Energy estimates for continuous and discretized electro-reaction-diffusion systems

We consider electro-reaction-diffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistic relations. We investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value. Here the essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly. The same properties are shown for an implicit time discretized version of the problem. Moreover, we provide a space discretized scheme for the electro-reaction-diffusion system which is dissipative (the free energy decays monotonously). On a fixed grid we use for each species different Voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species

Integrating mobile devices into a scalable Grid Computing architecture designed to perform distributed computations

The idea of Grid Computing originated in the nineties and found its concrete applications in contexts like the SETI@home project where a lot of computers (offered by volunteers) cooperated, performing distributed computations, inside the Grid environment analyzing radio signals trying to find extraterrestrial life. The Grid was composed of traditional personal computers but, with the emergence of the first mobile devices like Personal Digital Assistants (PDAs), researchers started theorizing the inclusion of mobile devices into Grid Computing; although impressive theoretical work was done, the idea was discarded due to the limitations (mainly technological) of mobile devices available at the time. Decades have passed, and now mobile devices are extremely more performant and numerous than before, leaving a great amount of resources available on mobile devices, such as smartphones and tablets, untapped. Here we propose a solution for performing distributed computations over a Grid Computing environment that utilizes both desktop and mobile devices, exploiting the resources from day-to-day mobile users that alternatively would end up unused. The work starts with an introduction on what Grid Computing is, the evolution of mobile devices, the idea of integrating such devices into the Grid and how to convince device owners to participate in the Grid. Then, the tone becomes more technical, starting with an explanation on how Grid Computing actually works, followed by the technical challenges of integrating mobile devices into the Grid. Next, the model, which constitutes the solution offered by this study, is explained, followed by a chapter regarding the realization of a prototype that proves the feasibility of distributed computations over a Grid composed by both mobile and desktop devices. To conclude future developments and ideas to improve this project are presented

Exponential decay of the free energy for discretized electro-reaction-diffusion systems

Our focus are electro-reaction-diffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistical relations. We introduce a discretization scheme (in space and fully implicit in time) using a fixed grid but for each species different Voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species. This scheme has the special property that it preserves the main features of the continuous systems, namely positivity, dissipativity and flux conservation. For the discretized electro-reaction-diffusion system we investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value. The essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly

Art of Modeling Stellar Mergers and the Case of the B[e] Supergiant R4 in the Small Magellanic Cloud

Most massive stars exchange mass with a companion, leading to evolution which is altered drastically from that expected of stars in isolation. Such systems result from unusual binary evolution pathways and can place stringent constraints on the physics of these interactions. We use the R4 binary system's B[e] supergiant, which has been postulated to be the product of a stellar merger, to guide our understanding of such outcomes by comparing observations of R4 to the results of simulating a merger with the 3D hydrodynamics code FLASH. Our approach tailors the simulation initial conditions to observed properties of R4 and implements realistic stellar profiles from the 1D stellar evolution code MESA onto the 3D grid, resolving the merger inspiral to within 0.02 R⊙. We map the merger remnant into MESA to track its evolution on the H-R diagram over a period of 10⁴ yr. This generates a model for a B[e] supergiant with stellar properties, age, and nebula structure in qualitative agreement with those of the R4 system. Our calculations provide evidence to support the idea that R4's B[e] supergiant was originally a member of a triple system in which the inner binary merged after its most massive member evolved off the main sequence, producing a new object of similar mass but significantly more luminosity than the A supergiant companion. The code framework presented in this paper, which was constructed to model tidal encounters, can be used to generate accurate models of a wide variety of merger stellar remnants

The Art of Modeling Stellar Mergers and the Case of the B[e] Supergiant R4 in the Small Magellanic Cloud

Most massive stars exchange mass with a companion, leading to evolution which is altered drastically from that expected of stars in isolation. Such systems are the result of unusual binary evolution pathways and, as such, may be used to place stringent constraints on the physics of these interactions. We use the R4 system's B[e] supergiant, which has been postulated to be the product of a binary stellar merger, to guide our understanding of such outcomes by comparing observations of R4 to the results of simulations of mergers performed with the 3d hydrodynamics code FLASH. Our approach tailors the simulation initial conditions to the observed properties of R4 and implements realistic stellar profiles generated by the 1d stellar evolution code MESA onto the 3d grid, resolving the merger inspiral to within $0.02\, R_{\odot}$. We then map the merger remnant into MESA to track its evolution on the HR diagram over a period of $10^4$ years. This generates models for a B[e] supergiant with stellar properties, age, and nebula structure in qualitative agreement with that of the R4 system. Our calculations provide concrete evidence to support the idea that R4 was originally a member of a triple system in which the inner binary merged after its most massive member evolved off the main sequence, producing a new object that is of similar mass yet significantly more luminous than the A supergiant companion. The potential applications of the code framework presented in this paper are wide ranging and can be used to generate models of a variety of merger stellar remnants

