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Home News Analysis GameChangers 2018: As Opioids and Cocaine Boom, the Americas Wilt
GameChangers 2018: As Opioids and Cocaine Boom, the Americas Wilt
Deborah Bonello, Ángela Olaya and Seth Robbins
While traditional criminal organizations have widened their portfolios dramatically in recent years, drug trafficking remains the most important earner in the region. And with opioid consumption surging and cocaine production at a record high, the underworld is reaping the rewards and reshaping itself to fit the times.
The biggest opium source nations in Latin America continue to be Mexico and Colombia, and to a much lesser extent, Guatemala. The opioid epidemic in the United States has been a shot in the arm for organized crime south of the US border, and a new player — fentanyl — has entered the portfolios of some of the most prominent criminal networks.
Mexico is now handily the main source of heroin in the United States, according to the Drug Enforcement Administration (DEA), which tells InSight Crime that 90 percent of the heroin found in the US comes from Mexico.
The amount of hectares dedicated to poppy plants in Mexico has skyrocketed in recent years, according to the DEA, which says poppy cultivation reached a record high of 44,100 hectares in 2017, up from 32,000 in 2016. Estimated production of heroin increased to 111 metric tons — a jump of more than 300 percent from the amount estimated in 2013 (26 metric tons). Figures from the Mexican government in 2017 reported 24,800 hectares of illicit poppy crops between July 2014 and June 2015, but Mexico has yet to publish similar figures for the 2015 – 2016 period.
The Sinaloa Cartel and the Jalisco Cartel New Generation are the biggest operators in heroin production, as well as the Guerrero-based Guerreros Unidos and Los Rojos, two splinter groups that emerged from the now mostly fragmented Beltran Leyva Organization (BLO). They also serve to transport heroin, and rely on partners including the Juarez Cartel and the Gulf Cartel to help move it across the central or eastern parts of the US – Mexico border rather than the Southwest corridor, where the majority of heroin is trafficked.
Other regional poppy producers cannot keep pace with Mexico. An estimated 1,000 hectares of opium poppy were under cultivation in Colombia in 2015, enough to produce about three metric tons of pure heroin, according to US Government figures quoted in the 2017 National Drug Threat Assessment. Guatemala's role is hard to assess, but it is the least significant among the producers. Figures from the United Nations Office on Drugs and Crime suggest that its share of poppy production dropped between 2014 (640 hectares) and 2015 (260 hectares), but then rose again in 2016, to 310 hectares.
Demand from the United States is the main reason for the Mexican surge in production. Users addicted to pharmaceutical prescription painkillers have been switching to Mexican heroin and the more-deadly synthetic drug fentanyl.
Overdose deaths from heroin increased slightly in 2017, according to U.S. Centers for Disease Control and Prevention data analyzed by the National Institute on Drug Abuse. The number of deaths, however, from synthetic opioid overdoses has grown at a staggering pace — from around 10,000 in 2015 to nearly 30,000 in 2017, a surge of nearly 200 percent. Synthetic opioids now kill far more Americans than any other kind of drug.
Fentanyl — which is mainly sourced from China either ready-made or via the import of precursor chemicals — is being laced into other drugs such as heroin and cocaine by Mexican groups, and also being moved across the border as a standalone product. In some smaller US markets, standalone fentanyl has supplanted heroin, according to InSight Crime research and media reports, but the drug is mainly mixed with other illegal substances.
It is not known what proportion of illicit fentanyl (a legal form is also produced by pharmaceutical companies) consumed in the United States comes through Mexico. A steady flow of very pure fentanyl reaches users in the United States who purchase it on the dark web and receive it in small quantities from China by mail and courier services.
Fentanyl seizures in Mexico have increased in the last several years, according to data in documents attained by InSight Crime following a Freedom of Information Act request. And for groups such as the Sinaloa Cartel and the Jalisco Cartel New Generation — which have existing networks and supply chains in China for their methamphetamine business — it seems like an obvious lateral move.
A DEA analysis of fentanyl profitability found that one kilogram of heroin stands to net a cartel around $80,000, while a kilogram of 99 percent pure fentanyl could net anywhere between $1,280,000 and $1,920,000. (It's important to note that most fentanyl brought in from Mexico is seven percent pure on average, while fentanyl brought in from China via the direct mail route is more than 90 percent pure.)
The fentanyl market may also be cutting into the heroin trade. Anecdotal reports suggest that there has been a drop in the price of a kilo of opium paste in the Mexican mountains, from some 18,000 pesos ($900) to around 8,000 pesos ($400), according to interviews with analysts and media reports.
Fentanyl is still not a huge market for Mexican criminal groups. But that could be set to change if demand and consumption in the United States continues to rise. What's more, Mexican groups seem to be adjusting already to the consumers in this burgeoning market. As of late 2018, most of the fentanyl seizures along the US – Mexico border were laced into counterfeit prescription pills.
In Colombia, meanwhile, the amount of land used for coca cultivation has hit an all-time high, allowing cocaine traffickers to further penetrate new markets, including in Asia and Africa, while continuing to feed demand in the US and Europe. Coca cultivation reached a record 209,000 hectares in 2017, a jump of 11 percent from the previous year's record of 188,000 hectares, according to the U.S. Office of National Drug Control Policy. What's more, law enforcement officials estimated that pure cocaine production in Colombia increased 19 percent between 2016 and 2017, from 772 metric tons to 921.
This trend marks a reversal from the early part of the decade, when Colombia saw land dedicated to coca cultivation fall, forcing criminal groups to resort to buying coca paste in Peru, which had overtaken Colombia as the top spot for cultivation. In 2012, coca in Colombia had dropped to 48,000 acres, a fourth of what it is today, according to the United Nations Office on Drugs and Crime (UNODC). But it began ticking back up in 2013, and has jumped every year since then. Colombia now accounts for 70 percent of the land used for illegal coca worldwide, according to the latest UNODC World Drug Report.
The reasons behind the spike are twofold: Ending aerial fumigation has hampered coca eradication, while an unintended consequence of the ongoing peace process with Colombia's largest guerrilla group has been more space and opportunity for coca cultivation to flourish.
When talks started between the government and the Revolutionary Armed Forces of Colombia (Fuerzas Armadas Revolucionarias de Colombia – FARC) in 2013, the guerrillas controlled over 60 percent of the coca crop in the country. Sensing that the peace process was likely to go forward, the rebels ramped up cocaine production, seeing a last opportunity to generate as much cash as possible before becoming a legal political entity. They convinced farmers in coca growing regions that sowing the crop would give them greater leverage when negotiating for resources from the government, according to InSight Crime research. The coca plants from that time would have matured in the past two or three years.
Additionally, the Colombian government ceased aerial fumigation of coca in 2015 after mounting evidence showed that spraying glyphosate chemicals was harmful to human health. The end of fumigation meant less risk to farmers growing coca, and criminal groups took advantage. In 2012, 100,000 hectares were destroyed through aerial spraying, and 30,000 more were eradicated manually, according to the UNODC's 2013 report. In 2017, just 52,000 hectares of coca were destroyed on the ground.
Colombia's newly elected president, Iván Duque, has said he wants to bring back aerial fumigation using different chemicals and targeting fields more precisely with drones. At the same time, Colombia's crop substitution program, which was implemented after the signing of the 2016 peace accords, has been beset by limited resources, difficulty accessing rural communities where security is lacking, and mistrust from local farmers who say they have yet to see real benefits.
Soldiers eliminating coca crops have met increased resistance from communities. In 2018 confrontations between growers and the government turned deadly in Tumaco, a southwestern port city in the department of Nariño where a large share of the nation's coca is now produced. In the city of Cúcuta, which borders Venezuela, protesters barricaded roads and managed to get authorities there to suspend eradication efforts, El Tiempo reported.
The FARC's disarmament and demobilization also left a power vacuum in coca growing regions. This has led to an uptick in violence. The group's dissident members, and the country's two remaining rebel forces — National Liberation Army (Ejército de Liberación Nacional – ELN) and Popular Liberation Army (Ejército Popular de Liberación – EPL), both of which had previously been lesser players in the cocaine trade — have fought to take control of these areas. The groups have also battled with established traffickers for control of smuggling routes.
But the bloody wars of previous decades, in which guerrillas battled paramilitary groups and cartels fought one another, seem to be over. Cooperating in the cocaine trade are criminals of all stripes: various guerrilla factions; the ex-paramilitaries that form the BACRIM ("bandas criminales"); and traditional traffickers like the Urabeños, Colombia's strongest criminal organization.
US Law enforcement officials report that the Urabeños regularly send multiple tons of cocaine to nearby Panama and other countries in Central America by go-fast boats. But the Urabeños' structure differs from that of the top-down cartels in Colombia's past, acting more like a network of independent nodes.
Flamboyant capos in the mold of Pablo Escobar have vanished. Today's traffickers at the center of Colombia's cocaine trade are largely invisible, preferring to never touch a kilo of cocaine and pass for ordinary businessmen. For them, security comes from anonymity. Yet all the recent transfigurations of Colombia's traffickers haven't diminished their power, and may have even spurred their expansion as transnational criminal organizations.
In South America, Colombia is not alone in seeing an increase of cocaine production. In Peru, pure cocaine increased by 20 percent, hitting 491 metric tons, the highest levels recorded in 25 years, according to the Office of National Drug Control Policy.
The boom in cocaine and the ease with which the drug is moving through various South American countries has also opened new smuggling routes. For example, the cocaine transiting Venezuela is then moved to the Dominican Republic. The Caribbean country has been identified as a primary source of cocaine destined for Europe.
Europe as a whole has increasingly become a destination for cocaine, and the amount seized there jumped 11 percent in 2016, according to UNODC's 2018 World Drug Report. Marked increases were reported in Southeastern Europe, where the quantity of cocaine seized more than tripled in 2016 when compared to the previous year. For the first time, Belgium seized the most cocaine, followed by Spain and the Netherlands.
The explosion in cocaine production has also allowed traffickers to further penetrate emerging markets in Africa and Asia. Though the quantity of cocaine seized there pales in comparison to Europe or the Americas, these regions saw some of the largest jumps in seizure amounts. In Africa cocaine seizures doubled, and the North African countries reported a six fold jump from 2015 to 2016. Africa has increasingly served as a transit hub for cocaine moving through Brazil that ends up in Europe.
Brazil is also the departure point for cocaine destined for Asia, where the amount of cocaine seized tripled. Much of that cocaine transited the United Arab Emirates. China, including Hong Kong, was cited most frequently as the primary destination country, followed by Israel.
But the United States remains the destination for the vast majority of cocaine. As it is with opioids, the US numbers are worrying. Nationwide seizures of cocaine have hit their highest level since at least 2010, reaching 34,000 kilograms in 2017, a 40 percent increase over 2016, according to the DEA. About 93 percent of cocaine samples tested in the US were of Colombian origin.
The cocaine boom has also seemingly led to an increase in the drugs use in the United States over the past three years, according to reports from the 2017 National Survey on Drug Use and Health. Most troubling, nearly 15,000 people died from overdoses involving cocaine in 2017, more than double the amount of people who died in 2015.
Among illicit drugs, cocaine trails only opioids as a killer.
Credit: AP Images
Jalisco Cartel
Sinaloa Cartel
Urabeños
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'Strategic Marketing': are you getting the real deal?
So, strategic marketing huh? Sure you've all heard about it but, as I have discovered, not many CEO's know when they are getting the real deal.
Many have attempted to clarify what these two words really mean, but it still seems to confound a lot of executives I meet (particularly in healthcare circles). Heidi Taylor, a good friend and expert B2B marketer writes eloquently on this. I've lifted this statement from one of them because she succinctly describes the issue at hand by saying "I'm uneasy because I constantly see a whole host of articles, blog posts and so-called thought leadership on the subject of Marketing Strategy which are actually not about strategy at all".
The marketer who comes to you having identified growth markets that fit with the company's purpose and direction, has all the necessary information to size the prize and who confidently says 'we need to enter this market because of X,Y,Z but that means letting go of a, b and c' is thinking strategically. Strategy is about winning and, therefore, about making tough decisions to do so.
The marketer who comes to you and chats about the 'things' they will do to promote a service or run a campaign, and doesn't help you make the tough decisions on which markets to enter and which not to invest in, is too focused on the tactics and therefore not thinking strategically.


