Statistics, distillation, and ordering emergence in a two-dimensional stochastic model of particles in counterflowing streams

In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile obstacles, whereas particles of one species move in opposite direction to the particles of the other species, or they can work as fixed obstacles remaining in their places during the time evolution. We conducted a detailed study about the statistics concerning the crossing time of particles, as well as the effects of the lateral transitions on the time required to the system reaches a state of complete geographic separation of species. The spatial effects of jamming were also studied by looking into the deformation of the concentration of particles in the two-dimensional corridor. Finally, we observed in our study the formation of patterns of lanes which reach the steady state regardless the initial conditions used for the evolution. A similar result is also observed in real experiments involving charged colloids motion and simulations of pedestrian dynamics based on Langevin equations, when periodic boundary conditions are considered (particles counterflow in a ring symmetry). The results obtained through Monte Carlo numerical simulations and numerical integrations are in good agreement with each other. However, differently from previous studies, the dynamics considered in this work is not Newton-based, and therefore, even artificial situations of self-propelled objects should be studied in this first-principle modeling.Comment: 27 pages, 13 figure

Mobile-to-clogging transition in a Fermi-like model of counterflowing particles

In this paper we propose a generalized model for the motion of a two-species self-driven objects ranging from a scenario of a completely random environment of particles of negligible excluded volume to a more deterministic regime of rigid objects in an environment. Each cell of the system has a maximum occupation level called σ max . Both species move in opposite directions. The probability of any given particle to move to a neighboring cell depends on the occupation of this cell according to a Fermi-Dirac-like distribution, considering a parameter α that controls the system randomness. We show that for a certain α = α c the system abruptly transits from a mobile scenario to a clogged state, which is characterized by condensates. We numerically describe the details of this transition by coupled partial differential equations (PDE) and Monte Carlo (MC) simulations that are in good agreement

Lattice Gas model to describe a nightclub dynamics

In this work, we propose a simple stochastic agent-based model to describe the revenue dynamics of a nightclub venue based on the relationship between profit and spatial occupation. The system consists of an underlying square lattice (nightclub's dance floor) where every attendee (agent) is allowed to move to its first neighboring cells. Each guess has a characteristic delayed time between drinks, denoted as $\tau$, after which it will show an urge to drink. At this moment, the attendee will tend to move towards the bar where a drink will be bought. After it has left the bar zone, $\tau$ time steps should pass so it shows once again the need to drink. Our model among other points show that it is no use filling the bar to obtain profit, and optimization should be analyzed. This can be done in a more secure way taking into consideration the ratio between income and ticket cost.Comment: 13 pages, 6 figure

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Ordenamento e destilação em um modelo estocástico de partículas interagentes sob contrafluxo

Neste trabalho estudamos uma dinâmica estocástica de partículas de duas espécies baseada em células. Basicamente, incorporamos algumas inovações em um modelo unidimensional proposto e resolvido por R. da Silva et al. (Physica A, 2015), que considera que em um célula, na ausência de partículas da espécie contrária, a partícula vai pra frente com uma probabilidade p, que representaria um campo na direção longitudinal de um corredor e fica na própria célula com q=1-p. Contudo, essa probabilidade p é reduzida de acordo com a concentração de partículas contrárias. Nosso trabalho não apenas estendeu o problema pra duas dimensões como também incluiu aspectos relativos a colisão e o espalhamento para células vizinhas. Nossos resultados são divididos em duas situações: a) Espécie contrária permanece imóvel funcionando como obstáculos b) Espécie contrária em movimento. Na primeira situação podemos ver uma interessante transição na distribuição dos tempos de travessia em função das concentrações dos obstáculos, por monitorar a curtose da distribuição. Quando a espécie contrária se movimenta, vemos que o tempo de destilação entre as partículas (tempo para que as espécies estejam geograficamente separadas no corredor) depende do parâmetro ligado ao espalhamento transversal das partículas, parâmetro este, que não influencia no caso das partículas paradas. Finalmente nós colocamos as partículas em um sistema com condições periódicas de contorno. Neste caso, podemos observar o aparecimento de padrões de bandas longitudinais ao campo, exatamente como ocorrem em problemas de coloides carregados sob a ação de campos longitudinais e em modelos de pedestres em corredores. Mostramos como o sistema relaxa para tal tipo de estado estacionário utilizando um adequado parâmetro de ordem ligado a segregação das partículas. Nosso modelo, diferentemente dos modelos para pedestres, não se baseia em equações tipo Langevin. Nossa abordagem é totalmente estocástica e por esse ponto de vista ainda mais fundamental e geral, podendo ser estendida para mais modelos de partículas em fluxos contrários. Nossa solução vem tanto através de simulações Monte Carlo bem como soluções das equações diferenciais parciais que descrevem o sistema e que são oriundas das recorrências estabelecidas para os caminhantes aleatórios. As simulações Monte Carlo e soluções via EDP mostram boa concordância em todos os aspectos analisados, tanto qualitativa quanto quantitativamente.In this work we study a stochastic dynamic of particles of two types based on cells. Basically we incorporate some innovations on a one-dimensional model proposed and solved by R. da Silva et al. (Physica A, 2015) which considers that in the absence of particles of the opposite species in the cell a particle goes toward the next cell with probability p and returns to the previous cell with probability q = 1 p. However this motion probability linearly decreases with the relative density of the contrary species. Our work not only expands the problem for two dimensions but also includes collision aspects by adding scattering to the neighbouring cells. Our results are divided into two di erent categories: a) One of the species remain xed in their places which means that such particles will work as obstacles; b) Both species can move in the environment. In the rst situation we can observe, by monitoring the kurtosis, that an interesting transition of the crossing time distribution arises as the concentration of the obstacles increases. When both species can move we can observe that the distillation time (spent time for the complete geographical separation of the species in the corridor) depends on the parameter related to the perpendicular scattering of the particles. This same parameter has shown no in uence over the time distributions in the rst situation. Finally we implement periodic boundary conditions in the eld's direction. In this case we are able to observe the arising of band patterns parallel to the eld's direction exactly as it does with oppositely charged colloids under the in uence of a uniform electric eld or pedestrian dynamics in corridors. We also show how the system relax to such stationary state by using a suitable order parameter related to the particles segregation. Di erently from other pedestrian dynamics models, our model is not based on a Langevin-type equation. Our approach is totally stochastic and from this point of view, more fundamental and general to be extended to more types of models considering particles under counter ow. Our solution is obtained by both Monte Carlo simulations and numerical integration of partial di erential equations (PDE) from recurrence relation of the directed random walkers. The Monte Carlo simulations and the solutions of the PDE show a good agreement in all aspects analysed both qualitatively and quantitatively

