The FreeGarden" RAIN 55 gallon Black rain barrel is designed with the homeowner/gardener in mind; affordable, attractive, easy to move, easy to install, and easy to use. With as many as three bins easily fitting in the back seat of a regular sedan, the average buyer doesn't need to arrange special transport. The barrel's square shape is ideal for attractive flush to wall and corner installations. The tall spigot placement accommodates most watering cans, and four additional spigot mount points are provided lower on the barrel. Manufactured with a maximum of recycled content (varying by colour option), the FreeGarden" RAIN contains enough virgin resin to ensure optimal product durability and lifespan.
Flat Back 50 USG Rain Barrel with Brass Spigot in Mud Embrace nature's solution to our emerging water shortage-collect rainwater! Our authentic oak barrel texture is moulded into each barrel and will not fade, rot or risk insect infestation.
Flat Back 50 USG Rain Barrel with Brass Spigot in Mud is rated 4.1 out of 5 by 527.
Rated 4 out of 5 by Rainbarrel from Easy set-up and durable. Easy set-up and durable.
Rated 5 out of 5 by Wayne from Easy to assemble. Works great. ... Easy to assemble. Works great.
Rated 5 out of 5 by Linda from Easy to install and seems to have caught the rain... Easy to install and seems to have caught the rain so far. Now I'm just hoping to get my rebate!
Rated 3 out of 5 by unhappy67 from The rain barrel itself is fine. Purchased the brass spigot instead of the plastic, but it inser... The rain barrel itself is fine. Purchased the brass spigot instead of the plastic, but it inserts into a plastic plece which does not fit properly. It leaks. Purchased this on-line, picked it up at the store and now have to take it back. My recommendation is do not purchase this product due to the spigot. Received no satisfaction from the store.
Rated 4 out of 5 by Desertwind from Easy assembly.... Easy assembly.
Rated 3 out of 5 by DontcallmeFrancis from The rain barrel is sturdy. It has the shape I... The rain barrel is sturdy. It has the shape I was looking for and it matches the color of my hot tub. The spigot threads are a little fragile even after adding plumbing tape. Its one of those situations where you'd like to tighten more but I'm nervous about damaging the threads themselves. It works.
What kind of plastic is this made of? Is it BPA free? I want to use it for drinking water.
I contacted the company, and they said yes, all of their rain barrels are BPA free.


While U-Street is quickly taking over the foodie scene in DC with its funky menus and unusual cocktails, places like Desperados Burgers & Bar still hold strong with their classic take on all american juicy burgers and frickles (fried pickles). Located at 1342 U Street NW, DC 20009 this classic burger joint could'd be in a better location. If you'er one of the lucky few to snag a spot outside, take it! If not, the underground bar with it's wood paneled interior sets the perfect scene for game-day drink or a midweek happy hour.
Cool & casual. This is my go-to Friday night dinner spot when I'm in the mood for a tasty, inexpensive and laid-back meal. Everything on the menu is good but I always come back to the amazing spicy broth noodle soup.
Head to Trader Joe's - Great Green Juice!
Trader Joe's is known for their cheap prices, wide selection of foods, and of course the discount wine selection. In addition to all of these things, they stock the shelves with a fresh pressed green juice that runs just $4.99. It's a great alternative to the much pricier options!
The historical significance of Ben's is well known, it's a landmark in DC. Of course DC has many landmarks but when you are hungry, you can't eat history or atmosphere. At Ben's the original half-smoke has high quality half pork, half beef charred on the flat top that must have cooked about 30 million of those since 1958. The bun was steamed, I enjoyed their unique chili and with the onions and yellow mustard. While they serve a really good chili dog, don't forget to enjoy some down home good chili as well.


text:
The Clean Air Act: EPA's charade to justify its war on coal plants
By Larry Bell |2014-01-24T00:35:48-04:00January 14th, 2014|CFACT Insights|4 Comments
The Environmental Protection Agency didn't let a Clean Air Act requirement that mandated technologies be "adequately demonstrated" hinder their new performance standards ruling that puts a limit of 1,100 pounds per megawatt-hour (lb/MWh) on carbon emissions from new coal power plants. Not only is there no scientifically supportable climate benefit for limiting such emissions, there is no viable commercial-scale technology to achieve that ideological pipedream. Even if it mattered, the most modern coal-fired plants can only reduce CO2 emissions to 1,800 lb/MWh. What's more, they already knew that.
Or at least they certainly should have known — after a fact-finding working group within EPA's own Science Advisory Board (SAB) informed them that such systems have never been proven outside the laboratory, and that pilot demonstration projects under development are over budget. These discoveries led SAB to issue a November 12, 2013, memo which raised questions regarding the technical feasibility of "sequestering CO2" (removing and storing it).
Challenging the credibility of research EPA was supposed to use for rule justification, the communication noted that "the peer-review of scientific and technical information presented for coal-fueled sources appears to be inadequate."
The SAB working group observation contradicted EPA's claims based upon speculative studies and models produced by a Department of Energy research unit that sequestration works. EPA had assured the SAB panel that those studies had been vetted by "industry experts, academia, and government research and regulatory agencies."
Yet upon further investigation the SAB found that "peer-review " for some of those Energy Department studies was conducted by none other than EPA itself over a brief few-weeks period, and that the rest never received unbiased scrutiny either. As reported, Energy could not provide "a documented or publicly available description of the peer review process," and EPA refuses to share such information with SAB.
Then something happened on the way to a December 5 meeting of the full SAB panel. Under pressure from EPA they tabled a vote on accepting their working group's recommendations. EPA officials argued that the SAB wasn't permitted to review sequestration science after all.
And why? Well because EPA wasn't really mandating sequestration per se, or making rules for sequestration. No…they were merely requiring coal plants to meet specific emission limits they set (whether achievable or not). How to accomplish that was a separate issue. That was the industry's problem, not theirs.
Actually, it's our problem too…a very big one. All of this costs money, and lots of it. First, it demands a huge amount of energy, requiring the coal-fired plant to burn about a quarter more coal to handle the sequestration while producing the same amount of electrical power. This is required to pay for capturing the CO2, compressing it, and transferring it for storage somewhere. The added fuel demand also expands necessary mining operations, coal transportation, and, unlike plant-nourishing CO2, the production of real pollutant byproducts, such as fly ash.
The Institute for Energy Research has estimated that this "regulatory assault" will eliminate 35 gigawatts of electrical generating capacity…10% of all U.S. power. As the Competitive Enterprise Institute observes, "If the carbon dioxide emissions standard for power plants proposed by the EPA today is enacted, the United States will have built its final coal-fired power plant."
The recent SAB incident certainly isn't the first time that the EPA has ignored advice that runs counter to their ideological agenda. In fact its entire 2009 "endangerment finding" decreeing that atmospheric concentrations of six greenhouse gases (including CO2) "threaten the public health and welfare of current and future generations" was refuted at the time by its in-house "Internal Study on Climate" report conclusions.
That report, authored by my friend Alan Carlin, a senior research analyst at EPA's National Center for Environmental Economics, stated: "…given the downward trend in temperatures since 1998 (which some think will continue until at least 2030), there is no particular reason to rush into decisions based upon a scientific hypothesis that does not appear to explain most of the available data."
It was political science, not climate science, which demanded hasty EPA action. As then-presidential candidate Barack Obama promised in 2008 while pushing a CO2 cap-and-trade priority: "So if somebody wants to build a coal-powered plant, they can. It's just that it will bankrupt them because they're going to be charged a huge sum for all that greenhouse gas that's being emitted…That will also generate billions of dollars that we can invest in solar, wind, biodiesel, and other alternative energy approaches."
He went on: "The only thing I've said with respect to coal, I haven't been some coal booster. What I have said is that for us to take coal off the table as a (sic) ideological matter as opposed to saying if technology allows us to use coal in a clean way, we should pursue it."
Candidate Obama also said: "Under my plan of a cap-and-trade system, electricity rates would necessarily skyrocket. Coal-powered plants, you know, natural gas, you name it, whatever the plants were, whatever the industry was, they would have to retrofit their operations. That will cost money. They will pass that money on to consumers."
When former EPA director Lisa Jackson's lieutenant Gina McCarthy (who now has Jackson's old job) was subsequently invited to explain before the House Energy and Commerce Committee how President Obama's war on coal "Climate Plan" would be expected to impact any of 26 outcome indicators defined on their website, she did little to inspire confidence.
Responding to a question from Rep. Mike Pompeo (R-KS), McCarthy said: "It is unlikely that any specific one step is going to be seen as having a visible impact on any of those impacts — a visible change in any of those impacts. What I'm suggesting is that climate change [policy] has to be a broader array of actions that the U.S. and other folks in the international community take that make significant effort towards reducing greenhouse gases and mitigating the impacts of climate change."
And now, following 17 years of flat global temperatures despite rising atmospheric CO2 levels isn't it high time to reassess once again what we're getting for all that money? Even the UN's alarmist Intergovernmental Panel on Climate Change (IPCC) has finally been forced to admit that their climate models have grossly exaggerated climate sensitivity to CO2.
Rather than set an example for that international community, wouldn't it be better to learn from their disastrous climate-action-premised debacles, Europe's in particular? Consider Germany and Denmark, for example, where so-called "Green energy" policies involving heavily subsidized investments in wind energy force their consumers to pay three times more for electricity than we do, and 30% more than their European neighbors.
Then there's Britain, which like Germany is closing some of its coal-fired plants, any one of which can produce nearly twice as much power as all of that nation's 3,000 wind turbines combined. This is less of a problem when there are reliable backup sources such as hydropower, coal, and nuclear plants to meet demand. But most of Europe lacks the former and is intentionally — to its detriment — cutting back on both of the latter.
In following these failed European policies, the Obama Administration is intentionally maiing energy more expensive for American citizens and job-producing industries. The war on coal, which presently provides about 42$ of our power, comes at a time when that industry is already under great economic pressure from abundant and inexpensive natural gas that will continue to replace coal for power and heating.
This blatant regulatory overreach, where government picks winners and losers, permeates virtually all aspectys of the current federal energy policy. In addition to attacking coal, an alphabet soup of agencies, including EPA, Interior, and others, are also waging wars on oil and gas drilling. THeir arsenal of weapons includes legal actions to preempt state and private land rigjhts; permitting cfomplexities, delays, and uncertainties on federal landsto discourage enterprise; punitive taxes on fossil fuels; and multi-agency regulatory threats against fracking.
There can be no wonder then to see such assaults continue to drive fossil energy costs higher in order to make heavily taxpayer and consumer subsidized prices for unreliable wind and solar boondoggles appear competitive. It will require a change at the White House and Congress, not in the climate, to make these agencies clean up their act.
jameshrust January 15, 2014 at 11:07 AM
THE U. S. GOVERNMENTS WAR ON THE POOR
A little philosophical thinking. The nation is celebrating the 50th anniversary(1964) of the War On Poverty. Many will say the war is lost because the percentage of poor today is the same as fifty years ago. Our energy policy may be the reason the War On Poverty was lost. Almost without exception, renewable energy programs are more expensive than fossil fuel sources they are supposed to replace. Since 1977, hundreds of billions, if not more than a trillion, of tax dollars was spent on programs pushing a variety of renewable energy sources–solar, wind, biofuels, biomass, etc. Tax dollars come from everyone in some form. The poor are hurt more by waste of tax dollars because the rich can withstand the losses. I maintain our renewable energy programs take from the poor and give it to the rich. This is the complete opposite of the War On Poverty which was supposed to take from the rich and give it to the poor. Thus the government is engaged in two economic programs that cancel each other. This government program should be labeled the War On The Poor. At this time the leader in the program is the EPA with its foolish rulemaking calling life saving carbon dioxide air pollution.
Without government interference in energy policy, the nation would produce more inexpensive energy, create millions of high-paying jobs, add trillions annually to our gross domestic product, and have a positive balance of trade. This has to be a successful War On Poverty.
James H. Rust, Professor of nuclear engineering
Eckenhuijsen Smit January 16, 2014 at 4:02 AM
Those incompetent idiotic stupids are still talking to diminish CO2, while CO2 is exactly so very necessary for all life on earth.
Get those brainless red/green alarmists thrown out of every important function they still hold, albeit completely worthless.
Michael Castillo January 18, 2014 at 12:21 AM
It's not about competence or saving the planet. it's only about two things. Rewarding Obama's political cronies and control!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
oeman50 January 20, 2014 at 5:54 PM
Very interesting. In some recently FIOAed e-mails, even the environmental activiest admitted that Gina McCarthy's pants were "on fire" when she said carbon capture and sequestration was "available" and could therefore be required for new power plants. It is a subterfuge to advance the agenda of getting rid of coal.