Hate to post an entirely new thread for this one - did anyone else get this car today? Want to know your thoughts.... but nothing about it says Galaxy finish to me. Maybe cause the drop out is white, but I am baffled by this one. It almost looks like a white drop out LC.
I thought Lionel only offered Galaxy for black parts of scheme.
Received mine today not a big fan of the white galaxy finish either.
Really strange. Factory issue/error with the paint drop out?
It's defintely interesting. Nothing like an old Galaxy - I guess they shouldn't have dropped out the white even though it was the dominant color.
I got the door though, so at least there is that.
that was my first thought... almost like it was packaged wrong and was actually the LC... glad Fred488 posted a pic to confirm I wasn't going crazy.
Galaxy color - and white is most likely the galaxy color part of the car.
Yes Galaxy Color is what they do now and it goes on the predominant color in the car design. I like Galaxy Color white personally but much like Galaxy Black everyone has their own preference. I feel it is a mix between standard metallic and flashcoat on the white especially.
Ahh... so only offered in Galaxy Color, not Galaxy?
Correct... when the listings say galaxy now, that is what they mean. Galaxy Color, and which ever the drop is, is the color with the finish treatment.
Ahh, got it. Thanks for the clarification all. In that case, I miss the OG Galaxy.
What black Galaxy look like ?
Standard metallic flake with flake on steroids. It is very nice depending on the car its on. For Dale Jr's Halo it was like having a star sky space them to it. Really neat.


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\section{Introduction}
\label{sec:intro}

When particles are accelerated by the Fermi process at a collisionless shock, the distribution takes the form of a power law in momentum, with an exponential cutoff. While energy gains from acceleration exceed losses, the distribution is that of a power law; above some momentum, however, energy losses dominate and the number of particles drops off exponentially. The resulting function may be written
\begin{equation}
  \frac{\mathrm{d} N}{\mathrm{d} p} = K p^{-\sigma} \mathrm{e}^{-(p/p_\mathrm{max})^{\chi}} .
  \label{eq:pl_def}
\end{equation}
In the above equation, $K$ is a normalization constant, $\sigma$ is the spectral index of the power law, $p_\mathrm{max}$ is the location of the exponential cutoff, and $\chi$ controls the curvature of the turnover.  In the case of Bohm diffusion limited by a free escape boundary, $\chi = 1$ \citep{CBA2009}.  If particle energies are instead limited by radiative losses such that $\dot{p} \propto p^{2}$, then $\chi = 2$ \citep{ZirakashviliAharonian2007,LKA2012}.  In the extreme limit $\chi \gg 1$, the exponential turnover behaves like a step function.  An additional component is expected in physical distributions, that of the particles that crossed the shock but were not further accelerated.  This ``thermal'' population is discussed elsewhere in the literature \citep{GianniosSpitkovsky2009,WEBL2015,ResslerLaskar2017}, but since it occurs at the low-energy end of the particle distribution we ignore it henceforth.  For this work we are not interested in how particles are injected into the acceleration process; we focus solely on what happens to the particles once they are being Fermi-accelerated.

Both $\sigma$ and $p_\mathrm{max}$ can be predicted analytically under certain simplifying conditions.  If particle orientations diffuse isotropically, and if the shock is assumed to be discontinuous, then $\sigma$ depends only on the shock Lorentz factor $\Gamma_0$; one can then recover $\sigma = 2$ in the non-relativistic limit $\Gamma_0 \rightarrow 1$ and $\sigma \approx 2.2$ in the ultra-relativistic limit $\Gamma_0 \rightarrow \infty$ \citep{KeshetWaxman2005}.  This result has been confirmed by many numerical studies both pre- and post-dating the analytical work \citep{Ostrowski1988, ERJ1990, EllisonDouble2002, Baring2004, AMN2008, EWB2013}.

To determine $p_\mathrm{max}$ one must assume an energy loss mechanism.  If radiative losses such as synchrotron (or synchrotron self-Compton) are responsible, then one may set the acceleration time equal to the loss time \citep{GallantAchterberg1999, Achterberg_etal_2001, Aharonian_etal_2002, LemoinePelletier2003, PiranNakar2010, Bykov_etal_2012SSRv, Lemoine2013}.  The resultant formula for $p_\mathrm{max}$ has many more dependencies than that for $\sigma$; as shown in the cited works $p_\mathrm{max}$ potentially depends on large-scale hydrodynamical parameters (e.g. shock speed) and microphysical parameters (e.g. magnetic field strength, turbulence characteristics, or scattering model).

Particle-in-cell (PIC) simulations \citep{Nishikawa_etal_2007, Spitkovsky2008, SSA2013, Ardaneh_etal_2015, ACN2016} offer a first-principles method for determining the distributions particles take as they interact with a collisionless shock.  By self-consistently treating both how particles self-generate magnetic field turbulence and how they scatter in it, PIC simulations act as the ``gold standard'' for numerical studies.  However, they are extremely computationally intensive, and this severely limits their ability to simulate the times and volumes needed to discuss the value of $p_\mathrm{max}$ in realistic settings. \footnote{The simulations presented in \citet{Spitkovsky2008} and \citet{SSA2013} do show a power law of electrons forming as a result of shock acceleration, but the power law spans less than an order of magnitude in energy.  An electron distribution accelerated at a collisionless shock may cover $5-6$ orders of magnitude; a back-of-the-envelope estimate suggests that PIC simulations like those cited would need to run for $10^{4}$, or more, times longer---with a correspondingly larger simulated volume---to approach a power law of such breadth.}

While PIC simulations can not yet address the value of $p_\mathrm{max}$, they are in general agreement about the structure of the magnetic field around the relativistic shocks they simulate.  Such shocks are susceptible to a wide variety of plasma instabilities \citep{MedvedevLoeb1999, BGD2010, LemoinePelletier2011}, and these instabilities drive small-scale ``microturbulence'' in the magnetic field that can exceed 10\% of the local energy density \citep[e.g.][]{SSA2013}.  This microturbulence decays rapidly behind (and also in front of) the shock, meaning particles probe magnetic fields of different strengths and turbulence spectra.  The maximum momentum attainable by particles can still be determined by equating acceleration time and loss time, but both of those quantities are more complicated than they are in a zeroth-order model \citep{Lemoine2013}.

Monte Carlo simulations \citep{Ostrowski1988, ERJ1990, EllisonDouble2002, LemoinePelletier2003, Baring2004, NiemiecOstrowski2006, EWB2013, WEBL2015} trade additional assumptions about the shock microphysics for substantially lower computational costs. Instead of handling magnetic field turbulence and particle scattering self-consistently, Monte Carlo schemes typically fix one or both.  The computational cost of Monte Carlo codes is sufficiently low that they can be used to probe $p_\mathrm{max}$, albeit sparsely, over a meaningful range of shock parameters and magnetic field configurations.

In this work, we apply an established Monte Carlo code \citep{Ellison1985, ERJ1990, EllisonDouble2002, VBE2008, EWB2013, WEBL2015, WEBN2017} to the problem of particle acceleration in the microturbulent field.  We simulate electron acceleration, and radiative losses, over a multidimensional physical parameter space.  From the accelerated particle spectra thus obtained, we identify an empirical formula that quickly computes $p_\mathrm{max}$ over a wide parameter space of astrophysical relevance.

\section{Numerical methods}
\label{sec:code}

The Monte Carlo (hereafter MC) model used here assumes a steady-state shock and explicitly defines how particles scatter in the magnetic turbulence, in effect solving the Boltzmann equation with collective scattering \citep{EllisonEichler1984, EWB2013}.  This steady-state approximation is valid as long as the particle acceleration time is shorter than the dynamical time of the system.

Particle motions, energy losses, and scatterings are treated in a series of discrete time steps $\delta t$.  The MC model assumes that particles scatter with a mean free path proportional to their gyroradius $r_{g} = \gamma m v c / (qB)$ in the local magnetic field $B$,
\begin{equation}
  \lambda_\mathrm{mfp} = r_{g} \eta_\mathrm{mfp}
  \label{eq:mfp}
\end{equation}
where $\eta_\mathrm{mfp}$ characterizes the strength of the scattering; the case of $\eta_\mathrm{mfp} = 1$ is called Bohm diffusion.  Bohm diffusion is commonly assumed because of its simplicity, but there is no conclusive evidence that $\eta_\mathrm{mfp}$ has any particular value, or indeed a single value at all.  Observations of rapid variability in bright knots of the supernova remnant RX J1713.7-3946 suggest that particle acceleration takes place with $\eta_\mathrm{mfp} \sim 1$ \citep{Uchiyama_etal_2007}.  In the ultrarelativistic limit, interpreting GeV emission in the afterglows of gamma-ray bursts (GRBs) as due to synchrotron emission places strict limits of $\eta_\mathrm{mfp} \lesssim 1$ on the acceleration process \citep{SagiNakar2012}.  Simulations of particle scattering in the relativistic regime variously suggest that $\eta_\mathrm{mfp} \;\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}\; 10$ \citep{LemoineRevenu2006} or $\eta_\mathrm{mfp} \sim 1$ \citep{RiordanPeer2019}.  Indeed, the discussion surrounding $\eta_\mathrm{mfp}$ is far from resolved (and the dependence of $\lambda_\mathrm{mfp}$ on $r_{g}$ may not be linear in some regimes \citep{PPL2011}), and for simplicity Equation~\ref{eq:mfp} is assumed to hold everywhere in the shock structures simulated.

