain. As channels are placed closer together, they interact more strongly, changing the transport properties.

\section{Acknowledgements}
This research was supported as part of the Center
for Enhanced Nanofluidic Transport (CENT), an Energy
Frontier Research Center funded by the U.S. Department
of Energy, Office of Science, Basic Energy Sciences under
Award \# DE-SC0019112 .
JPD acknowledges support from the National Science
Foundation Graduate Research Fellowship under Grant
No. 1122374.

redpajama_set_name: RedPajamaArXiv


text:
'It would be nice to have some kind of a plan.'
With the school year fast approaching, families and educators are swamped with uncertainty.
by Mara Silvers 07.14.2020 07.20.2020
Our independent reporting is funded in part by more than 1,400 members who care about high-quality Montana journalism. Will you join us? One-time $120 $180 $300 Other Donation amount $ Monthly $10 $15 $25 Other Donation amount $ Annually $120 $180 $300 Other Donation amount $ Your contribution is appreciated. Donate now! I'm not interested […] Credit: Adobe stock/license required
Vanessa Doane and her husband, Derek, have been looking forward to the upcoming school year for months. Their daughter Daviah, has been, too — she's supposed to start attending kindergarten in Shelby this fall. For Vanessa, the school year was meant to be an exciting chapter of her daughter's early education. It was also supposed to help the family scale back on their use of daycare.
"For two kids, it's $1,000 a month," Doane estimated, also accounting for the attendance of her 18-month-old daughter. "Which is steep. So we were really looking forward to kindergarten."
School administrators in Shelby, located in the county that saw one of Montana's earliest outbreaks of COVID-19, have yet to announce how they plan to conduct the upcoming school year. That leaves the Doane family, along with thousands of others across Montana, in limbo, waiting to see how they may need to restructure their lives come August and September.
"We've got to weigh the pros and the cons and kind of just go from there," Doane said, explaining that she and her husband work outside the home, at a bank and an electrical company, and would have limited ability to homeschool their oldest daughter. She said she's also concerned about the lack of clear school safety protocols.
"It would be nice to have some kind of a plan," she said. "And we haven't really heard anything."
THIN ON DETAILS
Many districts across Montana are still deep in the process of formulating how exactly to go back to school. Gov. Steve Bullock released a rubric in early June, drafted with administrators, teachers and union representatives, for how local school districts could reopen in conjunction with the state's phased economic reopening. The outline allows schools to return to in-person instruction under phase 1 and instructs them to do so during the current phase 2, all while providing accommodations for students and staff who need to continue learning or working remotely.
But Bullock's blueprint, which acknowledges the uniqueness of each district, is sparse on specific protocols and serves mostly as a list of options for administrators to "consider" when creating their own health and safety plans, including occupancy limits to allow social distancing, guidelines on the use of masks and procedures for disinfecting shared spaces. Separately, the state Office of Public Instruction released a more extensive guide for school operations in four potential scenarios depending on the course of the pandemic.
"We were concerned, and we still are concerned, about the social and emotional needs [of students]. Everyone recognizes that to be back in school in the traditional and normal format is probably the healthiest for everyone, pending the [COVID-19] situation."
Billings Public Schools Superintendent Greg Upham
Some school administrators have criticized Bullock and OPI for not presenting more rigorous guidance as many districts remain mired in the process of crafting detailed plans. In Missoula, a Return to School Workgroup made up of administrators, educators and school staff is scheduled to present a draft to the school district's Board of Trustees this week; on its web page, the group cautions that any eventual protocol will require the "flexibility, adaptation, and collaboration" of Missoula's school community. In Billings, Superintendent Greg Upham has repeatedly taken to Facebook Live to share broad updates with parents, including the district's intention to return to in-person instruction while still "exploring remote learning" for students who need it.
"In the end, we will have 17,000 students and 33 schools," Upham said in an early July video watched by roughly 3,000 people. "Regardless of how [we] design it."
STABILIZING STUDENTS AND COMMUNITIES
Administrators aren't alone in recognizing the complexity of making a back-to-school plan during a pandemic — many teachers and school staff are waiting to see how their job descriptions might change again after the initial turmoil of the sudden shift to remote learning this spring.
"I would hold up our public schools as an incredible example of flexibility and providing an amazing service," said Amanda Curtis, a former high school biology teacher and president of the Montana Federation of Public Employees, which includes teachers and school staff. "But I don't want to downplay this. This is a global pandemic, and what happened in March was completely out of anyone's experience. However, now all of us who are returning do know what it's like," she said. "We know what works well and what doesn't work well."
While details remain vague, many officials are urgent about the need to return to in-person instruction. Upham, in a later interview, said he's been motivated in part by the roughly 30% of students who were "disengaged" in academics during remote instruction. He also pointed out that roughly 40% of his student body relies on school for at least one meal of the day, highlighting a need for services that go well beyond academic instruction.
"We were concerned, and we still are concerned, about the social and emotional needs [of students]," Upham said. "Everyone recognizes that to be back in school in the traditional and normal format is probably the healthiest for everyone, pending the [COVID-19] situation."
As Montana's number of confirmed COVID cases continues to climb, the pandemic has also made plain the crucial role public schools play in stabilizing students and communities. During the 2018-2019 school year, 4,284 enrolled students were classified as homeless, according to data from Montana's Office of Public Instruction. Nearly 67,000 were eligible for free or reduced-price lunch based on federal income brackets or enrollment in other social welfare programs. Health officials have also sounded the alarm about the low number of child abuse reports, which often come from school counselors or teachers, during the spring school closures. And the most recent data from the state's Youth Risk Behavior Survey indicate a concerning need for mental health services among high school students, 23% of whom reported seriously considering suicide at least once during the preceding 12 months.
For Upham and other administrators, those statistics aren't surprising. In the weeks following Montana's transition to remote instruction, Billings Public Schools published a list of resources related to COVID-19 on its website — at the very top were instructions for responding to depressed or suicidal students; immediately below were locations for curbside meal deliveries.
"We follow Maslow's hierarchy of needs," Upham said, referring to educators and school administrators. "And that is safety and belonging first."
EXPOSURE RISK
Although reopening for in-person instruction may help relieve hardships for some Montana families, others feel that the unavoidable increase in exposure to fellow students and staff is simply too high of a risk.
Caryn Schwarze has two children preparing to enter second and ninth grade this fall in Missoula public schools. They were considering attending in person until recently, she said, when her husband began chemotherapy for a recurrence of cancer, making his immune system especially vulnerable. The family decided that returning to in-person education would only increase the likelihood of the kids exposing the family to COVID-19.