redpajama_set_name: RedPajamaCommonCrawl


text:
Priorities for the 114th Congress
2015-01-06T10:56:46-05:00https://images.c-span.org/Files/09d/20150106105816001_hd.jpgRepresentative-elect Barbara Comstock (R-VA) talked about legislative priorities of the 114th Congress. She was interviewed by remote video from the rotunda of the Cannon House Office Building.
Representative-elect Barbara Comstock (R-VA) talked about legislative priorities of the 114th Congress. She was interviewed by remote video from the rotunda of the Cannon House Office Building.
Filter by Speaker All Speakers Greta Brawner Barbara Comstock
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Rep. Barbara Comstock credits Metro Silver LIne with getting her to Congress today


I know this might be an invasive question, but I read on Twitter that you moved to Nicaragua. Is that true? If so, how did you do it and how would you recommend someone else doing the same? Thanks for your help in advance.
Alright, let me know when you can.
Hey, I haven't heard from you. Was wondering if you had any additional information to share.


text:
News World Africa African city of Goma under threat as Mount Nyiragongo volcano erupts in Congo
African city of Goma under threat as Mount Nyiragongo volcano erupts in Congo
Awakened from its slumber, Mount Nyiragongo threatens the town of Goma whose lights can be seen in the background. Photo: Twitter/Lynda Lacosta
The New Daily @TheNewDailyAU
Thousands of residents are fleeing their homes in the Congolese city of Goma as a nearby volcano spews lava and super-heated gases across the nearby terrain.
Lava from Mount Nyiragongo has reached the airport of eastern Democratic Republic of Congo, further accelerating the rush to safety.
Recalling Nyiragongo's last eruption in 2002, which killed 250 people and left 120,000 homeless, a spontaneous legion of evacuees took to the roads carrying mattresses and whatever valuables could be carried on their backs.
As the red glow of the volcano, one of the world's most active, tinged the Saturday night sky above the lakeside city of about two million, some fled east toward the frontier with neighbouring Rwanda, while others escaped to the west.
Dario Tedesco, a volcanologist based in Goma, said new fractures were opening in Nyiragongo, allowing the lava to flow southward toward Goma after initially flowing east toward Rwanda.
"Now Goma is the target," Tedesco told Reuters. "It's similar to 2002. I think that the lava is going towards the city centre."
"It might stop before or go on. It's difficult to forecast," he said.
A United Nations source said all UN aircraft had been moved to the city of Bukavu to the south and Entebbe in neighbouring Uganda.
Mt. Nyiragongo in Goma, (eastern) DRC erupts as we speak. What a crazy volcano… pic.twitter.com/MYodnf98WU
— Martin L. Kalere 🇨🇩 (@Kalereops) May 22, 2021
Power was also out across much of Goma and phone lines were busy.
In Kinshasa, the capital, Prime Minister Jean-Michel Sama Lukonde, convened an emergency meeting, where the government activated an evacuation plan for Goma.
Volcano watchers have been worried that the volcanic activity observed in the past five years at Nyiragongo mirrors that in the years preceding eruptions in 1977 and 2002.
Volcanologists at the Goma Volcano Observatory, which monitors Nyiragongo, have struggled to make basic checks on a regular basis since the World Bank cut funding amid embezzlement allegations.
In a bulletin on May 10, the observatory said there had been increased seismic activity at Nyiragongo earlier in the month.
– with AAP
Students march again for climate action


text:
\section{Introduction}
\label{}
Numerical modeling of groundwater flow in variably saturated soils is an important part of solution of various hydrogeological problems involving vadose zone. These problems arise in environmental sciences and include safety assessment of radioactive waste repositories and landfills, water resources management and fertilizers application optimization.
Groundwater flow in variably saturated conditions is governed by nonlinear partial differential Richards equation \cite{richards1931capillary,bear2010modeling} with additional constitutive relationships between water pressure head, water content and relative permeability of the soil. Existing analytical and semi-analytical solutions \cite{parlange1999analytical} of Richards equation are valid for limited cases, and numerical solution is the common choice. Nonlinearity of the equation makes numerical solution a challenging task with numerous approaches having been developed, an overview of which can be found in \cite{farthing2017numerical}.
\par
In addition to transient problems, steady-state problems are also of interest. Discretization of steady-state Richards equation leads to a system of nonlinear equations which then can be solved by an iterative method. Nonlinear solvers such as Newton method can experience severe convergence problems since obtaining a suitable initial guess is not trivial. Another approach is the pseudo-transient method \cite{farthing2003efficient}, which introduces time to the system and lets it evolve until equilibrium is reached, leading to solution of transient Richards equation. For stability reasons discretization in time usually employs fully implicit scheme which again results in a system of nonlinear equations at each time step, although now with ability to change time step size to improve convergence. Nonlinear solvers (modified Picard \cite{celia1990general} and Newton with techniques such as primary variable switching \cite{diersch1999primary}) within the pseudo-transient method can still exhibit poor convergence in case of dry and heterogeneous soils or highly nonlinear constitutive relationships, leading to a large number of time steps and overall high computational complexity. Therefore, it is desirable to have a solution approach which needs no time-stepping and works directly with discretized steady-state Richards equation. As mentioned before, the main problem is the lack of initial guess sufficiently close to solution. Techniques like line search \cite{farthing2003efficient} and combined Picard-Newton approach \cite{paniconi1994comparison} can improve convergence, but still can fail for complex problems.
\par
To overcome difficulties related to lack of suitable initial guess for Newton method a nonlinearity continuation method can be applied. In methods of this type a suitable initial guess for Newton method is obtained through solution of a series of other problems with incrementally varying nonlinearity \cite{continCFD}. This approach for steady-state Richards equation is implemented in GeRa \cite{kapyrin2015integral} hydrogeological modelling software, the authors being part of the GeRa development team. The nonlinearity continuation method is compared with the pseudo-transient method on several modeling cases.
\par
The article is organized as follows. In the second section the mathematical model of steady-state groundwater flow in unconfined conditions is formulated. In the third section the numerical methods used to discretize the problem and solve the arising nonlinear systems are stated, the algorithms of Newton method with line search and nonlinearity continuation method applied to the problem are presented. In the fourth section the proposed numerical technique is tested on a couple of problems featuring heterogeneous and anisotropic media properties with two types of finite volume discretization in space. Conclusions are provided in the end.