The MC model divides each gyroperiod into $N_{g}$ smaller propagation and scattering steps which take place over a time $\delta t$.  That is, $\delta t \propto r_{g}/N_{g}$.  The amount by which particle orientations are allowed to change at each scattering event depends on both $\eta_\mathrm{mfp}$ and $N_{g}$ \citep{EWB2013}: $\delta\theta_\mathrm{max} \propto (\eta_\mathrm{mfp} N_{g})^{-1/2}$.  In the continuous limit of $\delta t \rightarrow 0$ (equivalent to $N_{g} \rightarrow \infty$), we approach pitch-angle diffusion as used in \citep{KeshetWaxman2005}.  The value of $N_{g}$ used in the simulations was tested to confirm that larger values did not affect the results.

The only energy gain process used in the MC model is first-order Fermi acceleration, i.e. crossing the shock and scattering off of turbulence in the new rest frame.  There are numerous other mechanisms by which particles in the vicinity of a shock could gain energy, including wake field acceleration \citep{Tajima_Dawson_1979}, second-order Fermi acceleration \citep[][and references therein]{Virtanen_Vainio_2005}, and cross-shock potentials \citep[e.g.,][]{Tran_Sironi_2020}. We assume that once injection into the first-order Fermi process occurs, those energy gains dominate those from other sources.

The code can treat the acceleration process of particles with any charge to mass ratio, and has in the past been applied to electrons, protons, and heavier ions.  For this work we restrict ourselves to considering only electrons.  Electrons carry significantly less momentum and energy flux than do ions, and their ability to influence the shock structure is similarly limited.  Even in relativistic shocks with $\Gamma_0 \sim 30$, nonlinear interactions between the shock and the accelerated particles can change the velocity profile of the shock \citep{EWB2013}.  At higher particle energies, especially in the limit of relativistic shocks, the induced precursor is of sufficiently small extent that it is ignorable.  Since the primary objective of this work is to estimate the value of $p_\mathrm{max}$ for the electron spectrum given in Equation~\ref{eq:pl_def}, nonlinear effects can be reasonably neglected.

Another break from previous work with this code is the magnetic field profile used.  Non-relativistic versions of the code self-consistently handle generation and decay of magnetic field turbulence \citep{VBE2008, VBE2009, Bykov_etal_2014}, but the relativistic version assumed that the mean field was parallel to the plane of the shock and of uniform strength throughout the shock structure (both up- and downstream from the shock).  In the work presented here we assume that the magnetic field is dominated by isotropic turbulence, consistent with the downstream region in PIC simulations. The magnetic field upstream is more ordered due to the filamentation instability, but in relativistic shocks electrons spend the bulk of their time scattering in the downstream medium.  The strength of the magnetic field is related to the local energy density by the parameter $\epsilon_{B}$.  The peak value of both magnetic field and $\epsilon_{B}$ occurs at the shock, and may be expressed in terms of bulk hydrodynamical parameters,
\begin{equation}
  \epsilon_\mathrm{B,pk} = \frac{ B^{2} }{ 16 \pi \Gamma_0^{2} n_{0} m_{p} c^{2} } ,
  \label{eq:epsB_pk}
\end{equation}
where $B$ is the mean local magnetic field, $\Gamma_0$ is the Lorentz factor of the shock, and $n_{0}$ is the rest-frame ambient density the shock is presently encountering \citep[cf. the definition of proper energy density in][]{BlandfordMcKee1976, GranotSari2002}.

Upstream and downstream from the shock, the magnetic field used is consistent with PIC simulations \citep{Keshet_etal_2009, SSA2013} and previous analytical work \citep{Lemoine2013}:
\begin{equation}
  \epsilon_{B}(x) = \epsilon_{B,\mathrm{pk}}
  \begin{cases}
    10.4 \left|x\right|^{-0.6}  &  x < -50  \\
    1  &  -50 \leq x \leq 50  \\
    50 x^{-1}  &  50 < x
  \end{cases}
  \label{eq:epsB_form}
\end{equation}
in which the distance $x$ from the shock is measured in ion skin depths, $\lambda_\mathrm{sd} = (\Gamma_0 m_{p} c^{2} / 4 \pi e^{2} n_{0})^{1/2}$.  This functional form has a plateau within 50 plasma skin depths of the shock, then decays upstream (negative positions) and downstream (positive positions).  The plateau has been used in previous analytical treatments of microturbulence in GRB afterglows \citep{Lemoine2013}, but is a simplification of the sharper, exponential-like peak in $\epsilon_{B}$ found in PIC simulations.  The downstream decay rate of $x^{-1}$ is expected from PIC simulations \citep{CSA2008} and interpretations of GRB afterglows with microturbulence \citep{LLW2013}. The upstream decay rate matches the precursors presented in \citet[][Fig.~7]{SSA2013}; we have not seen an extended discussion of this decay rate in the literature, so we do not make any claims of universality here.

The oblique instability responsible for the microturbulence is expected to disappear when the shock speed drops below a certain critical value, $\Gamma_0 \sim 10$ for reasonable choices of physical parameters \citep{LemoinePelletier2011, Pelletier_etal_2017}. The calculation assumes a relativistic shock, however, and it is less clear what instabilities are present in the mildly relativistic regime.  At low Lorentz factors both analytical and numerical approaches encounter difficulty, and there are comparatively fewer studies in the literature.  Numerical work on mildly relativistic shocks suggests that short-wavelength turbulence exists in the shock precursor at Lorentz factors as low as $\Gamma_0 = 1.5$ \citep{RBO2018}.  We therefore assume here that amplified microturbulence is present at all Lorentz factors considered, and remain agnostic as to the precise source of the turbulence.

As particles scatter in the above-mentioned magnetic field turbulence, they experience radiative losses.  We consider only synchrotron losses in this work.  Electrons should additionally radiate away energy via the inverse Compton process, and in the strong magnetic fields present near the shock synchrotron self-Compton (SSC) can be significant \citep{SariEsin2001}.  The rate of SSC losses depends on the synchrotron spectrum at an electron's location within the shock structure, which in turn depends on the local electron distribution.  The full calculation of synchrotron-SSC cooling is thus highly nonlinear. \citet{SBM2010} discuss the problem of accelerating electrons that are simultaneously suffering synchrotron and SSC losses, but their work covers only interactions in the Thomson regime.  As magnetic field strengths and electron energies increase, the Klein-Nishina cutoff on SSC cross-section becomes relevant and serves to suppress SSC losses.  SSC in the Klein-Nishina regime has been considered by many authors, but their work assumed an injected electron distribution rather than calculating it self-consistently \citep{NAS2009, Wang_etal_2010, BDBK2012}.  We are unaware of an attempt to simultaneously treat electron acceleration and SSC cooling in the Klein-Nishina regime, and so we also ignore these complications to focus instead on the much simpler synchrotron loss process.

We include another means of limiting particle energy in the code: a free escape boundary (FEB) upstream of the shock.  Any particles reaching the boundary are considered to decouple from the shock, and are removed from the acceleration process.\footnote{As pointed out by \citet{Drury2011}, free escape boundaries are in tension with the assumptions of a planar, stationary shock used here.  However, the focus here is purely on electrons, which remain coupled to the shock for a shorter period of time than do ions, and so the shock does not evolve much while the electrons are being accelerated.  Further, the separation of the FEB and the shock is much smaller than the shock radius for the parameter space used here; particles confined by these FEBs would see the shock as planar.}  Particle escape from a shock can only be identified after the fact; particles scattering ahead of a shock have a non-zero probability of returning back to the shock regardless of how far from the shock they get, and this probability is increased with an expanding shock \citep{Drury2011}.  An additional complication arises since particle diffusion lengths increase in the weaker magnetic fields far upstream from the shock.  Rather than track all particles indefinitely, or introduce a random chance of escape between each scattering event, we approximate particle escape with the use of a sharp boundary.  The FEB acts as an additional limitation on particle energy since diffusion lengths are proportional to energy (Equation~\ref{eq:mfp}).  The location of the FEB for all MC simulations is
\begin{equation}
  x_\mathrm{FEB} = -10^{3} \frac{\Gamma_0 \, \beta_0 \, m_{p} c^{2} }{ e \, B_{0} }
  \label{eq:FEB}
\end{equation}
where the negative sign denotes a position upstream from the shock, and $\beta_0 = u_{0}/c = \sqrt{1 - \Gamma_0^{-2}}$. That is, the physical location of the FEB depends on both the shock speed and the ambient magnetic field $B_{0}$, which taken here to be $10^{-5}$~G.  Beyond setting the physical scale of the FEB, the ambient magnetic field is largely irrelevant because it is dominated everywhere in the MC simulations by the amplified turbulence.

It is easier for particles to scatter out to the FEB in mildly relativistic shocks for several reasons.  First, Equation~\ref{eq:FEB} shows that the physical location is closer to the shock when $\Gamma_0$ is lower.  Second, according to Equation~\ref{eq:epsB_pk} the magnetic field is weaker around slower shocks.  This means longer mean free paths per Equation~\ref{eq:mfp}, so the same physical distance represents fewer diffusion lengths when the magnetic field is reduced.  The weaker field also means that electrons experience smaller radiative losses; they therefore keep more of their energy as they scatter towards the FEB and can make the trip in fewer scattering steps.  Taken as a whole, if the FEB acts to limit the maximum electron energy we expect that maximum to be an increasing function of $\Gamma_0 \beta_0$; once electrons can no longer reach the FEB, the relationship between shock speed and maximum energy will change.

All shocks simulated in this work assume that acceleration occurs in the test-particle limit; that is, the presence of accelerated particles upstream from the shock does not modify the velocity profile.  In actuality, pressure from these accelerated particles acts to slow down inflowing plasma, generating a shock precursor via a nonlinear feedback loop.  This nonlinear shock modification occurs at all shock speeds, from nonrelativistic to ultrarelativistic \citep{EllisonEichler1984,RKD2009,EWB2013}.  However, the precursor in a relativistic shock is weak compared to those of non-relativistic shocks \citep{EWB2013}; so while nonlinear effects may be present, their treatment is deferred to future work.