"That's when our family locked down a little bit more and talked much more seriously about the likelihood that the kids will not go back to school, regardless of whether or not schools reopen," she said. "I can't picture sending them back."
"I think a lot more people are realizing how critical to the community childcare providers really are, not just to the child and family who are actively participating in them, but to all the facets of a functioning economy and functioning society."
Missoula County Public Schools trustee GRACE DECKER
But not all families can deal with homeschooling. Schwarze acknowledged that her family's situation is comparatively privileged; she could afford to quit her job when her husband first received his diagnosis in 2016, and has since remained her family's primary caretaker. When schools transitioned to remote instruction, she pivoted to homeschooling and identifying supplemental education for her children. To that extent, Schwarze wonders whether families who can keep their children home should decide to do so as a way to decrease density within schools and make them safer for students who need to be there.
"It's not a hardship for me, and in fact, honestly, I felt like it enriched my life," Schwarze said about homeschooling. "Because of that, maybe just two fewer bodies in the schools would be the ethical choice to make."
THE CHILDCARE CONUNDRUM
As families grapple with how or whether to put their kids back in school, many community-led initiatives are trying to find new childcare solutions before a highly unpredictable school year that may include staggered scheduling, forcing working parents to arrange care for their kids on their off days. But even before the pandemic hit the state, there were not enough licensed childcare providers in Montana to meet more than 40% of the estimated need, according to research conducted by the state Department of Labor and Industry. After the state's economic shut-down began in April, the nonpartisan research group Montana Budget and Policy Center estimated that 10,000 childcare slots were lost when hundreds of programs closed.
"I think a lot more people are realizing how critical to the community childcare providers really are, not just to the child and family who are actively participating in them, but to all the facets of a functioning economy and functioning society," said Grace Decker, Missoula County Public Schools trustee and coordinator for United Way's Zero to Five early childhood development initiative. "And we're kind of realizing like, oh my gosh, it really, really, really doesn't work to have a job and have your children all at the same time."
Bullock announced in May that $10 million in funding would go to support childcare providers in the state as part of the federal CARES Act Child Care and Development Block Grant. The Montana Budget and Policy Center has called for the governor to release five times that amount in order to fully fund childcare providers, including hazard pay, as they operate with fewer clients and additional sanitation expenses. The governor's office has yet to commit to such funding.
Still, advocates hope that securing a range of childcare options can help create a safety net for working parents and relieve some of the stress placed on public schools during the crisis.
"If we actually, as a community, are in a situation where it's not safe to have children in school the way that we did before, then we need to think about the different functions that schools serve and think about how we can deploy all the resources we have available to us to get those needs met," Decker said. "But it doesn't mean that they're going to be met by the same structures that they were met by before."
"What we're trying to do right now is get kids back in school, it seems like, as much as possible because we don't really have the imagination to think about doing services in a different way," she said.
PLANNING FOR A LONG HAUL
School district leaders have been candid in assessing their own limitations when it comes to delivering in-person and remote education as well as social and emotional services. Superintendent Upham of Billings said his district is preparing for the possibility of a staffing shortage if enough teachers and other employees opt to stay home given their age or medical vulnerabilities.
K-12 schools in Montana have received $41 million to help cover their operational expenses as part of the $13.7 billion in K-12 funding included in the CARES Act passed by Congress in March. But education experts in Montana and nationwide have long said that the total funding needed for a robust and sustainable reopening will be substantially higher. Several prominent organizations petitioned congressional leaders in May to allocate $250 billion for K-12 and higher education, saying the "economic hardship and the grief and trauma" associated with COVID-19 will be "unprecedented for today's school-age children and college students."
That funding has so far failed to materialize. House Democrats in May drafted additional legislation that would put $1 trillion toward state and local governments, with $90 billion specifically earmarked for education. Senate Democrats proposed a bill at the end of June that would increase funding for K-12 schools to $175 billion. Neither plan has passed both chambers of Congress.
In Montana, the long list of unknowns presents a daunting challenge for school administrators, teachers and families. And then, of course, there is the unpredictable nature of the virus.
"To me, it makes sense to plan as if we're going to be in phase 1, even if we never [are again]," Decker said, referring to restrictions that could be reimplemented if the virus continues to spread. "Putting resources and energy toward creating something really supportive for children and families in a more strict circumstance than we might be [in] seems like a good idea."
As Montana's case numbers continue to rise, Decker said she has noticed a shift in the way school communities are addressing the seriousness of the situation — and acknowledging how extensive the response will need to be.
"Last year in the spring, there was a whole lot of talk about how if we do this right, it will seem like we really overreacted," Decker said. "And I don't really hear people saying that anymore these days."
RELATED STORIES FROM MTFP
At-risk youth among most vulnerable to school closures
"The issues I'm hearing from my sector is people are genuinely concerned about kids' safety. School and after-school [programs] help keep kids safe, whole and OK."
As daycares close, employers and agencies create stop-gap solutions for essential workers
You might think the COVID-19-prompted closures would be a boon to childcare providers. It appears you'd be wrong.
Bullock details plan for phased reopening of Montana schools and businesses
"There's nobody at the state level at this point saying 'Mission Accomplished,'" Bullock said.
Tagged: Amanda Curtis, back to school, Billings Public Schools, CARES Act, child care, Child Care and Development Block Grant, Childcare, coronavirus, COVID-19, Grace Decker, Greg Upham, home schooling, homeschooling, Missoula County Public Schools, Montana, Montana Budget and Policy Center, Montana Federation of Public Employees, Montana Office of Public Instruction, OPI, pandemic, Phase 2, remote learning, school safety, Steve Bullock, United Way, Youth Risk Behavior Survey, Zero to Five
Mara Silvers
msilvers@montanafreepress.org
Mara covers Montana's social welfare and criminal justice systems, including public health matters such as substance use disorders and mental health care. She also tracks policy and social issues that affect LGBTQ+ people. Prior to joining Montana Free Press, Mara worked at Slate and WNYC, where she focused on radio and podcasts. She got her start in audio journalism as an intern at Montana Public Radio. Contact Mara at msilvers@montanafreepress.org, 406-465-3386 ext. 3, and follow her on Twitter.
More by Mara Silvers