\section{Governing equations}
\label{}
Steady-state groundwater flow in variably saturated conditions is described by steady-state Richards equation

\begin{equation}\label{eq:RichStat}
-\nabla \cdot (K_r(h)\mathbb{K}\nabla h) = Q,
\end{equation}

which is derived from Richards equation \cite{richards1931capillary} for transient flow, which can be formulated with additional storage term \cite{bear2010modeling} as:

\begin{equation}\label{eq:Richards}
\frac{\partial \theta(h)}{\partial t} + s_{stor}S(h)\frac{\partial h}{\partial t} -\nabla \cdot (K_r(h)\mathbb{K}\nabla h) = Q.
\end{equation}
Here the following variables are used:
\begin{itemize}
\item $h$ -- hydraulic head, related to capillary pressure head $\Psi$ as $h = \Psi + z$;
\item $\theta(h)$ -- volumetric water content in medium;
\item $S(h)$ -- water saturation in medium;
\item $s_{stor}$ -- specific storage coefficient;
\item $\mathbb{K}$ -- hydraulic conductivity tensor, a 3$\times$3 s.p.d. matrix;
\item $K_r(h)$ -- relative permeability for water in medium;
\item $Q$ -- specific sink and source terms.
\end{itemize}

In this paper the main goal is to solve steady-state equation \eqref{eq:RichStat}, although transient equation \eqref{eq:Richards} is considered within a pseudo-transient method.
\par

Expressions relating relative permeability $K_r(h)$, water content $\theta(h)$ and hydraulic head $h$ are required in addition to equations  \eqref{eq:RichStat} and \eqref{eq:Richards}. In this paper  piecewise linear dependencies proposed in \cite{anuprienko2018modeling} are considered. These functions are designed for numerical solution with the finite volume method and depend on spatial discretization, possibly varying from cell to cell.
Namely, the dependence of water content $\theta_E$ in a cell $E$ on hydraulic head $h_E$ in that cell is defined as follows
\begin{equation}\label{eq:MC}
\theta_E(h_E) =
\begin{cases}
\phi, h_E > h_{E,\max},\\
\phi \cdot \frac{h_E - h_{E,\min}}{h_{E,\max} - h_{E,\min}}, h_{E,r} < h_E \le h_{E,\max},\\
\phi \cdot (\alpha_{\phi} - \alpha_{\theta}(h_{E,r} - h_E)), h_E \le h_{E,r},
\end{cases}
\end{equation}
where $\phi$ is the medium porosity, $h_{E,\max}$ and $h_{E,\min}$ are the maximal and minimal vertical node coordinates of the cell $E$
and $h_{E,r}$ is such that water content calculated by the second linear part in \eqref{eq:MC} is equal to $\phi \cdot \alpha_{\phi}$, namely,
\begin{equation}
h_{E,r} = h_{E,\min} + \alpha_{\phi}(h_{E,\max} - h_{E,\min}).
\end{equation}
Therefore the model needs two parameters: $\alpha_{\phi}$ and $\alpha_{\theta}$ which should be small enough.
\par
Relative permeability for a cell $E$ is assumed to be equal to the saturation:
\begin{equation}\label{eq:Kr}
K_{r,E}(h_E) = S(h_E) = \frac{\theta_E(h_E)}{\phi}.
\end{equation}
\par
Compared to commonly used functions proposed by van Genuchten \cite{van1980closed} and Mualem \cite{mualem1976new} that are constructed for pressure head rather than hydraulic head, piecewise linear functions require smaller number of media parameters (which are often hard to obtain for real-life problems) and tend to more sharp water table boundary at the cost of ability to predict capillary effects.

\section{Approaches to solution of nonlinear problems}\label{label}
The considered nonlinear system arises from finite volume discretization of Richards equation on unstructured meshes. Two types of unstructured meshes are used: the first consists mainly of triangular prisms with occurence of tetrahedra or pyramids in cases like geological layer pinch-outs; the second includes octree-based hexahedral grids with cut cells on domain boundary \cite{plenkin2015adaptive}. Finite volume schemes used employ different flux approximations across cell faces:
\begin{itemize}
\item conventional linear two-point flux approximation (TPFA);
\item linear multipoint flux approximation (MPFA), O-scheme \cite{aavatsmark1998discretization}.
\end{itemize}

\subsection{Solution of nonlinear systems}
Due to nonlinearity in equation \eqref{eq:RichStat}, its discretization results in a system of nonlinear equations with respect to the grid unknowns of the form

\begin{equation}\label{eq:NonlinSys}
F(h) = 0,
\end{equation}

which is to be solved numerically. For this purpose iterative solvers such as Newton, Picard or their combination \cite{farthing2003efficient}\cite{paniconi1994comparison} can be used. In this work the Newton method is used, so that at $(k+1)$-th iteration a linear system

\begin{equation}\label{eq:JacSys}
\textbf{J}(h^k)\Delta h = -F(h^k),
\end{equation}

is created and solved, where $\textbf{J} = [\partial F_i / \partial h_j]_{ij}$ is the Jacobian matrix and $\Delta h$ is the update vector; then the update procedure is performed:

\begin{equation}
h^{k+1} = h^k + \Delta h.
\end{equation}

After the update, a correction procedure described in \cite{anuprienko2018modeling} is performed that takes into account use of expressions \eqref{eq:MC} and \eqref{eq:Kr} and ensures mass-conservative changes in hydraulic head; it was also noted to improve convergence of nonlinear solvers for transient problems.
\par
 The iterations continue until for the residual $r_k = F(h_k)$ its Euclidean norm is sufficiently reduced compared to the initial residual norm or maximal absolute value of its elements becomes small enough, that is, until one of the following conditions is satisfied:

\begin{equation}
||r_k||_2 < \varepsilon_{rel}\cdot ||r_0||_2,
\end{equation}
\begin{equation}
||r_k||_{\infty} < \varepsilon_{abs}.
\end{equation}

Sometimes it is useful to perform relaxation procedure \cite{paniconi1994comparison}, in which obtained solution is replaced by a convex linear combination of it with the solution from the previous iteration. A \textit{relaxation parameter} $\Omega: 0 < \Omega \le 1$ is chosen and the update procedure is changed to this:

\begin{equation}
h^* = h^k + \Delta h,
\end{equation}
\begin{equation}\label{eq:RelaxUpdate}
h^{k+1} = \Omega h^* + (1-\Omega) h^k = h^k + \Omega \Delta h.
\end{equation}

It can be seen from \eqref{eq:RelaxUpdate} that relaxation is equivalent to rescaling the update vector $\Delta h$ in the update procedure.
\par
Relaxation can prevent the Newton method from oscillating between several values \cite{paniconi1994comparison}, but it demolishes its quadratic convergence. Therefore, it is reasonable to use relaxation during first iterations and at the end converge to the solution quadratically. However, it is not clear how to choose that number of iterations and the relaxation parameter, and we turn to automatic approach of choosing relaxation parameter, a simple version of line search (more sophisticated versions of which can be found in \cite{farthing2003efficient}) that is described in algorithm \ref{alg:NewtonAutoRelax}.

\begin{algorithm}[H]\label{alg:NewtonAutoRelax}
\SetAlgoLined
    Set initial hydraulic head values $h_0$\;
    $k = 0$\;
    \While{$k < \text{maxiter}$}{
        \If{$k = 0$}{
            Compute $r_0$, $||r_0||_2$, $||r_0||_{\infty}$\;
        }

        Create and solve $\textbf{J}(h^k)\Delta h = -F(h^k)$\;
        \eIf{$k \ge 5$}{
            $\Omega = 1$\;
            \While{$\Omega > \Omega_{min}$}{
                Compute $r = F(h^k + \Omega \Delta h)$\;
                \eIf{$||r||_2 < ||r_k||_2$}{
                    $h^{k+1} = h^k + \Omega \Delta h$\;

                    break\;
                }{
                   $\Omega = \gamma \cdot \Omega$\;
                }
            }
            \If{didn't find $\Omega$}{
                failed\;
                stop\;
            }
        }{
            $h^{k+1} = h^k + \Delta h$\;
        }
        Perform correction of $h^{k+1}$ (see \cite{anuprienko2018modeling})\;
        $r_{k+1} = F(h^{k+1})$\;

        \If{$||r_{k+1}||_2 < \varepsilon_{rel} \cdot ||r_0||_2$ or $||r_{k+1}||_{\infty} < \varepsilon_{abs}$}{
            converged\;
            stop\;
        }
    $k = k + 1$\;
    }
 \caption{Newton method with line search}
\end{algorithm}
In this algorithm $\gamma$ is the decreasing factor, which is chosen to be $\gamma = 0.25$. $\Omega_{min}$ is chosen such that 7 iterations of $\Omega$ refinement can be done. Note that line search is not applied for the first 5 iterations. This approach is based on following observations: first, that finding suitable $\Omega$ at the first iterations is often not possible; second, that Newton method without line search can exhibit residual growth at several first iterations and then still converge quadratically.
\par
     The main problem of the Newton method is the need for an initial estimate sufficiently close to the solution. In some rather simple cases, the method can converge even with arbitrary constant hydraulic head distribution given as the initial estimate. However, for more difficult problems including heterogeneous domains with complex geometry and contrasting and anisotropic media, the task of choosing a good initial estimate is not trivial.