\section{Estimating $p_\mathrm{max}$ from the Monte Carlo results}
\label{sec:results}

The MC code described above was used to simulate particle acceleration at numerous points in a three-dimensional parameter space.  The proper speed of the shocks, $\Gamma\beta$, was allowed to vary between 0.83 (corresponding to $\Gamma_0 = 1.3$) to 340.  The plateau value of $\epsilon_{B}$ in the vicinity of the shock ranged between $10^{-4}$ and $10^{-1}$.  The acceleration efficiency $\eta_\mathrm{mfp}$ varied between 1 and 10.  The strongest magnetic fields in the simulations occur at the shock.  Their strength is, by the definition of $\epsilon_{B}$, a product of that parameter and the local energy density:
\begin{equation}
  B = \left( 16 \pi n_{0} \Gamma_0^{2} m_{p} c^{2} \epsilon_{B} \right)^{1/2}
  \label{eq:B_pk_strength}
\end{equation}
This strength depends on both $\Gamma\beta$, by way of $\Gamma_0^{2}$, and on the product $\epsilon_{B} n_{0}$ (where $n_{0}$ is the ambient density of the material being swept up by the shock). Each individual MC run can thus be characterized by a parameter triplet $\vec{\phi}_\mathrm{MC} = (\Gamma\beta, \epsilon_{B} n_{0}, \eta_\mathrm{mfp})$.

Over this wide, physically-relevant range of $\vec{\phi}_\mathrm{MC}$ parameters, the MC code was used to simulate 20 iterations (with a different initial random number seed) for each parameter triplet.  From the resulting 20 electron spectra, we estimated a posterior likelihood distribution (PLD) of the parameters $\vec{\pi}_\mathrm{pl} = (\log_{10} p_\mathrm{max}, \sigma, \chi, \log_{10} K)$ via Markov chain Monte Carlo (MCMC), as detailed in Appendix~\ref{sec:MCMC_details}.

\begin{figure}
  \includegraphics[width=0.5\columnwidth]{fig1.pdf}
  \caption{Comparison between the electron spectra obtained from the MC code, and the spectrum described by Equation~\ref{eq:pl_def} for the MCMC-identified highest-likelihood $\vec{\pi}_\mathrm{pl}$ (see Section~\ref{sec:fit}).  Histograms of electron spectra from 20 different MC iterations (using the same $\vec{\pi}_\mathrm{pl}$ but different random number seeds) are shown with light grey lines.  Their geometric average is plotted in red.  The black curve is Equation~\ref{eq:pl_def} using the highest-likelihood parameters identified via MCMC.  The input parameters for the MC simulation were $\vec{\phi}_\mathrm{MC} = (\Gamma\beta = 100, \eta_\mathrm{mfp} = 1, \epsilon_{B} n_{0} = 10^{-4})$. The corresponding highest-likelihood parameters estimated by MCMC were $\vec{\pi}_\mathrm{pl} = (\log_{10} p_\mathrm{max} = 5.13, \sigma = 2.18, \chi = 1.86, \log_{10} K = 60.7)$.}
  \label{fig:mc_results}
\end{figure}
An example of this process is given in Figure~\ref{fig:mc_results}, showing both the MC realizations and the MCMC-estimated spectrum.  The MC electron distribution has two components: a ``thermal peak'' (composed of electrons that crossed the shock but did not enter the acceleration process) and the non-thermal tail (made up of electrons that did shock-accelerate).  The sharpness of the thermal peak is an artifact of how the MC code handles energy gain upon shock crossing\footnote{Specifically, particles gain energy based on the velocity difference between their initial and final positions between scatterings.  For cold particles encountering a relativistic shock, the energy gain is much greater than the initial thermal energy the particles possessed.  The MC code does not try to artificially redistribute energy to recover a thermal distribution, but PIC simulations do show that such a distribution exists in the downstream region of the shock \citep[e.g.,][]{SSA2013}.}; it does not impact the acceleration process that produces the non-thermal tail.  The non-thermal distribution is well-captured by Equation~\ref{eq:pl_def}, including the extended power-law tail and the exponential turnover at $p_\mathrm{max}$.

The momentum value of the thermal peak in Figure~\ref{fig:mc_results} is a free parameter in this work.  Its position can be fixed using either a PIC simulation or by assuming a specific fraction of energy placed in the electron distribution ($\epsilon_{e}$ in the literature), but we are not interested here in the low-energy portion of the spectrum.  We instead place the thermal peak at a sufficiently small momentum that the power law generated by shock acceleration can cover several decades, allowing us to adequately estimate the $\sigma$ parameter in Equation~\ref{eq:pl_def}.

\begin{figure*}
  \includegraphics[width=\textwidth]{fig2.pdf}
  \caption{Dependence of Equation~\ref{eq:pl_def}'s $p_\mathrm{max}$ on $\Gamma\beta$ for the various combinations of $\epsilon_{B} n_{0}$ and $\eta_\mathrm{mfp}$ simulated.  The curves correspond to the $p_\mathrm{max}$ values predicted by the empirical expression (Equations~\ref{eq:broken_pl_used}-\ref{eq:W_def}) in its full (15-parameter, dashed line) and reduced (10-parameter, solid line) forms; the values of the parameters are provided in Table~\ref{tab:param_sets} below.  Gray shading marks regions of the parameter space where electrons were able to escape from the shock in the upstream direction.  The rightmost column compares MC runs with the same $\epsilon_{B} n_{0}$ but different $\eta_\mathrm{mfp}$.  The bottom row compares MC runs with the same $\eta_\mathrm{mfp}$ but different $\epsilon_{B} n_{0}$.}
  \label{fig:mcmc_round1}
\end{figure*}
The values of $p_\mathrm{max}$ for each $\vec{\phi}_\mathrm{MC}$ are shown in Figure~\ref{fig:mcmc_round1}.  While all four of Equation~\ref{eq:pl_def}'s $\vec{\pi}_\mathrm{pl}$ parameters are estimated for each $\vec{\phi}_\mathrm{MC}$, hereafter we focus only on $p_\mathrm{max}$.  Each dot in Figure~\ref{fig:mcmc_round1} represents the highest-likelihood value of $p_\mathrm{max}$ from a single $\vec{\phi}_\mathrm{MC}$ (cf. Figure~\ref{fig:mc_results}).  Within each subpanel, corresponding to a specific $(\epsilon_{B} n_{0}, \eta_\mathrm{mfp})$ doublet, $p_\mathrm{max}$ versus $\Gamma\beta$ appears to follow a broken power law.  The shaded area in each subpanel marks the region of $\Gamma\beta$ values for which electrons were able to scatter upstream to the FEB discussed in Section~\ref{sec:code}.  It appears from Figure~\ref{fig:mcmc_round1} that electron escape is, at the very least, strongly correlated with the break in the $p_\mathrm{max}$ curves.  That is, below the break the maximum electron energy is limited by escape at the FEB, while above the break the limiting process is radiative losses.

\section{An Empirical Expression for $p_\mathrm{max}$}
\label{sec:fit}

As seen in Figure~\ref{fig:mcmc_round1}, $p_\mathrm{max}$ appears to follow a broken power law in $\Gamma\beta$:
\begin{equation}
  p_\mathrm{max}(y = \Gamma\beta) = A \left( \frac{y}{B} \right)^{C} \left[ \frac{1}{2} \left\lbrace 1 + \left( \frac{y}{B} \right)^{E} \right\rbrace \right]^{-\frac{C+D}{E}}
  \label{eq:broken_pl_base}
\end{equation}
In this form, the parameters $A$, $B$, $C$, $D$, and $E$ do not have well-defined physical associations.  For example, while setting $y = B$ results in $p_\mathrm{max} = A$, it is not the case that $B$ corresponds to the location of the peak and $A$ to the height at the peak. Instead, both the location and the height of the peak also depend on $C$, $D$, and $E$.  It is therefore useful to re-arrange Equation~\ref{eq:broken_pl_base} so that the five parameters describe different, mostly independent features of the broken power law.  This yields
\begin{equation}
  p_\mathrm{max}(y = \Gamma\beta) = p_\mathrm{pk} \left( \frac{y}{\Gamma_\mathrm{pk}\beta_\mathrm{pk}} \right)^{L} \left[ \frac{1 + \frac{L}{H}}{1 + \left( \frac{L}{H} \right) \left( \frac{y}{\Gamma_\mathrm{pk}\beta_\mathrm{pk}} \right)^{W} } \right]^{ \frac{L+H}{W} }
  \label{eq:broken_pl_used}
\end{equation}
whose five features are $p_\mathrm{pk}$, the maximum value of the broken power law; $\Gamma_\mathrm{pk}\beta_\mathrm{pk}$, the value of $\Gamma\beta$ at which the function peaks; $L$ and $H$, the asymptotic power-law indices far below and above (respectively) the peak; and finally $W$, which controls the width of the peak.

We seek an empirical formula for $p_\mathrm{max}$ over the three-dimensional $\vec{\phi}_\mathrm{MC} = (\Gamma\beta, \epsilon_{B} n_{0}, \eta_\mathrm{mfp})$ parameter space.  Since Equation~\ref{eq:broken_pl_used} already explicitly depends on $\Gamma\beta$, this can be accomplished by assuming that all five features of Equation~\ref{eq:broken_pl_used} depend on the remaining two parameters, $\epsilon_{B} n_{0}$ and $\eta_\mathrm{mfp}$, such that
\begin{equation}
  p_\mathrm{pk} = p_{C} \, \left(\eta_\mathrm{mfp}\right)^{p_{\eta}} \, \left(\epsilon_{B} n_{0}\right)^{p_{\epsilon}} m_{p} c
  \label{eq:ppk_def}
\end{equation}
\begin{equation}
  \Gamma_\mathrm{pk}\beta_\mathrm{pk} = g_{C} \, \left(\eta_\mathrm{mfp}\right)^{g_{\eta}} \, \left(\epsilon_{B} n_{0}\right)^{g_{\epsilon}}
  \label{eq:gbpk_def}
\end{equation}
\begin{equation}
  L = L_{C} \, \left(\eta_\mathrm{mfp}\right)^{L_{\eta}} \, \left(\epsilon_{B} n_{0}\right)^{L_{\epsilon}}
  \label{eq:L_def}
\end{equation}
\begin{equation}
  H = H_{C} \, \left(\eta_\mathrm{mfp}\right)^{H_{\eta}} \, \left(\epsilon_{B} n_{0}\right)^{H_{\epsilon}}
  \label{eq:H_def}
\end{equation}
\begin{equation}
  W = W_{C} \, \left(\eta_\mathrm{mfp}\right)^{W_{\eta}} \, \left(\epsilon_{B} n_{0}\right)^{W_{\epsilon}}
  \label{eq:W_def}
\end{equation}
The subscript $C$ here denotes the coefficient parameter for each feature, and the subscripts $\eta$ and $\epsilon$ identify the power parameters that quantify the dependence of each feature on $\eta_\mathrm{mfp}$ and $\epsilon_{B} n_{0}$ respectively.  Note that $p_\mathrm{pk}$ is the only feature with units: specifically, it is scaled to $m_{p} c$.