redpajama_set_name: RedPajamaCommonCrawl


text:
using System;

namespace Appy.Logging.GrayLog
{
    /// <summary>
    /// Standard Syslog levels to be used according to the GELF format specification.
    /// </summary>
    /// <see href="http://docs.graylog.org/en/latest/pages/gelf.html"/>
    [Serializable]
    public enum SyslogLevel
    {
        /// <summary>
        /// System is unusable
        /// </summary>
        Emergency = 0,

        /// <summary>
        /// Action must be taken immediately.
        /// </summary>
        Alert = 1,

        /// <summary>
        /// Critical conditions.
        /// </summary>
        Critical = 2,

        /// <summary>
        /// Error conditions.
        /// </summary>
        Error = 3,

        /// <summary>
        /// Warning conditions.
        /// </summary>
        Warning = 4,

        /// <summary>
        /// Normal but significant condition.
        /// </summary>
        Notice = 5,

        /// <summary>
        /// Informational messages.
        /// </summary>
        Informational = 6,

        /// <summary>
        /// Debug-level messages.
        /// </summary>
        Debug = 7,
    }
}

redpajama_set_name: RedPajamaGithub


text:
Priestly celibacy rule 'is ignored'
Stephen Bates, religious affairs correspondent
Sun 28 Dec 2003 21.04 EST
Priestly celibacy in the Roman Catholic church has largely broken down in many parts of the world, Father Timothy Radcliffe, former master general of the Dominican Order, which has 200,000 members worldwide, said last night.
Fr Radcliffe, now a monk in Oxford but tipped by some as a future leader of the Roman church in England, said the church might have to consider ordaining married priests.
On the BBC Radio Four programme Analysis, broadcast last night, he said: "It is clearly the case that in many parts of the world celibacy has actually largely broken down - in many countries in Latin America, parts of Africa, to some extent in the United States...
"If it turns out to be the case that it is being largely ignored or bypassed, then... a very negative witness is being given; and so we have to ask is it possible now - either we have to provide celibate priests with considerably more support or we have to explore the possibility of them being married."
The Vatican and the Pope have rejected any question of altering the 1,200 year-old rule, but there is growing alarm in the church that the number of men coming forward to train for the priesthood in Europe and the US is declining, and that a high proportion of those in training are thought to be gay.
The Pope blames the decline in new priests and the steady exodus of others to marry on moral decadence and indiscipline in the western world.
The church in England has already relaxed the rule to some extent by letting some married Anglican priests who left the Church of England remain in holy orders.
Eamon Duffy, professor of the history of Christianity at Cambridge, told Analysis: "There is a real danger in the western Catholic church that the clergy will become a profession for homosexuals... many are first class, marvellous priests but I think everybody sees that it would be undesirable to have the clergy predominantly homosexual."