Estudo de sistemas magnéticos policristalinos através da equação de Landau–Lifshitz–Gilbert

A equação da dinâmica da magnetização, proposta por Landau e Lifshitz, é amplamente utilizada e é a base de muitos estudos de simulações de sistemas magnéticos. Neste trabalho, apresentamos uma revisão teórica dos conceitos básicos do micromagnetismo. Inicialmente, são estudadas as equações de Landau-Lifshitz e Landau-Lifshitz-Gilbert. Posteriormente, é descrita a construção de um modelo numérico, cuja dinâmica magnética baseia-se na equação de Landau-Lifshitz-Gilbert. É realizada a apresentação do algoritmo pelo qual o código, utilizado em nossas simulações, baseia-se. Uma breve descrição da linguagem de programação C-CUDA, na qual o código foi escrito, é feita. No final deste trabalho, são mostrados os resultados das simulações e discutidos brevemente os passo que pretendemos seguir na continuação deste trabalho.The equation of the magnetization dynamics proposed by Landau and Lifshitz is widely-used and is the base for numerous studies on simulations of magnetic systems. In this work we confer a theoretical review of the basic concepts of micromagnetism. First, the Landau-Lifshitz and Landau- Lifshitz-Gilbert equations are presented. After that, the construction of the numerical model used here is described, where the magnetic dynamics is based on the Landau-Lifshitz-Gilbert equation. A presentation of the algorithm on which the code used in our simulation is based is then performed. A brief description of the programming language on which the code is written is made as well. At the end of the study, some simulation results are shown and proposals for future development are presented

Numerical study of spacial patterns and condensates in models of counterflowing streams of particles

Neste trabalho, propusemos um modelo estocástico para descrever a dinâmica de duas espécies de partículas que se deslocam contrariamente em uma rede bidimensional com condições de contorno periódicas. Nossa proposta consiste em definir as probabilidades de transição dos agentes para suas primeiras células vizinhas como distribuições do tipo Fermi-Dirac adaptadas ao contexto de dinâmica de partículas. Assim, a partir de um parâmetro que controla o grau de estocasticidade do sistema (α), o modelo reproduz uma variedade de cenários partindo de um regime de dinâmica com alta aleatoriedade, onde partículas das duas espécies deslocam-se na rede de maneira descorrelacionada, até o regime de baixa estocasticidade, onde a dinâmica é fortemente correlacionada e o movimento na rede dependerá da relação entre o níıvel de ocupação das células vizinhas e o valor de ocupação máximo (σmax). A partir de simulações de Monte Carlo e integração numérica de equações diferenciais parciais acopladas, mostramos que existe uma transição abrupta em α = αc, onde αc depende da densidade média de partículas no sistema. Quando consideramos o caso em que há apenas interação entre entes de espécies diferentes, mostramos que o sistema passa a apresentar alta sensibilidade com as condições iniciais, de modo a poder relaxar para três estados estacionários: estado móvel com auto-organização, estado imóvel com formação de condensados e estado com coexistência de fases. Nesse cenário, o estado de coexistência mostra-se pouco provável de ocorrer, de maneira a observarmos o fenômeno de bimodalidade do estado estacionário (fase móvel ou fase imóvel). Entretanto, ao generalizarmos a dinâmica, a partir do estudo de magnitude dos fatores de interação, conseguimos mapear qualitativamente as condições de ocorrência dos fenômenos de bimodalidade e coexistência que o modelo apresenta.This work proposed a stochastic model to describe the dynamics of two species of particles moving in opposite directions on a two-dimensional lattice with periodic boundary conditions. Our proposition consists of defining the agent’s transition probabilities to the first neighboring cells as Fermi-Dirac-like distributions adapted to the context of particle dynamics. This way, by adjusting a single parameter (α), our model can describe a variety of scenarios ranging from a high level of randomness with uncorrelated particles moving along the lattice to a scenario with a low level of randomness with strongly correlated dynamics in which the movement in the lattice depends on the relation between the neighboring cells occupation level and the maximum level of occupation (σmax). Using Monte Carlos simulations and numerical integration of coupled differential equations, we show that an abrupt transition occurs when α = αc, which value depends on the average density of particles. When we consider only the interaction between particles of different species, we show that the system presents sensitive dependence with initial conditions, and we observe three different steady states: mobile state with lane formation, a jammed state with condensates, and a phase coexistence state (mobile phase and jammed phase). In this case, the latter state rarely happens, in the sense that we observe a bi-modality phenomenon on the steady-state (mobile or jammed). However, when we generalize the dynamics by studying different magnitudes of the interaction factor, we qualitatively map the occurrence conditions of the bi-modality phenomenon and the coexistence state that rises from the model

Interferometria de gotas e filmes sobre superfícies

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