The PLDs for the 15 parameters in Equations~\ref{eq:ppk_def}-\ref{eq:W_def} were estimated via MCMC as described in Appendix~\ref{sec:MCMC_details}.  The results are presented in Table~\ref{tab:param_sets}.  The estimates suggest that $p_\mathrm{pk}$ depends only weakly on $\epsilon_{B} n_{0}$, since $p_{\epsilon}$ is close to 0.  Similarly, $L$ and $H$ have a very weak dependence on both $\epsilon_{B} n_{0}$ and $\eta_\mathrm{mfp}$.  Therefore the parameter estimation procedure was repeated with a reduced 10-parameter expression, making the following modifications:
\begin{equation}
  p_\mathrm{pk} = p_{C} \left(\eta_\mathrm{mfp}\right)^{p_{\eta}} m_{p} c
  \label{eq:ppk_reduced}
\end{equation}
\begin{equation}
  L = L_{C}
  \label{eq:L_reduced}
\end{equation}
\begin{equation}
  H = H_{C}
  \label{eq:H_reduced}
\end{equation}
Parameter estimates for the reduced 10-parameter expression also appear in Table~\ref{tab:param_sets}.

\begin{table}[h]
\centering
\begin{tabular}{lll}
\hline
Parameter & 15-parameter & 10-parameter \\
\hline
$p_{C}$ & $\phantom{-}{7.88\xx{5}}\,^{+3400}_{-3100}$ & $\phantom{-}{6.35\xx{5}}\,^{+1100}_{-1100}$ \\
$p_{\eta}$ & $-0.575\,^{+0.0015}_{-0.0018}$ & $-0.548\,^{+0.0014}_{-0.0015}$ \\
$p_{\epsilon}$ & $\phantom{-}0.0297\,^{+0.00048}_{-0.0005}$ & $\phantom{-}0$ \\
\hline
$g_{C}$ & $\phantom{-}0.527\,^{+0.002}_{-0.0018}$ & $\phantom{-}0.532\,^{+0.0012}_{-0.0012}$ \\
$g_{\eta}$ & $\phantom{-}0.299\,^{+0.0016}_{-0.0016}$ & $\phantom{-}0.278\,^{+0.00092}_{-0.001}$ \\
$g_{\epsilon}$ & $-0.333\,^{+0.00054}_{-0.00048}$ & $-0.338\,^{+0.00032}_{-0.00032}$ \\
\hline
$L_{C}$ & $\phantom{-}1.98\,^{+0.024}_{-0.023}$ & $\phantom{-}2.12\,^{+0.0074}_{-0.007}$ \\
$L_{\eta}$ & $\phantom{-}0.0464\,^{+0.0033}_{-0.0044}$ & $\phantom{-}0$ \\
$L_{\epsilon}$ & $-0.00346\,^{+0.0014}_{-0.0013}$ & $\phantom{-}0$ \\
\hline
$H_{C}$ & $\phantom{-}1.07\,^{+0.0029}_{-0.0029}$ & $\phantom{-}1.01\,^{+0.0012}_{-0.0012}$ \\
$H_{\eta}$ & $\phantom{-}0.0282\,^{+0.0014}_{-0.0013}$ & $\phantom{-}0$ \\
$H_{\epsilon}$ & $\phantom{-}0.0183\,^{+0.00049}_{-0.00048}$ & $\phantom{-}0$ \\
\hline
$W_{C}$ & $\phantom{-}7.7\,^{+0.13}_{-0.11}$ & $\phantom{-}5.26\,^{+0.039}_{-0.042}$ \\
$W_{\eta}$ & $-0.179\,^{+0.006}_{-0.0054}$ & $-0.043\,^{+0.0026}_{-0.0026}$ \\
$W_{\epsilon}$ & $\phantom{-}0.136\,^{+0.0019}_{-0.0018}$ & $\phantom{-}0.11\,^{+0.00073}_{-0.00068}$ \\
\hline
\end{tabular}
\caption{\label{tab:param_sets} The mode of each parameter's PLD; and the boundaries of the 68\% credible region of the PLD for each parameter, marginalized over all others. For the five fixed parameters of the 10-parameter set, no credible region is given.}
\end{table}

The parameter estimates in Table~\ref{tab:param_sets} suggest that when electron energy is limited by the location of the FEB, the value of $p_\mathrm{max}$ scales as roughly $(\Gamma\beta)^{2}$; once radiation losses are the limiting factor, $p_\mathrm{max}$ scales as approximately $(\Gamma\beta)^{-1}$.  Neither the value of $L$ nor that of $H$ depends strongly on the acceleration efficiency ($\eta_\mathrm{mfp}$) or the peak magnetic field strength ($\epsilon_{B} n_{0}$), motivating the reduction from a 15-parameter set to just 10.  The location of the break in the power law, $\Gamma_\mathrm{pk}\beta_\mathrm{pk}$, decreases as the magnetic field strength goes up, and increases as acceleration efficiency drops.  The height of the break, $p_\mathrm{pk}$, decreases as acceleration efficiency drops, and shows almost no dependence on the magnetic field strength.  As for the width parameter $W$, it increases with larger values of $\epsilon_{B} n_{0}$ and with smaller values of $\eta_\mathrm{mfp}$; since larger $W$ means a sharper peak, however, the trend is for broader breaks in the power law when either the magnetic field is weak or acceleration is inefficient.

With the values presented in Table~\ref{tab:param_sets}, it is possible to compute the value of $p_\mathrm{max}$ for any desired $\vec{\phi}_\mathrm{MC}$.  First $\eta_\mathrm{mfp}$ and $\epsilon_{B} n_{0}$ are used in Equations~\ref{eq:ppk_def}--\ref{eq:W_def} to compute the five features of Equation~\ref{eq:broken_pl_used}.  The computed features are, in turn, used to obtain $p_\mathrm{max}$ by evaluating Equation~\ref{eq:broken_pl_used} at the desired value of $\Gamma\beta$.

\section{Discussion}
\label{sec:disc}

We now consider two applications of Equation~\ref{eq:broken_pl_used} to GRB afterglows.  The first is the upper limit on synchrotron photon energy produced by the external shock of a GRB, and the second is a brief discussion of the physical process that limits electron energy in our simulations.

\subsection{Maximum energy of synchrotron photons}
\label{sub:syn_phot_max}

GRB afterglows are routinely associated with emission above 100 MeV, and analytical treatments of particle acceleration suggest that electron synchrotron photons can exceed $\sim$GeV energies while the forward shock of the GRB is still moving ultrarelativistically \citep{PiranNakar2010,Kumar_etal_2012}.  The MC simulations presented in Section~\ref{sec:results} serve as a numerical check on previous analytical calculations, as they take place under largely the same assumed conditions (c.f. Section~\ref{sec:code}).  We now calculate $h\nu_\mathrm{syn,max} = 3 \gamma_\mathrm{max}^{2} h q B / (4 \pi m_{e} c)$ for electron distributions whose maximum momentum $p_\mathrm{max}$ is given by Equation~\ref{eq:broken_pl_used}.  This is the characteristic synchrotron frequency of such electrons; the resultant photon spectrum would peak at a frequency approximately $0.3 \nu_\mathrm{syn,max}$ \citep{RybickiLightman1979}.

Let us now restrict our focus only to the portion of Equation~\ref{eq:broken_pl_used} above $p_\mathrm{pk}$, where radiative losses rather than escape act to limit the maximum electron energy.  At shock Lorentz factors far above $\Gamma_\mathrm{pk}\beta_\mathrm{pk}$, Equation~\ref{eq:broken_pl_used} simplifies to
\begin{equation}
  p_\mathrm{max} \approx p_\mathrm{pk} \left[ \frac{1 + \frac{L}{H}}{\frac{L}{H}} \right]^\frac{L+H}{W} \left( \frac{\Gamma}{\Gamma_\mathrm{pk}\beta_\mathrm{pk}} \right)^{-H} ,
  \label{eq:broken_pl_simpl}
\end{equation}
where we have reduced the independent variable to $\Gamma$ rather than $\Gamma\beta$.  Using the 10-parameter values from Table~\ref{tab:param_sets}, the above equation can be expressed
\begin{equation}
  \gamma_\mathrm{max} = 9.4\xx{8} \, \eta_\mathrm{mfp}^{-0.267} \epsilon_{B}^{0.281} n_{0}^{0.281} \Gamma^{-1.01} ,
  \label{eq:elec_gam_max}
\end{equation}
having recast the equation in terms of Lorentz factor rather than momentum.  (The feature $W$ cannot be evaluated without knowing the value of $\epsilon_{B} n_{0}$; the dependence on $\eta_\mathrm{mfp}$ is weak enough to be ignorable.  For the range of conditions simulated in this work $W$ varies between 1.73 and 4.08.  We have taken 2.90 as a fiducial value to eliminate the dependence of $\gamma_\mathrm{max}$ on $W$.  The eventual result for $h \nu_\mathrm{syn,max}$ differs by a factor close to unity as a consequence of this simplification.)