text:
According to a recent Wood…
Banks Haven't Lost Their Appetite For Fossil Fuels Just Yet
Big banks are still pumping…
EU Gas Price Cap Could Trigger Significant Changes In Markets
The European Security and Markets…
The NOPEC Bill Could Send Oil Prices To $300
By Tsvetana Paraskova - May 11, 2022, 7:00 PM CDT
For decades, different forms of 'NOPEC' legislation designed to pave the way for lawsuits against OPEC have been considered by Congress.
Last week, the U.S. Senate Judiciary Committee approved the NOPEC bill, leading to pushback from both within and outside the U.S.
OPEC's most influential energy ministers warned that the bill could send oil prices soaring by 200 or even 300 percent.
If the U.S. passes the NOPEC bill, a bill designed to pave the way for lawsuits against OPEC members for market manipulation, the oil market could face even more chaos. OPEC's most influential energy ministers warned against passing the legislation, suggesting it could send oil prices soaring by 200% or 300%. "The last thing we want is someone trying to hinder that system," the UAE's Energy Minister Suhail al-Mazrouei said at a conference in Abu Dhabi, referring to the system OPEC has had in place for decades to ensure supply to the market is adequate (adequate according to OPEC's view).
"If you hinder that system, you need to watch what you're asking for, because having a chaotic market you would see … a 200% or 300% increase in the prices that the world cannot handle," al-Mazrouei said at a panel at the World Utilities Congress hosted by CNBC's Dan Murphy.
As gasoline prices in America hit record highs, some lawmakers are looking to resurrect the NOPEC legislation that would allow the U.S. Attorney General to sue OPEC or its member states for antitrust behavior.
Forms of a NOPEC bill have been considered in Congress committees for nearly two decades, but they have never moved past committee discussions.
Now OPEC is warning of greater market chaos if NOPEC becomes law. But it's not only OPEC that has been warning about the implications for America in setting a precedent to remove sovereign immunity. The most powerful oil lobby in the United States, the American Petroleum Institute (API), is also against such legislation, arguing it would bring unintended harm to America's oil and gas industry and American interests in the world. So is the U.S. Chamber of Commerce, while the White House expressed "concerns" about the potential implications of such a law.
Last week, the U.S. Senate Judiciary Committee approved the so-called No Oil Producing and Exporting Cartels Act (NOPEC).
Forms of antitrust legislation aimed at OPEC were discussed at various times under Presidents George W. Bush and Barack Obama, but they both threatened to veto such legislation.
This time, it's unclear if the bill would be moved for discussion at the Senate, or then to President Joe Biden's desk, and it's unclear whether he would sign such legislation into law.
Related: Europe May Lose The Energy Transition Race Before It Really Begins
Commenting on the U.S. Senate Judiciary Committee's approval of the NOPEC bill, White House Press Secretary Jen Psaki said last week:
"I don't have an official position on this legislation right now, but we do believe that this potential — the potential implications and unintended consequences of this legislation require further study and deliberation, particularly during this dynamic moment in the global energy markets brought about by President Putin's invasion of Ukraine."
"So, we're taking a look at it and certainly have some concerns about what the potential implications could be," Psaki added.
Major trade groups have already expressed opposition to the bill, arguing it could backfire on America's oil and gas industry and U.S. interests.
The bill could have an unintended negative impact on America's oil and gas industry, the API said in a letter seen by Reuters.
The API has opposed NOPEC legislation during previous discussions of a bill. In 2019, under President Donald Trump, the institute told the then-members of the Senate and House Judiciary Committees, "We see this legislation as creating significant detrimental exposure to U.S. diplomatic, military and business interests while having limited impact on the market concerns driving the legislation."
"The legislation threatens serious, unintended consequences for the U.S. natural gas and oil industry," and it "represents a political act aimed at removing a sovereign nation's litigation immunity from certain U.S. laws and opens the opportunity for reciprocal or even additional action on the part of those impacted countries," the API said more than two years ago.