Adaptive mesh and geodesically sliced Schwarzschild spacetime in 3+1 dimensions

We present first results obtained with a 3+1 dimensional adaptive mesh code in numerical general relativity. The adaptive mesh is used in conjunction with a standard ADM code for the evolution of a dynamically sliced Schwarzschild spacetime (geodesic slicing). We argue that adaptive mesh is particularly natural in the context of general relativity, where apart from adaptive mesh refinement for numerical efficiency one may want to use the built in flexibility to do numerical relativity on coordinate patches.Comment: 21 pages, LaTeX, 7 figures included with eps

Refitting industrial Cerdà: reorganising Cerdà blocks with Can Ricart precinct

The layout of Poblenou is complicated, combined with many layers, including the Cerdà Grid and practices following it, different kinds of industrial heritage and its layout, etc. They are different and contradictory, for carried out in different historical periods and from architectural thoughts. As Cerdà grid gradually approaching, many of industrial heritage sunk and scattered into the orthogonal grid. The old layout has been dissolved into new context. However, they brought ´diversity´ to Cerdà grid, which is the crucial value in the evolution of Cerdà in Poblenou. It naturally generates chances for evolution of new Cerdà to accommodate and integrate various and contradictory elements here, and can be identified as ´Industrial Cerdà´. Thus, ´Industrial Cerdà´ in Poblenou should not be simply described as ´orthogonal grid´, but the carrier of diversity and ´non-Cerdà´ layers in Poblenou as well. Thus, thesis mainly focuses on three basic question: How to insert industrial heritage into Cerdà block? How can industrial heritage refit the form of Cerdà? And how to integrate them together? The thesis will be divided into 3 aspects. Firstly, standard Cerdà, as well as many orthogonal planning in history, emphasizes the concept of ´unit´ and their solutions of generating public spaces. It shows a critical idea of individual but common cluster for safety and sense of belonging, while assembled for urban spaces. Thus, they are not enclosed, with some connections to context. Among some new Cerdà blocks in Poblenou, courtyards are reorganised as urban space in larger scale. Secondly, Cerdà plan can never be perfect standard model. Exceptional plots of it create horizontal diversity to various circumstances for Cerdà practices. It emerged from compromises when facing with reality, including function, entrance, landmark, etc. In order to establish positive interactions between courtyard and context with visual, functional and mobility connections in different types in different parts of a standard model. Thirdly, industrial heritages and its layout are supposed to contribute to reform of Cerdà blocks to improve the quality of pedestrian level spaces of Poblenou, which can be achieved by overlapping. Many architects expressed their ideas of integration different layers of activities and context, which could help to create vertical diversity for Cerdà forms. Meanwhile, heritages can also be well absorbed in pedestrian spaces for city life. To take Can Ricart as example, this thesis aims to practise formal strategies for industrial heritage to refit in Cerdà block in Poblenou, and also help them to assimilate into new communities there

On the relation between the second law of thermodynamics and classical and quantum mechanics

In textbooks on statistical mechanics, one finds often arguments based on classical mechanics, phase space and ergodicity in order to justify the second law of thermodynamics. However, the basic equations of motion of classical mechanics are deterministic and reversible, while the second law of thermodynamics is irreversible and not deterministic, because it states that a system forgets its past when approaching equilibrium. I argue that all "derivations" of the second law of thermodynamics from classical mechanics include additional assumptions that are not part of classical mechanics. The same holds for Boltzmann's H-theorem. Furthermore, I argue that the coarse-graining of phase-space that is used when deriving the second law cannot be viewed as an expression of our ignorance of the details of the microscopic state of the system, but reflects the fact that the state of a system is fully specified by using only a finite number of bits, as implied by the concept of entropy, which is related to the number of different microstates that a closed system can have. While quantum mechanics, as described by the Schroedinger equation, puts this latter statement on a firm ground, it cannot explain the irreversibility and stochasticity inherent in the second law.Comment: Invited talk given on the 2012 "March meeting" of the German Physical Society To appear in: B. Falkenburg and M. Morrison (eds.), Why more is different (Springer Verlag, 2014

Invariant Discretization Schemes Using Evolution-Projection Techniques

Finite difference discretization schemes preserving a subgroup of the maximal Lie invariance group of the one-dimensional linear heat equation are determined. These invariant schemes are constructed using the invariantization procedure for non-invariant schemes of the heat equation in computational coordinates. We propose a new methodology for handling moving discretization grids which are generally indispensable for invariant numerical schemes. The idea is to use the invariant grid equation, which determines the locations of the grid point at the next time level only for a single integration step and then to project the obtained solution to the regular grid using invariant interpolation schemes. This guarantees that the scheme is invariant and allows one to work on the simpler stationary grids. The discretization errors of the invariant schemes are established and their convergence rates are estimated. Numerical tests are carried out to shed some light on the numerical properties of invariant discretization schemes using the proposed evolution-projection strategy