We now assume that the large-scale hydrodynamics are governed by the \cite{BlandfordMcKee1976} solution for a relativistic impulsive explosion.  Further assuming an adiabatic shock, with neither energy injection nor significant radiative losses, one may derive the following expression for the shock Lorentz factor $\Gamma$:
\begin{equation}
  \Gamma^{2} = \left[ \frac{(17 - 4k) E_\mathrm{iso}}{8 \pi N m_{p} c^{5-k} \left[ 2(4-k)\right]^{3-k}} \right]^{\frac{1}{4-k}} t_\mathrm{obs}^{-\frac{3-k}{4-k}} .
  \label{eq:BM_gamma}
\end{equation}
In this equation, $k$ controls the density dependence of the circumburst medium (0 for constant density, and 2 for a wind-like medium); $E_\mathrm{iso}$ is the isotropic-equivalent explosion energy of the GRB; $N$ is the density parameter (such that the number density encountered by the shock is $n_{0} = N R^{-k}$ at some distance $R$); and $t_\mathrm{obs}$ is the time since the start of the GRB in the observer frame.  (Cosmological redshift may be significant, but we omit the factors of $(1+z)$ for the sake of simplicity.)  A similar application of the Blandford--McKee solution results in an expression for the ambient density $n_{0}$:
\begin{equation}
  n_{0} = N c^{-k} t_\mathrm{obs}^{-k} \Gamma^{-2k} \left[ 2(4-k) \right]^{-k}.
  \label{eq:BM_n0}
\end{equation}

The characteristic frequency of synchrotron emission depends on the electron Lorentz factor, $\gamma_\mathrm{max}$ as shown in Equation~\ref{eq:elec_gam_max}, and on the magnetic field strength $B$ as defined by Equation~\ref{eq:epsB_pk}.  We can specify $k = 0$ or $k = 2$ in these two equations, replacing $N$ with $n_\mathrm{ism}$ or $A_{\star}$ as appropriate:
\begin{equation}
  \gamma_\mathrm{max}^{2} =
  \begin{cases}
    4.72\xx{18} \, \eta_\mathrm{mfp}^{-0.534} \, \epsilon_{B}^{-0.682} \, n_\mathrm{ism}^{-0.43} \, E_\mathrm{iso}^{-0.253} \, t_\mathrm{obs}^{0.758} \, m_{p}^{0.253} \, c^{1.26}  &  k = 0  \\
    3.79\xx{18} \, \eta_\mathrm{mfp}^{-0.534} \, \epsilon_{B}^{-0.682} \, A_{\star}^{-0.859} \, E_\mathrm{iso}^{0.177} \, t_\mathrm{obs}^{1.19} \, m_{p}^{-0.177} \, c^{0.833}  &  k = 2
  \end{cases}
  \label{eq:elec_gam_instantiated}
\end{equation}
\begin{equation}
  B =
  \begin{cases}
    3.10 \, \epsilon_{B}^{1/2} \, n_\mathrm{ism}^{3/8} \, E_\mathrm{iso}^{1/8} \, t_\mathrm{obs}^{-3/8} \, m_{p}^{3/8} \, c^{3/8}  &  k = 0  \\
    3.24 \, \epsilon_{B}^{1/2} \, A_{\star}^{3/4} \, E_\mathrm{iso}^{-1/4} \, t_\mathrm{obs}^{-3/4} \, m_{p}^{3/4} \, c^{3/4}  &  k = 2
  \end{cases}
  \label{eq:B_pk_instantiated}
\end{equation}
The preceding two equations are sufficient to compute the maximum synchrotron frequency in the rest frame of the emitting plasma.  Boosting to the observer frame requires multiplying by the Doppler factor $\mathcal{D}$,
\begin{equation}
  \mathcal{D} \approx 2 \Gamma =
  \begin{cases}
    0.873 \, E_\mathrm{iso}^{1/8} \, n_\mathrm{ism}^{-1/8} \, t_\mathrm{obs}^{-3/8} \, m_{p}^{-1/8} \, c^{-5/8}  &  k = 0 \\
    1.09 \, E_\mathrm{iso}^{1/4} \, A_{\star}^{-1/4} \, t_\mathrm{obs}^{-1/4} \, m_{p}^{-1/4} \, c^{-3/4}  &  k = 2
  \end{cases} \\
  \label{eq:doppler_boost}
\end{equation}
Finally,
\begin{align}
  h \nu_\mathrm{syn,max} &= \frac{3 q h}{4 \pi m_{e} c}
  \begin{cases}
    1.26\xx{19} \, \eta_\mathrm{mfp}^{-0.534} \,
    \epsilon_{B}^{-0.182} \,
    n_\mathrm{ism}^{-0.18} \,
    E_\mathrm{iso}^{-0.003} \,
    t_\mathrm{obs}^{0.008} \,
    m_{p}^{0.503} \,
    c^{1.01}  &  k = 0 \\
    1.34\xx{19} \, \eta_\mathrm{mfp}^{-0.534} \,
    \epsilon_{B}^{-0.182} \,
    A_{\star}^{-0.359}
    E_\mathrm{iso}^{0.177}
    t_\mathrm{obs}^{0.187}
    m_{p}^{0.323}
    c^{0.833}  &  k = 2
  \end{cases} \nonumber \\
  &=
  \begin{cases}
    660 \, \mathrm{MeV} \, \eta_\mathrm{mfp}^{-0.534} \, \epsilon_{B}^{-0.182}
    \left( n_\mathrm{ism,0} \right)^{-0.18}
    \left( E_\mathrm{iso,53} \right)^{-0.003}
    \left( t_\mathrm{obs,2} \right)^{0.008}  &  k = 0 \\
    920 \, \mathrm{MeV} \, \eta_\mathrm{mfp}^{-0.534} \, \epsilon_{B}^{-0.182}
    \left( A_{\star,34} \right)^{-0.359}
    \left( E_\mathrm{iso,53} \right)^{0.177}
    \left( t_\mathrm{obs,2} \right)^{0.187}  &  k = 2
  \end{cases}
  \label{eq:syn_phot_max}
\end{align}
where we have used the notation $Q = Q_{x}\xx{x}$, e.g. $A_{\star} = A_{\star,34}\xx{34}$~cm$^{-1}$, and all quantities use cgs units.  We remind the reader that the observed peak of the photon distribution would occur at energies roughly 30\% of those given in Equation~\ref{eq:syn_phot_max}.

In the $k = 0$ case, the exponents of energy and time suggest that they may be due to uncertainty in the parameter $H_{C}$, and that the value of $h\nu_\mathrm{syn,max}$ may not depend on either quantity: if $H_{C}$ were precisely 1 instead of 1.01, neither factor would appear in Equation~\ref{eq:syn_phot_max}.  That is, the results presented in Figure~\ref{fig:mcmc_round1} suggest that the maximum observed synchrotron energy is essentially independent of both explosion energy and time.  For the $k = 2$ case, the maximum synchrotron frequency grows with time; though both Doppler factor and peak magnetic field decay with time, they are more than compensated for by the growth in maximum electron Lorentz factor.

The above limits should hold as long as (1) the motion of the blast wave is given by the adiabatic Blandford--McKee solution, (2) the shock Lorentz factor is above $\Gamma_\mathrm{pk}\beta_\mathrm{pk}$ given by Equation~\ref{eq:gbpk_def}, and (3) there is amplified microturbulence that decays on either side of the shock as prescribed by Equation~\ref{eq:epsB_form}.  Condition (1) means that Equation~\ref{eq:syn_phot_max} may not apply very early on in the afterglow, if the shock is still in the acceleration or coasting phases of its expansion. Condition (2) is satisfied for $\Gamma\beta \;\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}\; 10$.  Using this limitation in Equation~\ref{eq:BM_gamma} leads to the following restriction on $t_\mathrm{obs}$:
\begin{equation}
  t_\mathrm{obs} \lesssim
  \begin{cases}
    3.2\xx{4} \, \mathrm{s} \left( E_\mathrm{iso,53} \right)^{1/3} \left( n_\mathrm{ism,0} \right)^{-1/3}  &  k = 0 \\
    2\xx{6} \, \mathrm{s} \, E_\mathrm{iso,53} \, \left( A_{\star,34} \right)^{-1}  &  k = 2
  \end{cases}
  \label{eq:tobs_limit}
\end{equation}

As shown above, both ISM and wind media allow for electron synchrotron photons that reach GeV energies; but the extremely high energy photons detected in events like GRB 090902B \citep[33.4 GeV;][]{Abdo_etal_2009ApJ706}, GRB 130427 \citep[95 GeV;][]{Ackermann_etal_2014}, and GRB 190114C \citep[$>300$ GeV;][]{Mirzoyan2019ATel12390} suggest that an additional channel produces the highest-energy photons detected in GRB afterglows.  \citep[Alternately, electron acceleration could proceed in a more exotic scenario than modeled in this work, e.g.][who consider acceleration in the presence of clumpy magnetic field condensations.]{Khangulyan_etal_2020}  Though thermal electrons were ignored in this work, the synchrotron self-Compton mechanism in this population is a straightforward way to produce emission that peaks in the GeV--TeV range well into the afterglow \citep{WEBN2017}.

\subsection{What process limits electron energy?}
\label{sub:process}

The idea of using the synchrotron cooling break to interpret afterglow observations is nearly as old as afterglow observations themselves \citep{SPN1998}; for a recent example of a work using this formalism, see \citet{Fraija_etal_2020}, or the numerous citations within.  There are multiple approaches to determining the location of the cooling break.  One method is to assume that the electron distribution immediately behind the shock extends to infinity \citep{GranotSari2002}; synchrotron losses then quickly cool the highest-energy electrons and limit the extent of the electron distribution downstream from the shock.  Another, more realistic, way is to equate the electron acceleration time to the synchrotron cooling time to determine the energy at which acceleration stops \citep{Lemoine2013,Khangulyan_etal_2020}.

None of the previous analytical methods would seem to apply to the acceleration scenario presented in this work.  For example, consider the simplest case: electrons scattering in a homogeneous magnetic field.  In this setting, the synchrotron loss time is given by
\begin{equation}
  t_\mathrm{syn} = \frac{ 5 \xx{8} }{ B^{2} \, \gamma_\mathrm{elec} }~\mathrm{s} \propto B^{-2} \, \gamma_\mathrm{elec}^{-1}
  \label{eq:syn_loss_time}
\end{equation}
for electrons with energy $\gamma_\mathrm{elec}$ moving in a homogeneous field of strength $B$.  The maximal electron energy may be calculated by comparing the above loss time to the typical residence time of an electron in the downstream region of the shock. In keeping with the Bohm approximation above, we assume that the residence time is proportional both to the gyroperiod of the electron and to the Bohm factor:
\begin{equation}
  t_\mathrm{res|d} \propto \frac{ \eta_\mathrm{mfp} \, 2 \pi r_{g} }{ c } \propto \eta_\mathrm{mfp} \, \gamma_\mathrm{elec} \, B^{-1} .
  \label{eq:tres_DwS}
\end{equation}
For electrons with the maximum achievable energy, $t_\mathrm{syn}$ and $t_\mathrm{res|d}$ should be roughly equal, yielding
\begin{equation}
  B^{-2} \gamma_\mathrm{max}^{-1} \propto \eta_\mathrm{mfp} \gamma_\mathrm{max} B^{-1} .
  \label{eq:gammax_prop_1}
\end{equation}
The magnetic field is determined by Equation~\ref{eq:B_pk_strength}.  Substituting that equation into Equation~\ref{eq:gammax_prop_1} leads to the proportionality
\begin{equation}
  \gamma_\mathrm{max} \propto \eta_\mathrm{mfp}^{-1/2} n_{0}^{-1/4} \Gamma_{0}^{-1/2} \epsilon_{B}^{-1/4}
  \label{eq:gammax_prop_2}
\end{equation}
Equation~\ref{eq:gammax_prop_2} has a different dependence on $\Gamma_{0}$ ($-1/2$) than displayed in Figure~\ref{fig:mcmc_round1} and Table~\ref{tab:param_sets} ($\approx -1$).  This suggests that the above scenario does not reflect the energy-limiting process occurring in the MC simulations.  This is unsurprising, as Equations~\ref{eq:syn_loss_time} and \ref{eq:tres_DwS} assumed a homogenous magnetic field of strength $B$, while the MC simulations took place in a decaying microturbulent magnetic field.