Last week, the U.S. Chamber of Commerce addressed the Senate Committee on the Judiciary, saying it opposes the bill known as S. 977.
"Although S. 977 is intended to be limited to restraint of trade in oil, natural gas or petroleum products, the Committee should be wary of the precedent it would create. Once sovereign immunity has been eliminated for one action of a state or its agents, it can be eliminated for all state actions and the actions of agents of the state," the Chamber of Commerce said.
"Under reciprocal legal regimes, the United States and its agents throughout the world could be tried before foreign courts – perhaps including the military – for any activity that the foreign state wishes to make an offense," it added.
Upstream Oil Industry To See Highest Profits Ever In 2022
The Call For Windfall Taxes On Energy Firms Is Growing
Kyiv Halts Russian Gas Shipments Through Key Hub
The EU Has A Major Problem With Securing Non-Russian Gas
What Does The EU Need To Do To Wean Itself Off Russian Fossil Fuels?
Lars Eden on May 12 2022 said:
Hi, 300% of 100 USD actually equals 400 USD.
Dennis Basco on May 12 2022 said:
may as well make it 500 we can afford gas or diesel now
Mamdouh Salameh on May 12 2022 said:
I don't think the NOPEC bill could send the crude oil price to $300 a barrel because OPEC members aren't going to reduce their production if the NOPEC bill is signed into law and the United States decided to sue OPEC or any of its members for cartel-like practices. Moreover, the NOPEC Bill doesn't pose any threat to OPEC for the following reasons.
1- The first is that the NOPEC bill is unenforceable against OPEC since it isn't a cartel. A cartel is defined as an association of manufacturers and suppliers whose goal is to increase their collective profits by means of price fixing, limiting supply, preventing competition or other restrictive practices. OPEC has never once tried to fix a specific price nor has ever been able to achieve this goal. For instance, OPEC was not able to prevent prices from falling in the 1980s even after it adopted the production quota system in 1982. Moreover, OPEC was neither able to temper oil prices in 2008 when prices rocketed to $147 a barrel nor was it able to stop the 2014 oil price crash. When it comes to limiting oil supply, a true cartel like the "Seven Western Sisters" was able to do exactly that because it was virtually in control of global oil resources. OPEC accounts for only 34.7% of the global oil market and 30.8% of exports according to the 2021 BP Statistical Review of World Energy. Both the United States and Russia have 12% of the market each.
2- The second reason is that if the United States tries to sue OPEC or any of its members, the organization could stop all its oil exports to the US. NOPEC only has jurisdiction in the United States but no extraterritorial jurisdiction under international law.
3- The third reason is that if, however, the United States persists with mounting law suits against OPEC or its members, they could retaliate by withdrawing their investments and funds in the US and even replace the petrodollar with the petro-yuan. This would be the most serious retaliation against the US. Once Saudi Arabia and UAE have made the switch, the overwhelming majority of OPEC members will follow suit exactly as they did in 1975 when they adopted the petrodollar. This will literally pull the rug from under the petrodollar and the US financial system it underpins.
The petrodollar provides at least three immediate benefits to the United States. (1) It increases global demand for US dollars. (2) It also increases global demand for US debt securities and (3) it gives the United States the ability to buy oil with a currency it can print at will. In geopolitical terms, the petrodollar lends vast economic and political power to the United States. Maintaining the petrodollar is America's primary goal.
Were Saudi-led OPEC to replace the petrodollar with the petro-yuan, China to pay for its almost 13.0 million barrels a day (mbd) of crude imports by petro-yuan, Russia to sell its 8.0 mbd of exports in ruble, Venezuela and Iran to accept the petro-yuan for their exports, the petrodollar will certainly lose an estimated 80% of global oil trade and its status as the oil currency of the world. This could lead to a loss of one quarter to one third of its value against other major currencies. For this reason we will never see oil prices rise to $300.
Rob Grant on May 12 2022 said:
When will the Biden administration understand that the world oil market is subject to the laws of supply and demand and allow the US Energy companies get back to producing the supply side without all the restrictions placed by Biden and his cronnies?