Since the Newton method for discretized equation \eqref{eq:RichStat} generally doesn't converge even with line search, another strategies are desired. Here two of them are described: the pseudo-transient method \cite{farthing2003efficient}\cite{anuprienko2018modeling}, and a continuation method based on varying nonlinearity of the equation \eqref{eq:RichStat}. Application of the pseudo-transient method to the steady-state Richards equation and its comparison with other solvers can be also found in \cite{farthing2003efficient}.

\subsection{Pseudo-transient method}
This method is based on solution of transient equation \eqref{eq:Richards} until the solution reaches steady state. More details on numerical solution of transient problem in GeRa can be found in \cite{anuprienko2018modeling}, including comparison of Picard and Newton methods and brief mention of the pseudo-transient method.
\par
Discretization in time is done using fully implicit scheme, which at each time step results in a system of nonlinear equations, that is again solved with the Newton method. Initial guess is the solution from the previous time step, which means better convergence, since with sufficiently small time step size that initial guess becomes good enough. Therefore, in transient case convergence of the Newton method usually can be achieved without sophisticated techniques such as line search. Similar results were reported by other researchers \cite{farthing2003efficient}.
\par
After solution of the nonlinear system at a time step the residual of the system \eqref{eq:NonlinSys} is evaluated and convergence check for the steady-state problem is performed. Then the time step size $\Delta t$, which may vary in user-specified limits, is increased to $\Delta t = 1.5\Delta t$ if the number of nonlinear iterations at the time step did not exceed user-specified number $numit_{inc}$, and in case of failure of the Newton method the time step is decreased to $\Delta t = 0.5\Delta t$.
\par
      The pseudo-transient method has the following drawbacks:
\begin{itemize}
\item the time which the system takes to achieve steady-state can be very large and is not known, although it can be estimated by calculation on a coarse grid;
\item severe time step restrictions can be experienced in case of highly heterogenous and relatively dry soils;
\item the method can be sensitive to initial hydraulic head distrubution.
\end{itemize}

\subsection{Nonlinearity continuation method}
	The method proposed in this paper is based on continuation methodology. Continuation methods, when applied for nonlinear systems obtained by discretization partial differential equation in form \eqref{eq:NonlinSys}, solve the systems by incrementally approaching the solution through series of intermediate problems. Methods of this type have been successfully applied for numerical solution of partial differential equations in computational fluid dynamics \cite{continCFD} and nonlinear solid mechanics \cite{continMechNewt}\cite{continMechAdap}.
\par
      As described above, the main problem when trying to solve discretized equation \eqref{eq:RichStat} with the Newton method is to provide a good initial guess. The idea of our nonlinearity continuation method is to find such initial guess as a solution of some "simpler" problem or a sequence of such problems.
\par
A \textit{continuation parameter} $q$ is introduced which controls "degree of nonlinearity" of the problem. Namely, an equation is introduced:
\begin{equation}\label{eq:ContinEq}
-\nabla \cdot (\mathcal{K}(h, q)\mathbb{K}\nabla h) = Q,
\end{equation}

where $\mathcal{K}(h, q)$ is some function such that
\begin{equation}\label{eq:ContinFuncProp}
\mathcal{K}(h, 1) \equiv K_r(h), ~~~~ \mathcal{K}(h, 0) \equiv 1.
\end{equation}
\par
There are several possibilities to choose such function $\mathcal{K}(h, q)$ of which two are tested:

\begin{equation}\label{eq:ContinPow}
\mathcal{K}_{pow}(h, q) = (K_r(h))^q
\end{equation}
and
\begin{equation}\label{eq:ContinLin}
\mathcal{K}_{lin}(h, q) = 1 + q \cdot (K_r(h) - 1).
\end{equation}

\par
     Combining properties \eqref{eq:ContinFuncProp} with equation \eqref{eq:ContinEq} one can check that with $q = 1$ equation \eqref{eq:ContinEq} is the original equation \eqref{eq:RichStat} and with $q = 0$ it becomes a simple linear equation, to solve which only a linear system has to be solved. Now, with the solution of the linear problem obtained, an attempt may be made to solve "more nonlinear" problem with $q > 0$ with the Newton method and solution of the linear problem taken as initial guess. The algorithm of incremental increasing of the continuation parameter $q$ to $1$ is described in algorithm \ref{alg:Contin}.

\begin{algorithm}[H]\label{alg:Contin}
\SetAlgoLined
    $q = 0$\;
    Solve linear problem $-\nabla \cdot (\mathbb{K}\nabla h) = Q$\;
    $\Delta q_{last} = 1$\;

    \While{$q < 1$}{
    	$\Delta q = \min(1-q~,2\cdot\Delta q_{last})$\;
    	\While{$\Delta q > 10^{-4}$}{

            Try to solve $-\nabla \cdot (\mathcal{K}(h, q+\Delta q)\mathbb{K}\nabla h) = Q$ with Newton\;
            \eIf{solved}{
                save $h$\;
                $\Delta q_{last} = \Delta q$\;
                break\;
            }{
                $\Delta q  = \Delta q /2$\;
            }
        }
        \If{didn't find $\Delta q$}{
            failed\;
            stop\;
        }
    }
 \caption{Nonlinearity continuation method}
\end{algorithm}

\subsection{Implementation details}
GeRa is written in C++ with its MPI-parallel computational part based on INMOST \cite{danilov2016parallel}, a parallel computation platform that provides tools for working with meshes consisting of arbitrary polyhedral cells, mesh partitioners and linear solvers as well as some other useful features. Automatic differentiation capabilities of INMOST are used to construct the Jacobian matrix. For solution of system \eqref{eq:JacSys} we use algorithms based on Bi-CGSTAB \cite{van1992bi}:
\begin{itemize}
	\item ILU(3)-preconditioned solver from PETSc package \cite{balay2019petsc};
	\item Inner\_MPTILUC, an internal INMOST solver based on second order Crout-ILU with inverse-based condition estimation and maximum product transversal reordering as preconditioner.
\end{itemize}
\par Of these solvers the latter is more robust and is used when PETSc solver fails to converge, such behavior was noted for some complex problems, especially when using MPFA scheme.

\section{Numerical experiments}
This section includes a number of tests comparing approaches described above on model and real-life problems.

\subsection{Problems setup}
Numerical experiments were performed for 3 different problems, of which the first is a two-dimensional model problem describing groundwater flow through a dam and the remaining two problems are real-life problems describing groundwater flow in sites that will be further denoted as site A and site B.
\par
The first test, a model problem taken from \cite{polubarinova2015theory}, describes two-dimensional groundwater flow through a dam. The dam is a 10 m $\times$ 10 m square composed of homogeneous material with isotropic hydraulic conductivity $K = 0.864$ m/day. The left boundary has prescribed hydraulic head value $h = 10$ m, while the right boundary has prescribed hydraulic head value $h = 2$ m up to the point where $z = 2$ m, above that point a seepage boundary condition is imposed. Top and bottom boundaries have zero-flux boundary conditions. Some aspects of numerical solution of the dam problem are described in \cite{anuprienko2018modeling}. The problem was considered as a quasi-two-dimensional: a third dimension was added, along which only one layer of cell was present, and zero-flux boundary conditions were imposed on boundaries orthogonal to the added dimension axis.
\par
Real-life site A is a domain of approximately 64 km$^2$ with 3 geological layers, 7 different media and presence of lakes and rivers. All media have diagonal anisotropic hydraulic conductivity tensor of the form $\mathbb{K} = \text{diag}\{K, K, 0.1K\}$ with K varying from 0.011 to 4.76 m/day. This problem was also mentioned in \cite{anuprienko2018modeling}.
\par
Real-life site B is a domain of approximately 100 km$^2$ with 4 geological layers, 4 different media and presence of lakes and rivers. All media have diagonal anisotropic hydraulic conductivity tensor of the form $\mathbb{K} = \text{diag}\{K, K, 0.1K\}$ with K varying from 0.14 to 16 m/day.
\subsection{Comparison of pseudo-transient and nonlinearity continuation methods on the dam problem}
Computations were carried out on two cubic grids with 1600 cells (cell size 0.25 m) and 10000 cells (cell size 0.1 m). Discretization scheme was TPFA with upwind approximation of $K_r$. The following parameters were used: $\varepsilon_{rel} = 10^{-5}$, $\varepsilon_{abs} = 10^{-5}$, $maxit = 25$ and (in pseudo-transient method) $numit_{inc} = 15$.
\par
Computation time, number of steps (time steps for pseudo-transient method and continuation steps for continuation method) and total number of Newton iterations are presented in tables \ref{tab:dam1600} and \ref{tab:dam10000}; saturation profiles are presented in figure \ref{pic:damTPFA}. Experiments showed that on both meshes continuation method took only 1 step to converge and much smaller number of Newton iterations compared to pseudo-transient method, leading to significantly faster calculations.