Another straightforward limit on the maximum attainable energy of a shock-accelerated particle is to equate the acceleration time to the dynamical time of the shock.  The former quantity is conservatively given by the downstream residence time in Equation~\ref{eq:tres_DwS}.  The latter is proportional to $t_\mathrm{shock}/\Gamma$ for a shock of age $t_\mathrm{shock}$.  Setting the two to be roughly equal leads to the proportionality
\begin{equation}
  \gamma_\mathrm{max} \propto \eta_\mathrm{mfp}^{-1} n_{0}^{1/6} \Gamma_0^{-2/3} \epsilon_{B}^{1/2},
  \label{eq:gammax_tacc_tdyn}
\end{equation}
where we have substituted Equation~\ref{eq:B_pk_strength} into Equation~\ref{eq:tres_DwS}.  This approach also fails to reproduce the dependence on $\Gamma$ seen in Figure~\ref{fig:mcmc_round1} and Table~\ref{tab:param_sets}, suggesting either that the assumptions made are not correct or that the maximum electron energy is not limited by time.

The broad structure visible in Figure~\ref{fig:mcmc_round1} is that of a broken power law, which suggests that two processes control $p_\mathrm{max}$ in our model of electron acceleration.  There are hints, however, of more structure---particularly at the top right corner (high $\eta_\mathrm{mfp}$ and low $\epsilon_{B} n_{0}$), where the empirical equation seems to slightly overestimate $p_\mathrm{max}$, and at the bottom left corner (low $\eta_\mathrm{mfp}$ and high $\epsilon_{B} n_{0}$), where there may be an additional power law segment at higher $\Gamma\beta$ values.  These possible additional features could be physical in origin, something we intend to investigate in future work.

\section{Conclusions}
\label{sec:concl}

We have presented here the results of numerous Monte Carlo (MC) simulations of diffusive shock acceleration of electrons.  Acceleration took place in a highly turbulent magnetic field that decayed upstream and downstream from the shock, as observed in particle-in-cell simulations of relativistic shocks.  The accelerated electron spectra are well-described by power laws with an exponential turnover (Equation~\ref{eq:pl_def}, Figure~\ref{fig:mc_results}), and the likelihood distributions of their parameters $\vec{\pi}_\mathrm{pl} = (p_\mathrm{max}, \sigma, \chi, \log_{10}K)$ were estimated using a Markov chain Monte Carlo (MCMC) approach.  We focused here only on the parameter $p_\mathrm{max}$, i.e. the location of the exponential turnover and the energy at which acceleration gains balance loss processes.  When the estimates of $p_\mathrm{max}$ are plotted across a 3-dimensional parameter space of astrophysical interest, they appear to form broken power laws as a function of the shock speed $\Gamma\beta$ (Figure~\ref{fig:mcmc_round1}).  The peak in each curve lies close to the shock speed at which electrons cease to escape upstream from the shock, which suggests that upstream escape and radiation losses are the two limiting processes that control the maximum electron energy.

Based on the broken power law observed for $p_\mathrm{max}$ as a function $\Gamma\beta$, we proposed an empirical expression in terms of physically-motivated features (Equation~\ref{eq:broken_pl_used}).  Another round of MCMC was used to estimate its parameters (Table~\ref{tab:param_sets}).  The resulting expression allows for prediction of the peak electron energy---and correspondingly the synchrotron cooling energy---in scenarios where relativistic shocks accelerate electrons, without the need for time-consuming numerical simulations.  Extensions to this work will involve increasing the size and dimensionality of the MC-simulated parameter space $\vec{\phi}_\mathrm{MC} = (\eta_\mathrm{mfp}, \epsilon_{B} n_{0}, \Gamma\beta)$ from what was considered here, as well as quantitative treatments of the $\sigma$ and $\chi$ parameters in Equation~\ref{eq:pl_def}.

redpajama_set_name: RedPajamaArXiv


text:
Данаєць Хрисипп (Danaus chrysippus) — вид денних метеликів родини сонцевиків (Nymphalidae).

Етимологія
Вид названо на честь персонажа давньогрецької міфології Хрисиппа.

Поширення
Вид поширений по всій Африці, Південній Європі, тропічній та субтропічній Азії, в Океанії та Австралії. В Україні один раз спостерігалася залітна особина у Криму.

Опис
Досить великий метелик. Розмах крил становить 7-9 см, довжина переднього крила — 33-43 мм. Крила забарвлені в яскравий помаранчевий колір, який максимально інтенсивний на верхніх крилах. Малюнок виконаний у вигляді темного або чорного канта. По верхньому крилі хаотично розташовані білі плями. Самиці практично нічим не відрізняються від самців.

Спосіб життя
Метелики активні протягом всього року. За сприятливих умов можуть давати до 12 поколінь у рік. Гусінь живиться рослинами з родини барвінкових, але може траплятися і на інших рослинах.

Посилання
 AdaMerOs — Butterflies Watching & Photography Society in Turkey
 Sri Lanka Wild Information Database

Сонцевики
Комахи Європи
Комахи Африки
Комахи Австралії
Комахи Азії
Метелики України
Комахи, описані 1758

redpajama_set_name: RedPajamaWikipedia


Geographic information systems (GIS) and special mobile applications for forestry and agriculture support mobile and smart farming. The management of cultivated areas and the storage of data sets, such as harvest results or fertilizer inputs, are efficient and available on site at any time. Area surveying with GPS support and parallel driving assistant are two further keywords for the use of mobile hardware solutions in this area.
The acceptance of mobile and rugged tablet PCs in forestry and agriculture is increasing. Normal notebooks and conventional mobile solutions can only be used to a limited extent in the field due to their sometimes uncomfortable handling. Ergonomics and good readability are particularly important when mobile devices are used.
Mettenmeier's rugged PCs, such as the Getac F110 or V110, guarantee ideal readability with a large display. This is very important when working with large amounts of data such as aerial photographs, field maps or cadastral maps, as small locations or details often have to be checked and supplemented.
A large working memory and a high storage capacity are also necessary for forest inventories, as there are many attributes for areas and individual trees.
The extreme sturdiness of Mettenmeier's equipment is another important feature for field work and all weather conditions, e.g. external mapping in the field of forest ecology.
The devices are operated both via conventional office applications and via the use of special software, with the active pen or with your fingers (Multi-Touch). Its numerous interfaces enable the extensive use of peripheral devices such as GNSS receivers and many more.


text:
Duquesne University of the Holy Spirit is a private Catholic university in Pittsburgh, Pennsylvania. Founded by members of the Congregation of the Holy Spirit, Duquesne first opened its doors as the Pittsburgh Catholic College of the Holy Ghost in October 1878 with an enrollment of 40 students and a faculty of six. In 1911, the college became the first Catholic university in Pennsylvania. It is the only Spiritan institution of higher education in the world.
Duquesne has since expanded to over 10,000 graduate and undergraduate students within a self-contained 49-acre (19.8 ha) hilltop campus in Pittsburgh's Bluff neighborhood. The school maintains an associate campus in Rome and encompasses ten schools of study. The university hosts international students from more than 80 countries although most students — about 80% — are from Pennsylvania or the surrounding region. Duquesne is considered a research university with high research activity institution by the Carnegie Foundation for the Advancement of Teaching.
There are more than 79,000 living alumni of the university including two cardinals and the current bishop of Pittsburgh.
The Duquesne Dukes compete in NCAA Division I. Duquesne men's basketball appeared twice in national championship games in the 1950s and won the NIT championship in 1955.
Motto: Spiritus est qui vivificat (Latin)
Motto in English: It is the Spirit that gives life.
Established: October 1, 1878
Type: Private, Religious affiliation, Roman Catholic (Congregation of the Holy Spirit)
Endowment: $171 million (2011)
Postgraduates: 4,505
Former Names: Pittsburgh Catholic College of the Holy Ghost
Colors: Red and Blue
Athletics: NCAA Division I – A-10, NEC
Mascot: The Duke
Website: www.duq.edu

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We are delighted that Niall McLaughlin joins the Society this year to deliver our annual Alexander Thomson lecture.
We are incredibly grateful that sponsorship for this event once again comes from Taylor Maxwell.
Niall McLaughlin was educated in Dublin and received his architectural qualifications from University College Dublin in 1984. He worked for Scott Tallon Walker in Dublin and London between 1984 and 1989. He established his own practice in London in 1990. Niall McLaughlin Architects make high quality modern buildings with a special emphasis on materials and detail. Niall won Young British Architect of the Year in 1998, he was one of the BBC Rising Stars in 2001 and his work represented Britain in a US exhibition Gritty Brits at the Carnegie Mellon Museum.
His designs have won many awards in the UK, Ireland and the US, including RIAI Best Building in the Landscape and the RIBA Stephen Lawrence Award for the Best Building under £1million and was on the Stirling Prize Shortlist in 2013 and 2015. Niall is a professor of architecture at University College London, Lord Norman Foster visiting Professor of Architecture, Yale, 2015, and visiting Professor University of California Los Angeles, 2012-2013 a Member of the Architectural Review Editorial Board and an Honorary Royal Designer of Industry.