Hello, fellow wiki users. I'm Almo. My name is Alex. You may call me by either name. I've been a fan of Homestar Runner since mid-fall 2003. I think my first email was 2 years. I'm not exactly 100% on that, however.
Keep checking out this page, I'll be adding more stuff to it as the days go by. If you have any ideas on what to put here, drop me a line on my talk page.
UPDATE: I haven't been on here in a while, so naturally I was suprised to see Cool Tapes (a page I started) as a featured article.
This page was last modified on 23 June 2007, at 07:50.


Insomnia is a condition that affects 60 million people and probably yourself hence why you're here checking this article out. You're probably also interested in natural remedies for insomnia and we're here to help you out!
Insomnia essentially is the inability to fall, and stay, asleep. But it goes a bit deeper than that. Researchers are starting to recognize insomnia as as a problem of your brain unable to stop being awake.
Sleep is when it all goes down. This is when your body repairs and rejuvenates itself. It's also the time where your mind basically files everything that's been happening in the day creating your memories.
Even though you're asleep, your body springs into action when a ton of different processes that are critical to keeping you alive and healthy. But there's a big problem when you don't get enough sleep.
So a little stress hormone is actually needed but when something like cortisol is constantly elevated over the long term, this is when you're looking at trouble. Cortisol is raised by lack of sleep because your body thinks it must be facing some sort of trauma, or else why wouldn't you be sleeping?
Seems pretty straight forward and simple, but you really need to make it a point to get going to bed at least an hour before you normally do.
You might feel that you may as well stay up late due to your insomnia but you have to give your body a fighting chance and that means starting to turn in earlier.
Sleep experts say this is the most important thing for helping your body get to sleep. Your body craves routine and structure and the main thing with a routine at night is your body recognizes that sleep is about to happen.
So it may be a warm bath, then reading or writing in a journal and listening to some relaxing music. The main thing is with whatever routine you have stick with it and begin it at the same time each night.
This may be at the root of a lot of people's sleep problems including yours. Your electronics: phone, tablet and T.V etc give off a blue light that is really disruptive in the brain. Blue light throws off your circadian rhythm and prevents your brain from releasing melatonin which is really important with sleep.
When you use electronics and bright lights late at night, it's like standing outside at noon on a bright sunny day according to your brain. Start to eliminate or reduce screen use 1 to 2 hours before you're wanting to go to bed.
This is one of the best insomnia cures and it's free, the best price anything can be!
People who exercise regularly report better sleep. It also doesn't have to be that much even just 30 minutes 3 to 4 times a week can help to combat insomnia and improve sleep.
Exercising earlier in the morning also seems to help. When you exercise early, it helps to naturally engage your circadian rhythm and that in turn means your body will more naturally wind down later in the day helping you sleep.
This has the same effect as early morning exercise. The sun forces you to wake up and makes your body realize what time of day it is. It pumps out wake up hormones and allows your body clock to be engaged properly leading to better melatonin release later at night when you need it.
Basically daylight tells your body when to feel awake and when to feel tired.
These last few tips are all interconnected. Remember when I mentioned about your house springing to life with all the electronic light late at night? You want to combat this by keeping things as dark as possible.
Ideally, you've cut out light from screens an hour or so before bed; and now you want your bedroom as dark as possible. Since most people don't go to bed when it gets dark out, keeping your room dark tells your body the day is done. Darkness also helps to secrete melatonin which it can't do if there's always blaring light coming through your eyes.
You're aware of the effects of caffeine I'm sure, but you might not know it can last in the body a lot longer than you realize. The noticeable effects of caffeine kick in within 10 to 20 minutes and can last 2 to 3 hours.
Caffeine has what's called a 'half-life' which can extend its effects on your blood stream. There can still be an impact 6 or more hours later. So if you're having a coffee at 4-5 pm, this may be why you can't fall asleep at 11 pm that night.
You might have to play around with when you cut off caffeine, but ideally you wouldn't have any past 2-3 pm.
While we're talking about beverages, here are a few that can help combat insomnia. Chamomile tea has been used for relaxation for quite a long time now. It can help calm the nerves, combat anxiety and also works like a mild sedative.
Similar to the chamomile, valerian has been used for a long time. It's seen to help people fall asleep faster and stay asleep. It might be something to discuss with your doctor as it may not be best to use in the long term even though it's natural.
You've probably seen this too as it's in most health food shops and even grocery stores. St. Johns wort, even though it sounds like a great name for a band, is a flowering plant that can help with depression, anxiety, and insomnia — three things that tend to be connected a lot of the time.
You can find capsule forms but also fresh to make tea out of.
Another natural sedative that's technically a tropical flower. You can steep a teaspoon of it in boiling water for ten minutes to help with sleep.
This one you might not have heard of but it's not the name of an exotic dancer.
The bright orange leaves from California poppy can be steeped in hot water for about ten minutes and will help to combat anxiety along with making you feel relaxed.
Again, it's about giving your body the signals that it's time to sleep. A warm shower naturally helps to slow down and relax your nervous system and encourages you to feel sleepy.
You know how a warm shower in the morning can make you feel drowsy when you need to be waking up? You might want to forgo it then and start showering before bed.
Your body temperature drops when you sleep and keeping a cool environment can encourage your body to get to sleep, and stay asleep, quicker.
You want your room between 60 to 72 degrees so you may have to play around with thermostat (that I'm still not allowed to touch) or keeping your windows open.
Basically, your sheets should feel cool to the touch when you lie down.
If you're suffering from insomnia, realize that you are definitely not alone. It's frustrating but can be managed. There are a lot of great natural remedies for insomnia to help get your body to sleep and stay asleep.
 ^ National Sleep Foundation: What Causes Insomnia?


text:
Q: Facebook API: Post to wall with multiline message I'm posting to a User's wall using the Post API. I want the message which gets posted to have line breaks and links. Eg -
screenshot http://dl.dropbox.com/u/5154158/shot.png
Line 1 (Sid is ...) is Post#title.
Line 2 (Venmo is.. ) is Post#description
Line 3 and 4 (See more and If you) look to be Post#message. Its a link and there is a line break.
I want to achieve line 3. The documentation says Post#message is a JSON string, so far I've tried giving it HTML (tags get stripped), encoded tags( tags get printed instead of actually applied) - nothing seems to be working.
Not sure how to go about this ? Ideas anyone ?