\begin{table}
	\begin{center}
		\begin{tabular}{ c| c| c| c }
			& $T_{comp}$, s & \# of steps & \# of Newton iterations \\\hline
			Pseudo-transient & 2.65          &  8          &  49   \\
			Continuation     & 0.85          &  1          &   8
		\end{tabular}
		\caption{Comparison of pseudo-transient and continuation methods for the dam test, mesh with 1600 cells, TPFA}
		\label{tab:dam1600}
	\end{center}
\end{table}

\begin{table}
	\begin{center}
		\begin{tabular}{ c| c| c| c }
			& $T_{comp}$, s & \# of steps & \# of Newton iterations \\\hline
			Pseudo-transient & 18.9          &  8          &  63   \\
			Continuation     &  6.2          &  1          &  13
		\end{tabular}
		\caption{Comparison of pseudo-transient and continuation methods for the dam test, mesh with 10000 cells, TPFA}
		\label{tab:dam10000}
	\end{center}
\end{table}

\begin{figure}
	\centering
	\includegraphics[width=0.4\textwidth]{pic/dam1600.png}
	\includegraphics[width=0.4\textwidth]{pic/dam10000.png}
	\caption{Saturation profiles for the dam test on cubic grids}\label{pic:damTPFA}
\end{figure}

\subsection{Comparison of pseudo-transient and nonlinearity continuation methods on the site A}
Computations were carried out on triangular prismatic mesh of 171450 cells. The following parameters were used: $\varepsilon_{rel} = 10^{-5}$, $\varepsilon_{abs} = 10^{-6}$, $maxit = 25$ and (in pseudo-transient method) $numit_{inc} = 15$.
\par
To compare pseudo-transient and continuation methods the problem was solved using TPFA scheme; additional calculation was performed with continuation method and MPFA scheme to show that with continuation method it is possible to solve problem with more accurate and complex MPFA scheme still faster than with pseudo-transient method and simple TPFA. All calculations employed central approximation of $K_r$.
\par
Computation time, number of steps (time steps for pseudo-transient method and continuation steps for continuation method) and total number of Newton iterations are presented in table \ref{tab:obj1_171k}.

\begin{table}
	\begin{center}
		\begin{tabular}{ c| c| c| c }
		                         	& $T_{comp}$, s& \# of successful (failed) steps & \# of Newton iterations \\\hline
			Pseudo-transient, TPFA & 868.4         &  65(10)     & 377   \\
			Continuation, TPFA     & 124.4         &   1(0)      &  10   \\
			Continuation, MPFA     & 444.3         &   1(0)      &  13
		\end{tabular}
		\caption{Comparison of pseudo-transient and continuation methods for site A, mesh with 171450 cells}
		\label{tab:obj1_171k}
	\end{center}
\end{table}

\subsection{Effect of line search and comparison of linear and power functions in continuation method}
Line search in Newton method is a useful tool which often allows to increase continuation parameter $q$ from 0 to 1 in a single step, as can be seen in tables \ref{tab:dam1600}, \ref{tab:dam10000} and \ref{tab:obj1_171k}. In these cases, there is no difference between using power \eqref{eq:ContinPow} and linear \eqref{eq:ContinLin} functions as continuation functions. To show the difference, either line search should be omitted or more complex problems should be regarded.
\par
Computations for site A on the same mesh were performed with no line search in the Newton method and maximal iterations number decreased to $maxit = 15$. Computation time, number of steps and total number of Newton iterations are presented in table \ref{tab:obj1_linpow}. Effect of line search on Newton performance in contiuation method is shown in figure \ref{pic:ls_effect}; a single iteration needed application of line search, but that drastically changed overall convergence. When using TPFA, there is little difference between computational effort with linear and power functions; however, when using MPFA, linear function leads to one more failed continuation step and subsequently slows down the computation.
\par
To further investigate difference between linear and power functions, another tests were performed on a fine mesh with 12 million cells and MPFA discretization. The computations were carried out using 140 cores of the INM RAS cluster \cite{cluster}. The results are shown in table \ref{tab:obj1_cluster}, the hydraulic head and saturation distributions are presented in the figure \ref{pic:12m_head_sat}. Example of convergence behavior of the Newton method with line search  is shown in figure \ref{pic:conv}. In case of such fine mesh resolution nonlinearity continuation required more than one step even with line search in the Newton method. Unlike in the case of coarse grid, the power function in the continuation method lead to smaller number of steps in the continuation method and smaller total number of Newton iterations, but solution time was comparable to that of the linear function.

\begin{table}
	\begin{center}
		\begin{tabular}{ c| c| c| c }
			& $T_{comp}$, s & \# of successful (failed) steps & \# of Newton iterations \\\hline
			Power, TPFA    & 325.8         &   2(1)      &  32   \\
			Power, MPFA    & 1069.3        &   2(1)      &  32   \\
			Linear, TPFA   & 347.5         &   2(1)      &  34   \\
			Linear, MPFA   & 1445.1        &   3(2)      &  51
		\end{tabular}
		\caption{Comparison of power and linear continuation functions, site A, mesh with 171450 cells, Newton method without line search}
		\label{tab:obj1_linpow}
	\end{center}
\end{table}

\begin{figure}
	\centering
	\includegraphics[width=0.6\textwidth]{pic/ls_effect.png}
	\caption{Effect of line search for site A. A single iteration with line search ($\Omega = 0.25$ at iteration 7) allows Newton method then to converge quadratically, otherwise Newton doesn't converge}\label{pic:ls_effect}
\end{figure}

\begin{table}
	\begin{center}
		\begin{tabular}{ c| c| c| c }
			& $T_{comp}$, s & \# of successful (failed) steps & \# of Newton iterations \\\hline

			Linear  &  8776         &  3(2)       &  55   \\
			Power   &  8374         &  2(1)       &  30
		\end{tabular}
		\caption{Results of parallel computations for site A, mesh with 12 million cells, MPFA}
		\label{tab:obj1_cluster}
	\end{center}
\end{table}

\begin{figure}
	\centering
	\includegraphics[width=0.8\textwidth]{pic/cluster_12m_head.png}
	\includegraphics[width=0.8\textwidth]{pic/cluster_12m_sat.png}
	\caption{Hydraulic head and saturation, site A, mesh with 12 million cells, MPFA}\label{pic:12m_head_sat}
\end{figure}
\begin{figure}
	\centering
	\includegraphics[width=0.45\textwidth]{pic/12m_lin.png}
	\includegraphics[width=0.45\textwidth]{pic/12m_pow.png}
	\caption{Example of convergence behavior of the Newton method with line search. On the left is linear continuation function, increasing $q$ from 0.75 to 1, on the right is power continuation function, increasing $q$ from 0.5 to 1. Site A, mesh with 12 million cells, MPFA}\label{pic:conv}
\end{figure}
\par
Site B turned out to be harder problem in the sense that even with line search in Newton method continuation method takes several steps even on relatively coarse grids. The following parameters: $\varepsilon_{rel} = 10^{-6}$, $\varepsilon_{abs} = 10^{-6}$, $maxit = 25$, central approximation of $K_r$ and a trinagular prismatic mesh of 56820 cells were used. Computation time, number of steps and total number of Newton iterations are presented in table \ref{tab:obj2_linpow}. When using TPFA, there is again little difference in computational time with linear and power functions, although power functions takes twice more steps; when using MPFA, linear function performs better leading to less continuation steps and Newton iterations.

\begin{table}
	\begin{center}
		\begin{tabular}{ c| c| c| c }
			               & $T_{comp}$, s & \# of successful (failed) steps & \# of Newton iterations \\\hline
			Power, TPFA    &  171.1        & 10(9)       & 133   \\
			Power, MPFA    &  732.3        &  7(8)       & 117   \\
			Linear, TPFA   &  163.9        &  5(4)       & 104   \\
			Linear, MPFA   &  393.6        &  5(4)       &  61
		\end{tabular}
		\caption{Comparison of power and linear continuation functions, site B, mesh with 56820 cells, Newton method with line search}
		\label{tab:obj2_linpow}
	\end{center}
\end{table}

\begin{figure}
	\centering
	\includegraphics[width=0.8\textwidth]{pic/obj2_mpfa_58k_head.png}
	\includegraphics[width=0.8\textwidth]{pic/obj2_mpfa_58k_sat.png}
	\caption{Hydraulic head and saturation distributions for site B, mesh with 56820 cells, MPFA}\label{pic:obj2_58k}
\end{figure}

\section{Conclusion}
A nonlinearity continuation method for solution of nonlinear systems arising from discretization of steady-state Richards equation for modeling  groundwater flow in variably saturated conditions is proposed. Through solution of a series of problems with increasing nonlinearity the method gets a suitable initial estimate required by the Newton method. The continuation procedure is implemented in the GeRa software package.
\par Combined with line search for improved convergence of Newton method, the continuation method allows for solution of complex problems with MPFA discretization scheme consuming less time than previously used pseudo-transient method does with simpler TPFA discretization scheme.
\par Two continuation functions, linear and power, were compared on two real-life problems; however, the tests didn't show that any of the two is superior than the other, with their performance in the continuation method depending on the problem, discretization scheme and mesh size.