text:
This frame grab from video provided by Fox News shows White House adviser Kellyanne during her interview with "Fox News Fox and Friends" Thursday, in the briefing room of the White House in Washington. Conway defended Ivanka Trump's fashion company, telling Fox News that Trump is a "successful businesswoman" and people should give the company their business. | FOX NEWS VIA AP
Conway seen violating ethics law by pitching Ivanka's goods from White House
Online: Feb 10, 2017
Last Modified: Feb 10, 2017
WASHINGTON - A top White House aide on Thursday promoted the clothing line named after President Donald Trump's daughter, Ivanka, drawing criticism from ethics experts one day after the president attacked a retailer for dropping her products.
"Go buy Ivanka's stuff … I'm going to go get some myself today," Trump senior adviser Kellyanne Conway told Fox News in an interview from the White House. "I'm going to give a free commercial here: Go buy it today, everybody."
Norman Eisen, who served as an ethics adviser to Democratic President Barack Obama, said Conway's comments amounted to an advertisement and violated government ethics law.
"It's a violation of the rule," Eisen told MSNBC. "It's a serious matter."
Former Office of Government Ethics chief Don Fox told the Washington Post Conway's comments appeared to violate rules barring the use of public office for anyone's private gain.
Ivanka's brand was thrust into the headlines after her father on Wednesday attacked department store chain Nordstrom Inc. for dropping her products, in a highly unusual move that drew criticism for his use of a White House Twitter platform to intervene in a commercial matter.
The White House did not immediately respond to a request for comment over the ethics issue regarding Conway's remarks, and the Office of Government Ethics could not be immediately reached.
Other retailers that have dropped the Ivanka line include Neiman Marcus and HSN Inc., while Macy's Inc., TJX Cos, Hudson's Bay Co., which runs high-end chains like Lord & Taylor, and Dillards Inc. still carry it.
An ongoing campaign called #GrabYourWallet encourages shoppers to boycott products with ties to President Trump and his family. Separately, supporters have launched an alternative social media campaign called #BuyIvanka.
Ivanka Trump has said she would step away from her company when her father took office in the White House. A spokeswoman for the Ivanka Trump brand declined comment on Wednesday.
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text:
U.S.-led troops end Iraq combat mission, as planned – military officials
By Tom Balmforth and Andrey Ostroukh
FILE PHOTO: Iraq's National Security Advisor Qasim al-Araji wearing a protective mask speaks after he took up the post from the former security advisor Falih al-Fayyadh in Baghdad
BAGHDAD (Reuters) -U.S.-led forces have ended their combat mission in Iraq, a move that transfers all remaining troops into a training and advising role, Iraqi military commanders and officials from the coalition led by the United States said on Thursday.
Western security officials and diplomats say privately that this will make little difference to the number of troops stationed in the country – currently more than 2,000 – since those forces have had limited involvement in any combat operations for the last couple of years.
The U.S.-led coalition began its mission in 2014 to defeat Islamic State, after the militants took over vast areas of Iraq and neighbouring Syria.
Since the group's military defeat in 2017, Islamic State fighters have been unable to hold territory but are waging a continued low-level insurgency that regularly kills Iraqi soldiers and civilians in remote mountain and desert areas.
The coalition has also come under dozens of rocket and drone attacks by Iran-backed Shi'ite militias that helped defeat the Sunni extremist Islamic State and which say there is no longer a justification for Western forces to be in Iraq.
"As we complete our combat role, we will remain here to advise, assist, and enable the ISF (Iraqi security forces), at the invitation of Republic of Iraq," coalition commander Major General John W. Brennan, Jr. said in a statement.
Iraqi commander Lieutenant General Abdul Amir al-Shammari said Iraqi forces were ready to handle the Islamic State threat.
"Today, we renew our partnership with the Coalition, who are now serving in a new capacity – with a mission to advise, assist, and enable our brave military warriors," he said.
U.S. President Joe Biden and Iraqi Prime Minister Mustafa al-Kadhimi sealed an agreement in July to formally end the U.S. combat mission in Iraq by the end of 2021.
Iraqi Shi'ite militants have vowed to wage new attacks against coalition forces in 2022.
Western security and diplomatic officials say that calling the shift a withdrawal, as it has sometimes been characterized by the Iraqi government, is misleading because it changes little in terms of the number of forces based in Iraq.
The U.S. has kept around 2,500 troops in Iraq since 2020. The Western officials say that most of those forces have been operating only in a training and advising role for some time.
(Reporting by Ahmed Rasheed in Baghdad, John Davison in Erbil; additional reporting by Enas Alashray in Dubai; Writing by John Davison; Editing by Alex Richardson)
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Soccer-Spurs Premier League match at Brighton postponed due to COVID-19
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Cricket-Sloppy England left to rue Leach selection at Gabba


text:
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Tel: +386 41 982 860 (Peter Keršič)
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SEE&DO
MOŽINA'S HOUSE
From the past...
Možina's house is a rare example of a preserved historical house of a wealthy farmer in Polhov Gradec Hills. It is built in classical rural style. With its 106 hectares of land it used to be the wealthiest house in the Šentjošt area and its size was adequate for the owner to get hunting rights. It is built of stone, and so are the entrance portals. Years 1842 on one portal and 1894 on the other are the years the house was renovated. However, the house is much older as it has a gothic window on the east facade and was first mentioned in writing in 1652.
After the Second World War there were a farm building, a small double hayrack, a fruit dryer and a cottage next to the house. It had been a butcher's shop, and a municipal office from the mid-19th century to 1945. Možina's house was multiple times a school building and a shop. Before the war it was a pub with guest rooms. Locals and travelers were stopping by to have a bite, play cards, pool or a local popular game called "marjanca". After the Second World War the new authorities seized the property and gave the pub to the administration but it was closed shortly after that.
… to the future
Možina's house was inhabited until the 90's of the 20th century and then started to crumble slowly. The current owners bought it in 2003 and decided to preserve its beauty for the future generations. Of all the properties only the house is still standing.
The main idea behind the renovation was to preserve as many historical materials and house proportions as possible. Read more.
… inspiring new life
Even at the stage of renovation (when it was without the plaster, windows, doors…) it was already a place of exhibitions, cultural events and social gatherings and with its interesting interior it appeared in a music video. Today it opens its door to the locals and travelers on numerous occasions The locals and travelers are welcome again. It is meant to be a gathering place for all who cherish homeliness and hospitality.
… little fun facts
The name Možina was first mentioned in 1625 when Andrej, the son of Simon Možina, was brought to the church by his godfather Matija Kogušek and godmother Špela Štanta to be baptized. Even though the original family name Možina was not in use for a long time it sticked with the house until today. Read more.


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text:
CHI Tribune: Breaking News: Chicago State trustees back interim provost
http://www.chicagotribune.com/news/education/ct-chicago-state-board-meeting-20140212,0,5455691.story
http://www.chicagotribune.com/news/education/ct-met-0114-chicago-state-provost-gfc-eps-20140113,0,2594813.graphic
Chicago State trustees back interim provost
Her dissertation scrutinized over plagiarism allegations
By Jodi S. Cohen, Tribune reporter
7:09 PM CST, February 11, 2014
Chicago State University trustees Tuesday publicly backed the campus' interim provost, Angela Henderson, who has faced allegations that parts of her doctoral dissertation were plagiarized.
The board's support came after it met in a two-hour closed-door session. Reading a statement, board Chairman Anthony Young said the board "accepts the Ph.D. conferred" on Henderson in August by the University of Illinois at Chicago, and "the current process being followed" at UIC, which began reviewing Henderson's work in December.
"Therefore the board supports Dr. Henderson in her role as the interim provost and senior vice president," Young said. "The board also expresses its full confidence in President (Wayne) Watson."
The board's support comes days after the university's faculty senate voted "no confidence" in Watson and Henderson, the university's top officials. The 44-member Senate, the faculty's governing body, voted 25-2, with three abstentions and 14 members absent.
"I guess academic dishonesty is accepted by this board of trustees," faculty senate President Phillip Beverly said following Tuesday's meeting. "That is the only way I can interpret this. It would never happen at another university."
Chicago State's spokesman said Henderson declined to comment. She attended the public part of the board meeting, and then left the room about a minute before trustees returned from their private session.
Henderson, 48, who took over in July as interim provost, the campus' senior academic official, received her doctorate in nursing from UIC in August. She had served as Chicago State's vice president for enrollment for two years.
UIC officials began examining her dissertation in December after a Chicago State professor raised concerns that parts of it were copied from other sources, without proper attribution or with inadequate citation.
UIC Graduate College Dean Karen Colley was expected to decide last month whether any action should be taken in respect to Henderson's dissertation. UIC spokesman Bill Burton declined to discuss the review or its possible outcome Tuesday, citing privacy concerns.
UIC removed Henderson's dissertation from its online database in December pending the outcome of the review. It remained offline Tuesday.
The charges against Henderson are noteworthy because, as provost, she is responsible for overseeing the academic side of the university. That includes operations and policies related to academic standards and integrity, graduate education and disciplinary matters.
Henderson's five-member dissertation committee, which had to approve her thesis in order for her to graduate, included Watson.
Her 129-page dissertation is titled: "Predicting Consistent Condom Use in African-American, Emerging, Adult Males Enrolled in Community College." Her work included surveying 186 African-American students at two community colleges to determine what influences them to use condoms, and then analyzing the results.
jscohen@tribune.com
Copyright © 2014 Chicago Tribune Company, LLC
Voiced Feb 11, 2014, 8:13:00 PM
Reasonable people would follow UIC's lead and DISENGAGE from Henderson's reckless disregard for academic integrity. Is there no trustee with any shred of morality? Doesn't this mean any student accused of plagiarism now has a right to defer to this public decision? To treat students any differently is DISCRIMINATION.
Ditto for UIC. Re. Plagiarism and Discrimintion. If they do not retract plagiarized degree, they lose right to call any other student out for this as well.
Teacher Feb 18, 2014, 11:53:00 AM
I do not see the administration's actions in the wake of the Henderson dissertation scandal as unusual in a such an authoritarian system. What is wonderful and unusual about this whole thing is that a small group of faculty members has actually turned on a bright light and aimed it at the group of highly paid 'leaders'.
Things are quite different at Governors State University, the sister university (at least in the past) of Chicago State. The president, Ms. Maimon, suspended the Constitution when she was hired and substituted an administratively-controlled process as a substitute. The GSU administration has been informed that a faculty member lied about academic credentials on hiring and in yearly reviews until the truth was discovered. That person's dean has said that such lying was just fine because the degree that the person actually had qualified her for the position (the dean's view but not the faculty view). The same faculty member wrote a doctoral study, not a dissertation, in which an 'expert panel' was supposedly used to develop/approve research questions. At least one of the panel members did not do this work. Reporting this lapse in ethics was also ignored. The reporter in these two instances was terminated and the termination has been arbitrated.
So, Chicago State University is not the only Illinois university to have administrators bent on protecting incompetents and silencing anybody who speaks out.
Unknown Apr 25, 2014, 1:09:00 AM
Everyone is responsible to all of his/her doings. If we will be talking about writing dissertation, maybe with the same thought but it should be in different and unique content and usage of words. Wish this a calling to all and a lesson.
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