A: You can at least do something "similar" this ways:
1) Pass your link target as "link" parameter and "see more" as caption.
2) pass an actions parameter like this:
 {"name": "see more", "link": "http://mylinktarget.foo"}

A: Line breaks do not work but using  tags does.
{"description":"line 1line 2"}

A: The Facebook API appears to honor ASCII Code 10 for newlines.

redpajama_set_name: RedPajamaStackExchange


text:
Up & Coming: Arshan Gailus
You may not know it, but you've probably heard Arshan Gailus' work in Boston theatres. Sound Design can be an incredibly subtle (and incredibly important) element of an audience's experience. In his work for SpeakEasy Stage, Company One, Lyric Stage, Actors' Shakespeare Project, and throughout the Boston area, Arshan has created music, effects, and soundscapes that have a tremendous impact on the emotional weight of a play.
In our special Up & Coming interview, Arshan talks about his process for Sound Design, and what Clybourne Park has in common with a video game.
How did you first get involved in the Boston theatre scene?
The year after I graduated from MIT, I served as the House Sound Engineer at the Calderwood Pavilion for the Huntington Theatre Company for their '06-'07 season, as well as serving as Sound Supervisor for their 2007 production of Brendan. The contacts I made there led to me getting my first professional sound design gig the following season with Company One.
Did you do theater in high school?
I was involved in my high school theater, primarily as an actor, actually. I also composed music for our submission to the Massachusetts High School Drama Guild Festival my senior year. I suppose that would have been my first experience as a theatrical sound designer.
Most people don't think of MIT as a place to study music. What was it about their program that attracted you?
I initially went to MIT to study electrical engineering. About halfway through my time there, I realized that while I felt intellectually stimulated by my studies, I didn't really feel excited about what I would do with that degree once I graduated, so I switched to something I did feel passionate about: music. MIT has some really outstanding music faculty, and, because of the small department size, you're able to develop a personal rapport with all the professors and lecturers.
How would you describe theatrical Sound Design? It might seem to some people that it is all about choosing songs and making doorbells ring.
That's a great question, and something I could go on for pages about in and of itself! The most concise description I like is that the Sound Designer is responsible for the entire sonic landscape of the play, which could include music, sounds, live voices, sounds of objects onstage, the sound of the room etc. What this means in practice depends a lot on the particular play, as the goal is always to support the intentions of the piece. Some productions call for a full, realistic soundscape like you might find in a documentary, while others want something more abstract or fantastical. Some of the work is clearly recognizable (such as those songs and doorbells you mention) while some can act on a more subtle or even subliminal level. A great example of some of this subtle sound work in my design for Clybourne Park is the trunk. When the trunk is moved or dropped, a deep, rumbly sound is played in sync with the live sound of the trunk itself. This adds a weight to the sound, which I wanted to help reflect the physical and emotional significance of the trunk. The audience may never realize anything extra is happening, but their experience is altered, even if subliminally.
With all the composition and engineering involved, Sound Design seems like a solitary craft. How do you share your creative process with the rest of the team outside of the studio?
One of the most exciting parts of working in theatre is discussing the general artistic goals of the production with everyone involved (director, actors, other designers, etc.), then figuring out how to translate these ideas into each of our individual disciplines. So while it is true that much of the heavy lifting in sound work is often done alone, the work I am doing is directly inspired by the collective vision for the production. Furthermore, sound and music can create an instinctive reaction in people, even if they can't describe exactly why or how. So when I share my work with the team as it develops, everyone is generally able to give feedback, regardless of how much training they may or may not have in the specifics of sound or music.
What's the first thing you do when designing a new show? How do you start?
The first thing I do with a new show is to try to get a sense of the play as a whole. I do this through a combination of my own reading of the script and discussions with the director and design team. Sometimes, these early thoughts and discussions can have very little to do with sound specifically. What I really want to do is get an idea of what it is we want to say about the play, its characters, and the world it creates. All the specifics, then, spring forth from these initial concept discussions.
What kind of influence does the performance venue have on your design?
No matter how lofty the concepts are, eventually, they need to be distilled into something we can actually implement, so of course the venue can have a huge impact on the design. Some obvious ways this can happen are in terms of what resources I have for the sound system, the acoustics of the space, and the audience layout. In general, I am trying to create a particular environment through sound: Does the space want to sound big? Small? Do we want to feel like we are a part of the action, or that we are watching something happen from the outside? Do we want to feel like it is all in our heads? How these effects are created is largely dependent on the space I have to work with.
You do a lot of composing and design in other media, including video games. Do you find that work informs your theatrical work at all?
I would actually say that all of my work informs all of the other work. While there are some obvious technical and structural differences between, say, live theatre and a video game, the overall goal on my end is very similar: to support the story, themes, and moods through sound and music. Almost all of the techniques and approaches I develop for one medium can be in some way translated to another.
Your work last season on SpeakEasy's production of The Divine Sister has been licensed for use by other companies producing the show. How did that come about?
The first re-licensing came about through Jeffery Roberson (aka Varla Jean Merman) who played Mother Superior in the show. He appeared in another production of The Divine Sister, and arranged for my work to be licensed for that production. The other cases were once via a connection through Jeffery, and the other through Larry Coen, the director of the SpeakEasy production.
What do you think it is about your work on that show that has attracted such interest?
Well, first off, I very much enjoyed creating the music and sound for the show, and I'm thrilled that others connected to my work as well! If I had to say what might have attracted people's attention, I think it has to do with the commitment we made to a strong overall design choice. Early on, Larry Coen felt it was important to support an epic, over-the-top, Hollywood feel to the show, but more as a loving tribute to the style and all its quirks, as opposed to parody. In all the music I wrote for the show, I tried to keep this idea at heart, relishing in the melodrama, but still staying true to the emotions of each moment. I think this approach to the show really resonates with the characters and the story in a very natural way.
What were the specific challenges of Sound Design for Clybourne Park?
Some shows call for overtly dramatic sound (such as The Divine Sister) whereas others want a more restrained, subtle approach. Clybourne Park was definitely one of the latter. The challenges of a show like this often center around decisions of when to use sound and when not to, and just how present or subtle sound wants to be in each moment. I want to make sure that each sound choice is specific and present enough to have the intended effect, but not so present that it overwhelms the senses and distracts from the audience's focus and investment in the world of the show. It's a game of constant tweaks and reassessment to hit just the right balance.
Talk a bit about the pre-show and intermission music. What were you hoping to achieve with your work on those portions of the show?
Both the pre-show and intermission music choices were intended to give a sense of time and place, but with different goals. I wanted the pre-show music to firmly place us in the 1950s, while also building on the cultural stereotype of an idyllic, happy, little '50s suburb, as a starting point and something to grapple with and push against through the first act.
The intermission music is intended to track the neighborhood through the 50 years between acts. I tried to be sensitive not only to the time period of each piece of music, but also to the demographics they reflect and the societal states and issues they address. And, of course, I wanted to make sure that the pieces were selected to create a smooth and enjoyable musical progression.
Besides the music, what are the differences for the Sound Design between the two acts inClybourne Park? How does 1959 sound different from 2009?
One of the concepts the artistic and design team kept coming back to was the idea that while many things have changed over those 50 years, many of the fundamentals have stayed the same. To this end, instead of trying to draw a huge contrast, I tried to show how the same kinds of things are filtered through time. So in both cases, for example, there are kids playing, dogs barking, and some cars driving by, but the choices become: What are the kids doing? What kind of dog is it? How do the cars sound different?
I'm currently in the early stages of working on Pericles with Actors' Shakespeare Project, and am working on a few different video game and film projects.
Previous: Race and the City: Chicago Next: Behind the Scenes of Clybourne Park