\section*{Acknowledgements}
This work was partially (namely development and testing of line search technique in Newton method) supported by Russian Science Foundation through the grant 18-71-10111 and partially (namely preparation and execution of parallel computations) supported by the Russian Academy of Sciences Research program No. 26 "Basics of algorithms and software for high performance computing".

\bibliographystyle{elsarticle-num}

redpajama_set_name: RedPajamaArXiv


text:
HomeTechToshiba moves in on record-breaking $6.3bn shares buyback
Toshiba moves in on record-breaking $6.3bn shares buyback
1 year ago No comment
Toshiba has revealed it will be buying back $6.3bn (£4.71bn) in stock that has seen its share price rise as much as 11 per cent.
The decision was made as part of a pledge made by Toshiba to share the proceeds of an $18bn sale of its memory chip business to US private equity firm Bain Capital, which closed earlier this month.
The news has created a wave of relief for some, who were awaiting the decision as a sign of positive news for the company after it began selling off its chip unit and other assets.
Read more: Toshiba completes £13bn sale of chip arm to Bain-backed consortium
Toshiba is also making history, as its decision to repurchase is reportedly the largest ever buyback planned on the Japanese market. Toshiba reached an intra-day high of ¥351 earlier today, before slightly falling to an overall increase of 6.7 per cent by market close.
Investors had planned to raise the issue of Toshiba keeping too much cash from its recent sales at the companys annual shareholder meeting later this month.
The firm itself has only recently come out of a period of financial turmoil, narrowly avoiding a de-listing following an accounting scandal and massive cost overruns at its US nuclear business Westinghouse.
Toshiba raised ¥600bn in fresh capital last December to bolster its balance sheet. According to data from MarketWatch, foreign investors who took part in the capital raising are currently sitting on a 28 per cent gain after yesterdays announcement.
Toshiba also recently sold a majority stake in its personal computer business to Japanese electronics maker Sharp, in a deal which briefly caused Sharps share price to rise before falling to a 17-month low.
CityAM
Center-right grouping proposes tough security offer for EU election
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Deliveroo today confirmed Amazon is leading a $575m (£450m) funding round in the food delivery busin..
On GDPR anniversary, French privacy watchdog says penalties are looming
PARIS — Europes privacy rules are about to get very real. According to the head of Frances data pro..


text:
Solar Energy Corporation of India
Madhya Pradesh Inks Contract For World's Largest Floating Solar Power ProjectAmit MishraAug 4, 2022 03:52 PM +05:30 IST
Solar Energy Corporation Of India Initiates Project To Set Up 2000 MWh Standalone Energy Storage SystemSwarajya StaffJul 25, 2021 02:12 PM +05:30 IST
Shining Bright: Solar Tariffs In India Plunge To Record Low Of Rs 2.00 Per Unit In Latest SECI AuctionSwarajya StaffNov 24, 2020 09:21 AM +05:30 IST
With Renewable Energy Sector Growing At Hectic Pace, MNRE Issues Guidelines For Setting Up Dispute Resolution MechanismIANSSep 25, 2019 03:34 PM +05:30 IST
Government Plan For Rs 45,000 Crore, 7,500 MW Solar Energy Plant In Ladakh Runs Into Environmental ConcernsSwarajya StaffAug 16, 2019 06:03 PM +05:30 IST
Ministry Of New And Renewable Energy Pushes States To Identify Land Parcels For Solar And Wind Power ProjectsSwarajya StaffMay 13, 2019 01:09 PM +05:30 IST
Solar Power Bonanza For J&K: Tender Issued For Setting Up 7.5 Gigawatt Solar Capacity In LadakhSwarajya StaffJan 2, 2019 01:44 PM +05:30 IST
India To Float Its Largest Solar Tender by 15 December For 23,000 MW Ultra Mega Solar Projects In Leh, LadakhSwarajya StaffDec 2, 2018 10:13 AM +05:30 IST
Shapoorji Pallonji Wins Bid For India's First Large-Scale Floating Solar Plant At Rihand Dam Along UP-MP BorderSwarajya StaffNov 29, 2018 07:03 PM +05:30 IST
Good For Nature Bad For Pocket: Wind Energy To Potentially Become Expensive Due To Transmission Costs Swarajya StaffSep 26, 2018 05:13 PM +05:30 IST


text:
Tom Brady Reveals He 'Imagined Not Playing' But Cannot Deal With It
Tom Brady has changed the very dynamics of the sport by competing against younger and quicker athletes being in his mid-40s. Despite that, delivering better numbers than them. Even in his current season, he has taken Tampa Bay Buccaneers to be on the top seeded teams in the NFC yet again.
Article continues below this ad
He has set up an unachievable high bar for younger generation of athletes who strive to achieve the success the GOAT has throughout his career as a professional football player. Although it seems that his legacy will go untouched for generations to come. And that his career will be remembered as the time when NFL peaked.
Oct 10, 2021; Tampa, Florida, USA; Tampa Bay Buccaneers quarterback Tom Brady (12) celebrated with wide receiver Mike Evans (13) after a touchdown in the second half against the Miami Dolphins at Raymond James Stadium. Mandatory Credit: Jonathan Dyer-USA TODAY Sports
However, it is hard to believe that the quarterback is still in his mid-40s since he can be seen sometimes delivering inhuman stats, owning teams one after another. Brady looks to be far from his retirement stage right now. In fact, he seems to be in his prime. Ever since turning 40 he has won two Super Bowls, and he seems to be Enroute to win his third pretty soon.
'There's a Lot on the Line': Tom Brady Opens up on Feeling Immense Pressure Ahead of the Playoffs
Tom Brady has no intentions to retire anytime soon
Tom Brady's secret to his longevity has mostly been his dedication, discipline and commitment to the sport. However, what has helped him on the way is his TB12 program, which is now gaining a lot of attraction in the sporting community. A lot of younger athletes have started adapting those methods.
And since Tom Brady happens to be in such an incredible shape, he rejects to retire from the sport. Not until when he finds physically incapable of doing what others can do too. When asked about why he has not decided to retire yet, the Tampa Bay Buccaneers quarterback came up with a perfect answer.
ying," Brady said. "And I imagine watching football on Sundays going 'These guys suck. I could do way better than them.' And then still knowing in my heart that I actually could still do it."
One of his biggest fears has been to retire even when he had a lot of football left in him. Which would make him regret and wish if he could have stayed a little longer.
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Students celebrate black history month
The NUSU African Canadian Cultural Club (A.C.C.C) hosted an evening of celebration to wrap up Black History Month in the Nipissing University Theatre Friday night.
Mar 1, 2008 2:10 PM By: Kate Adams
The theme of the first annual event was 'The Power of Knowledge: educating our generation,' and featured a glimpse of African history, and people of African ancestry who have made great contributions to the world, as well as showcasing cultural dance, poetry and dramatic performances.
"It's a cultural exhibition that hasn't been done in North Bay," states Kwanwo Adusei, NUSU ACCC President.
"But they celebrate Black History Month in the GTA so I just wanted to do it here."
Adusei also says the club was launched at the start of the 2007-2008 academic year with the objective to educate students and the North Bay community on social, economic, political and cultural matters that affect African Canadians.
With a noticeable increase in international students, the club wants to heighten awareness around the growing diversity in the city of North Bay as well as Education Centre.
"I have been here now for 3 years and there has been a marked increase of non-Caucasians," he says.
"So we just want to show the city's growing diversity."
The evening wrapped up with a cultural fashion show.
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text:
The Stretch Headphones Avoid Cable-Tangling Nightmares
We've recommended plenty of tactics for avoid tangled headphones, ranging from careful wrapping techniques to using binder clips. However, if you're like me, you don't always remember to do that properly, and you just want a set of headphones that don't go nuts when you shove them in a travel bag in a hurry. On the front, the O'Neill Stretch headphones from Philips do a fine job.
The Stretch is one of a series of headphones carrying the O'Neill branding. O'Neill specialise in surf gear, so the big selling point for the range is durability (it's made from TR55LX, an "ultra-durable and temperature-resistant material"). However, the big attraction for me is the "tangle-free" cord, which is wrapped in cloth like a shoelace. That means it doesn't tend to tangle up even when you just throw it in a bag — in a week of travelling around with the Stretch, I only encountered one knot, and that took only seconds to undo, rather than the traditional macrame-like approach often seen with conventional headphones.
At $149.95$129.95, the Stretch isn't cheap, and it's a lot bulkier than a set of earbuds (so it probably wouldn't qualify for No Luggage Week). However, it does sound great, stays tangle-free and promises to be long-wearing.
Update: Following publication, we got word from Philips that the price of the stretch has been dropped to $129.95. Still not cheap, but $20 isn't to be sneezed at!
spiderlama Guest
At $149.95, the Stretch is a bit of a Stretch... :)
Munaum Guest
Got them for $60 at Best Buy.
Lav Guest
If shoelace type cords are supposed to be tangle-free, there's far cheaper earbud options on dealextreme with such cords.
pdf Guest
For cans like these, a cloth cord is not a problem, but for IEMs, you'll get massive microphonic noise from the cable.
is there... like... a link where we can see more about these headphones? or....?
mucous @Michele
Aug 30, 2011, 1:01pm
A much cheaper solution is to use the retractable earphones/earbuds, you can pick them up under $5 e.g. http://www.dealextreme.com/p/retractable-3-5mm-stereo-earphone-70cm-23860
Just make sure you hold the wire to pull them out and pull both at the same time.
trentmodo @Trent
Tangle resistant more like it. More often than not, its keys and other cords in my bag my headphones tangled with.
Would love someone to bring out a retractable cord that goes into ear-piece?
Karan Guest
Sony used to make a set of over-ear headphones like that, but unfortunately that seems to have gone out of fashion or something. Mine fell apart last year =(