COLUMBIA — South Carolina's most powerful Democratic politician, U.S. Rep. Jim Clyburn, threw his support behind state Rep. James Smith for governor over two other primary candidates Saturday at the state party convention.
"James Smith has shown us that the best way to tell what a man will do is to look at what he has done," Clyburn said. "When you look at his record in the Legislature, it's a record that all of us can be proud of."
The endorsement from Clyburn does not come as much of a surprise. Given Smith's 22 years in the Statehouse and Clyburn's 25 years in Congress, the pair from Columbia have known each other for a long time. Last month, Smith toured parts of Clyburn's district alongside the congressman.
But Clyburn held off on declaring his support for Smith until standing before hundreds of party loyalists Saturday in Columbia, sending a strong message that the state's top Democratic powerbrokers are solidifying behind the longtime state lawmaker.
Pulling out all the stops, Smith entered the convention with a full marching band from Benedict College and an introductory video from former Vice President Joe Biden.
"I've known him for a long time, and I believe he has the character, the courage and the integrity to make a great governor for South Carolina," Biden said. "And he can win."
Despite Smith's strong fundraising numbers and widespread support from the Democratic establishment, recent polls have shown the three-way Democratic primary could be a closer race than many observers expected.
One poll conducted by Michigan-based firm Target-Insyght this month put Smith in a dead heat with Charleston businessman Phil Noble and just six points ahead of Florence antitrust attorney Marguerite Willis. But about a quarter of Democratic voters said they were still undecided about the race.
Clyburn said his daughter Angela, who has been working on Smith's campaign, suggested he should publicize his endorsement at the convention to maximize the impact. Clyburn said he has long liked Smith, particularly his shift to a combat post after 9/11.
"I don't think that there's anybody in this race on either side that is more committed to public service than James Smith," Clyburn said.
Five Republicans are seeking the GOP nomination: Gov. Henry McMaster, former health agency director Catherine Templeton, Lt. Gov. Kevin Bryant, Greenville businessman John Warren and former Lt. Gov. Yancey McGill.
Follow Jamie Lovegrove on Twitter @jslovegrove.