text:
Cy-Borges
Memories of the Posthuman in the Work of Jorge Luis Borges
Edited by Ivan Callus and Stefan Herbrechter
Cy-Borges—this compound word seems almost destined. It allows the associations of cyber—and cyborg to converge around the name of Jorge Luis Borges, many of whose writings are strangely prescient thought-experiments in the impossible and the unconfigurable. For though Borges speaks scantily of technology and hardly at all of the cyber-cultural futures that make it possible, his speculative fictions and other prose writings contrive glimpses of posthuman conditions that are more typically associated with writers like William Gibson and Philip K. Dick or films like Blade Runner and The Matrix. Yet the posthuman, as that which reconfigures the actual and the possible once technology re-engineers human potential and institutes a new physics, is everywhere in Borges. As this collection shows through a series of close readings of his work, Borges is therefore the precursor whom posthumanism would have had to invent had he not existed.
University Press Copublishing Division / Bucknell University Press
Pages: 224 • Trim: 6¾ x 9¾
978-1-61148-310-9 • Hardback • January 2009 • $91.00 • (£60.00)
Subjects: Literary Criticism / Reference, Biography & Autobiography / Literary Figures, Literary Criticism / Books & Reading, Literary Criticism / Science Fiction & Fantasy
Stefan Herbrechter is professor of English and cultural studies at the University of Heidelberg and research fellow at Leeds Trinity and All Saints College (UK). Ivan Callus is senior lecturer and head of the Department of English at the University of Malta.


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SELF HELP EXERCISES
Use Music to Find Solutions to Problems
by Adam Zwig, PhD | November 15, 2019
Here's a fun exercise to connect with your process and discover solutions to your problems.
Think of a problem you want to work on. Take a minute and review your experience of it. Then put it aside and do the following:
Step One: Close your eyes and listen for music. What's the first song that pops into your head? Don't think about it; just let it present itself. It doesn't matter if you like it or hate it. Just let it happen. Listen to it in your mind's ear. You may want to sing a few bars. Feel it, sense it, and describe the state of mind and body it puts you into. Is it fun? Exciting? Peaceful? Melancholy? Sentimental? Sad? Angry? Powerful? Annoying? Feel into it as much as you're able to, and reflect on it for a minute. Do this before going on to Step Two.
Step Two: Close your eyes again, and listen for a second song that song pops into your mind. Do it like last time—just let it happen. Don't think about it. And again, listen, feel, sense, and notice your experience of the song. Sing it if you want. Really get into it, and describe the state of mind and body it puts you into.
Step Three: Stay with this second song, and amplify your experience by feeling into it further. Feel it in every part of your body. Embody it throughout your entire being. Make your mind this way too.
Step Four: In your mind make a picture of the feeling. Visualize an image that expresses the same thing as the feeling, not something different. For example, if you feel happy, an image might be a playful, smiling child or a bright sunny day. If you feel melancholy an image might be a lonely road or a cloudy sky. If you feel calm and peaceful and your image is of a bomb exploding you didn't translate the feeling.
Step Five: Stand up and move your body in a way that expresses the feeling and image. Be the feeling and image; be the song!
Step Six: Describe your experience.
Step Seven: How can you use this state of mind/body to respond to your problem? Identify with it as the solution to what's bothering you.
Understanding Your Process:
Your experience of the first song reflects a state of mind / way of being you tend to identify with. I call this your First Mind because it's the primary, most familiar way of being you lean toward; it's part of your consciousness and identity, and is therefore known to you.
Your experience of the second song is where your growth is. It's your higher self—the more evolved and aware person you're in the process of becoming. I call this your Second Mind because it's further from your consciousness and identity, and therefore comes into your awareness only secondarily. Getting to know this part of yourself will bring you healing and enlightenment. It's your ticket to personal liberation.
Ask yourself how this Second Mind way of being can help you in life. How would you deal with your problems? How would you relate to people? How would you be in the world?
Great work! You've just learned how to connect with your process and discover solutions to problems by letting two songs pop into your head, amplifying your experience of the second song, and contemplating how you can bring this more into your life.
A thirty-year-old, client, Karen, felt oppressed in her marriage. She had a sweet and gentle personality and didn't know how to deal with her verbally aggressive husband. The first song she heard was Ed Sheeran's "Give Me Love," which she experienced as a feeling of longing to be loved. It was clear to her that this was what she was identified with. The second song she heard was Katy Perry's "Roar." Karen laughed as soon as the song popped into her head because it was obviously a girl-power song about standing up for herself. We amplified her experience of "Roar" as the antidote to her fear of expressing strength in her relationship. Eventually, she was able to express her power, and it actually changed her relationship for the better.
A fifty-eight-year-old client, Pete, was having a mid-life crisis. He'd just lost his job, became depressed, and didn't know what to do. The first song he heard was Bob Dylan's "Tangled Up in Blue", which despite being a relationship breakup song, was experienced by Pete as a song about feeling lost. He said he totally identified with this feeling. The second song he heard was a classical song: Stravinsky's "Firebird." He said this song made him feel nervous. We amplified his nervousness and it unfolded into an experience of energy and a feeling to get to work to find a new job instead of sitting around moping and being depressed. Within a few months he found a new job and his depression lifted.
A twenty-three-year-old client, Jake, had a conflict: People he didn't particularly like frequently asked him to spend time together, and he'd meet up with them because he loved people in general, and liked going out and having fun. But at some point during the night he'd always think to himself, "Why am I hanging out with this person? I don't even like him!". The situation stressed him out. The first song that came to him was an ACDC song. He couldn't remember the title but said it rocked his brain. It made him feel totally inside his ecstatic, fun self where he just follows his passion to party and have fun, and doesn't think about or analyze what he feels toward someone. It was obvious to him that this represented his tendency to hang out with whoever asks him—just go with the flow.
The second song he heard was "Rap Devil" by Machine Gun Kelly. I asked him how this song made him feel and he said it was a tougher take on things—not just being in his party-time feelings and letting them take him wherever they want, but rather a sense of strength, toughness, firmness. He said it made him feel in charge of his feelings rather than them being in charge of him. I asked him how this he could use this power to solve his dilemma, and he replied that he could use it to be more selective about who he hangs out with. He tried it and discovered he has way more fun when he's with someone he genuinely likes.
©2020 Dr. Adam Zwig
Meet Dr. Adam Zwig—psychologist-musician, educator, and author. He holds a PhD in clinical psychology, has had 9 Top Ten hit singles on the U.S Adult Contemporary charts, and is an internationally renowned workshop leader and lecturer. He has been featured on Billboard, Forbes, Sirius XM Radio, Huffington Post, and many other media outlets, and has over 100 million views on YouTube. Dr Zwig has released 7 albums and his songs can regularly be heard on NBC, Fox, and Fuel TV. His forthcoming book, Music in the Mayhem: Tales of Total Transformation from a Rock n Roll Psychotherapist, shows how life problems are not pathological but rather personal growth processes trying to happen. His podcast, The Dr. Zwig Show, posts new episodes every Tuesday.
DISCLAIMER: The content contained herein is for inspirational, educational, and entertainment purposes only. Nowhere in this Blog does Dr. Zwig diagnose or treat a viewer with any kind of psychological, mental, emotional or physical disorder as might be diagnosed and treated by a personal psychologist or other professional advisor. The content is not intended to be a substitute for working with a therapist but is for the purpose of educating the viewer about new approaches to working on personal problems. Viewers should use this Blog at their own risk, with the understanding that Dr. Zwig is not liable for its impact or effect on its users. Viewing this Blog does not form a practitioner/client relationship between the viewer and Dr. Zwig. Dr. Zwig is not responsible for any action taken by a viewer based upon any information in this Blog. Never disregard professional medical advice or stop taking psychiatric medication based on something you have read on this Blog without a doctor's supervision and ongoing therapeutic support. Dr. Zwig is an educator, author, and life coach in the U.S., and a psychotherapist in Switzerland. He holds a PhD in clinical psychology. He is also a rock n roll musician.
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Stay Centered and Aware, Especially in Difficult Times
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One-Step Method to Transform a Problem
Self Help Ideas and Exercises: Part 2
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Floor-to-ceiling, full-length glass composes the lakeside façades of two prefabricated modules, so that each offers a distinct, expansive view of the lake and its islands.
Cedar facets reveal the connection point of the two modules.
Private living spaces occupy the far ends of the modules, where the end walls angle toward the tree canopy.
KISS-KISS House
Rainy Lake, Ontario
Perched above the bedrock at the shore of a remote Canadian lake, the cedar-clad Kennedy House takes formal cues from driftwood. The three-bedroom house, dock house, garage, and walled vegetable garden are linked by a series of wood walkways and decks. At the "kiss line" between two prefabricated modules, the lineal form of the house snaps like a branch held together only by bark. The open break forms a V-shaped outdoor room facing the water.
The walls frame a courtyard like a clearing in the forested area along the shore. While the garage and garden doors blend into the wood, the main entry interrupts it with an irregularly shaped sheet of glass, as though the surface has begun to tear at the kiss line. Floor-to-ceiling, full-length glass on the lakeside façades of both modules allows each to present a distinct, expansive view of the lake and its islands. Being inside the house feels like floating over the water.
The organization and details of the interior living space reinforce the sense of openness established by the glass. The kitchen counter is shifted slightly back from the glass, a thin slab of back-cut soapstone forms a dining island, and the fireplace is transparent on three sides. Polished teak surfaces continue from the walls and ceiling of the master bathroom to the counter, sink, and tub. Private living spaces occupy the far ends of the modules, where the end walls angle toward the tree canopy.


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Verdi considered Shakespeare's MacBeth to be 'one of the greatest creations of man'. The opera's unbroken dramatic line, incisive libretto and range of expression from the comic to the sublime, made it a work that was way ahead of it's time. Verdi explores unusual theatrical characters with MacBeth, the darkness of which resonated with his desire to convey Shakespeare's brutal realism in a visionary masterpiece that would only be fully appreciated by the mid-1900s. MacBeth is performed here in it's rarely heard 1865 French language version.
Label: Dynamic
MacBeth (1865 French Version)
Artist: Verdi / Abbado


I'm a Seattle-based product design manager just trying to learn something new everyday.
Detect identifies & reduces suicide risk of hospital patients.
I was contracted to design it from the ground up.
PwC's DeNovo is a FinTech monitoring platform designed to help C-suite banking execs take action.
After identifying team needs through surveys and interviews, I created Egencia's design workshop series amongst many other org design tests.
During Egencia's rebranding, I directed illustration concept creation via workshops based on engagement KPI's.
Egencia's design research team was swamped. To help, I managed our team's guerilla research to identify key pain points in the customer journey.
Periodically, I work on side gigs to keep things fresh. Check 'em out.
Owning design efforts to lower Egencia's call propensity KPI, I designed a new self-service experience featuring text & voice bots, that saved over $5 million in 2018.
B2B apps with captive users don't need onboarding, right? Wrong. Here's how I reshaped the Egencia user learning curve.
Following DeNovo's initial launch, we redesigned filtering and saw an immediate lift in usage.
Detect identifies & reduces suicide risk. I designed it from the ground up.
Glad you've scrolled this far! Allow me tell you a little about myself.
First, you should know that I'm a hybrid -- I blur the line between product management and design. How so? Maybe it's because I'm fascinated with understanding the complete product picture? Or maybe it's because I'm ambidextrous? Not sure. Regardless, I can speak Bauhausian and ROI.
My duality became apparent after graduating with a business strategy degree and starting my career in management consulting. I quickly found myself attracted to the intersection of product strategy, research and design. I reoriented my career into product design, yet I find myself drawn to understand all aspects of product.
After learning design on-the-job at PwC's 'intraprenuership' tech lab and Analytics Apps teams, I worked for a few startups, including Voi, a mental healthcare company. Then, in early 2018, I left San Francisco for Seattle to join the design team at Egencia. While there, I led design efforts to reduce calls to customer service (including our self-serve bot experiences) and in late 2018, I began managing our North America design team.
I'm a believer in RESEARCH and PROCESS. To design the most optimal solution, I first seek to understand the problem. After forming a solid hypothesis, I rapidly iterate on solutions, trying my best to never lose sight of the goal to impact desired KPI's.
HOW DO I SPEND MY FREE TIME?
I enjoy endurance sports, reading, cutting hair, volunteering in the community, and helping my lovely wife with her designer textile company, Klaede.


Including the Latest Project News!
White Rock Event is Here! Sept. 7!
Final preparations are underway for the WBA display of classic wooden and fiberglass boats on the shores of historic White Rock Lake on September 7, 2013. We'll be featuring our North Texas-built Willis, Yellow Jacket and Chrysler boats on shore, and our Chris-Crafts, Centurys and other marques in the water. The White Rock Boat Club is rolling out the red carpet, so let's show our support!
White Rock Boat Club members will also have three wooden sailboats, both hand-built and restored, along their docks for visitors to see. Below are Lew White and Bob Adair putting the finishing touches on their 14-foot Yellow Jacket custom, which will debut at White Rock. If you are able to bring your boat to this enjoyable day, please let David Kanally know at david@historywithheart.com .
Rockwall Pulling out all the Stops! Ride 'n Show Sept. 27-29!
Water Ski Shows, new and classic boats, sailing lessons...all will figure into the great Ride 'n Show weekend of Sept. 27-29. The Rockwall Chamber is really promoting this expanded event in the local media. The Hilton Bella Harbor will again be the location of the event at Lake Ray Hubbard. The City of Rockwall docks will provide a high-quality venue for our display of antique and classic boats.
The schedule will include our usual dining and revelry, in addition to a Sunday morning ride on the lake. We've even heard from some members of the Bayou Chapter of the ACBS who are planning on attending. Let's match their enthusiasm with a great turnout of WBA boats! Don't miss this great show! Register Now!
Since he acquired the creaking hulk of a once-noble Coronado seven years ago, Jim Wolfe has been painstakingly restoring both hull and engine in his home shop/garage. At the August WBA meeting, the large assemblage of members was treated to a detailed photo reportage of the restoration, including frame replacement and re-alignment, new battens, planks, decking, upholstery...and full re-build of the boat's Chrysler Hemi engine. On Saturday, August 24, a group of WBA members gathered at the ramp of the Arrowhead Park in Lake Dallas to witness the first water test of the boat. Join them via video, and watch the amazing performance and breathtaking beauty of this craft. Thanks, Jim for a great presentation and achievement. The WBA is fortunate to have members like you!!
(Above) Robin McGeorge sands the gunwale of the 1951 Chris-Craft Riviera he and Troy Marshall are restoring at the Lucas Shop. Deck work is currently underway. (Below) Mark Wilson attaches deck planking to his '68 Chris Craft Grand Prix.
(Above) Robin and Troy's Riviera's side planking is already starting to shine, while the deck is still in the reconstruction phase. (Below) Mark Wilson's deck planking is nearly complete, giving him a hint of what his finished boat will look like. Congrats to all for great progress.
Next Meeting September 19th. Don't miss it!
Join us on Thursday, September 19th at 7 p.m. at Two Guys from Italy at 11637 Webb Chapel Road, just south of Forest Road. WBA Treasurer and benefactor John Parish will be giving away one of his many boating and woodworking related books as a door prize.
Steve Griffitts will share photos of a couple Lake Tahoe Concours d' Elegance that he's attended in recent years. That show is the top of the line in our hobby, and Steve has prepared a worthy presentation. Join us for a light meal and moderate libation at 5:30 p.m. at Two Guys from Italy prior to the meeting. We encourage you to join us for dinner, so we'll always have the required minimum number of diners to avoid a room charge.
Steve Griffitts is helping to build the WBA fleet having just purchased a Thompson cedar-strip runabout. He dipped it into Lake Lewisville a week or so ago and learned that there is some space between the cedar strips that could quickly keep the boat from floating. So he's in touch with our buddy and cedar strip expert Chuck Webb to see what to do about the problem. What a pretty little boat, though! We're looking forward to seeing this outboard at upcoming shows, and eventually we'll see her watertight and holding her own on the lake. Steve also has a major Chris-Craft restoration underway, and he has a couple other interesting boats in his collection. All this is to say that the WBA fleet is growing, including the boats under restoration at the Lucas Shop, in Lew White's garage, in Jim Wolfe's shop, in Phil Wolff's garage, in the Indrieri's garage in Horseshoe Bay, and wherever else dedicated WBA members may be working. Thanks to all for making the WBA better.