Interaction Pressure Tensor for a class of Multicomponent Lattice Boltzmann models

We present a theory to obtain the pressure tensor for a class of non-ideal multicomponent lattice Boltzmann models, thus extending the theory presented by Shan (X. Shan, Phys. Rev. E 77, 066702 (2008)) for single component fluids. We obtain the correct form of the pressure tensor directly on the lattice and the resulting equilibrium properties are shown to agree very well with those measured from numerical simulations. Results are compared with those of alternative theories.Comment: 7 Pages, 5 figure

On the non-convergence of the Wang-Landau algorithms with multiple random walkers

This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and $1/t$ algorithms. The classical algorithms are modified by the use of $m$ independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number $\pi$ by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, $t$; then, the average over $m$ walkers is performed. It is observed that the error goes as $1/\sqrt{m}$. However, if the number of walkers increases above a certain critical value $m>m_x$, the error reaches a constant value (i.e. it saturates). This occurs for both algorithms; however, it is shown that for a given system, the $1/t$ algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value $m_x$, since it does not reduces the error in the calculation. Therefore, the number of walkers does not guarantee convergence.Comment: 10 pages, 12 figures, Regular Articl

Lattice Boltzmann Simulations of Droplet formation in confined Channels with Thermocapillary flows

Based on mesoscale lattice Boltzmann simulations with the "Shan-Chen" model, we explore the influence of thermocapillarity on the break-up properties of fluid threads in a microfluidic T-junction, where a dispersed phase is injected perpendicularly into a main channel containing a continuous phase, and the latter induces periodic break-up of droplets due to the cross-flowing. Temperature effects are investigated by switching on/off both positive/negative temperature gradients along the main channel direction, thus promoting a different thread dynamics with anticipated/delayed break-up. Numerical simulations are performed at changing the flow-rates of both the continuous and dispersed phases, as well as the relative importance of viscous forces, surface tension forces and thermocapillary stresses. The range of parameters is broad enough to characterize the effects of thermocapillarity on different mechanisms of break-up in the confined T-junction, including the so-called "squeezing" and "dripping" regimes, previously identified in the literature. Some simple scaling arguments are proposed to rationalize the observed behaviour, and to provide quantitative guidelines on how to predict the droplet size after break-up.Comment: 18 pages, 9 figure

Fluctuating Multicomponent Lattice Boltzmann Model

Current implementations of fluctuating lattice Boltzmann equations (FLBE) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem (FDT) directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the ortho-normal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and non-ideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.Comment: 30 pages, 6 figure

Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error

In this work we present a theoretical analysis of the convergence of the Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] which was introduced years ago to calculate the density of states in statistical models. We study the dynamical behavior of the error in the calculation of the density of states.We conclude that the source of the saturation of the error is due to the decreasing variations of the refinement parameter. To overcome this limitation, we present an analytical treatment in which the refinement parameter is scaled down as a power law instead of exponentially. An extension of the analysis to the N-fold way variation of the method is also discussed.Comment: 7 pages, 5 figure

Verification of Hierarchical Artifact Systems

Data-driven workflows, of which IBM's Business Artifacts are a prime exponent, have been successfully deployed in practice, adopted in industrial standards, and have spawned a rich body of research in academia, focused primarily on static analysis. The present work represents a significant advance on the problem of artifact verification, by considering a much richer and more realistic model than in previous work, incorporating core elements of IBM's successful Guard-Stage-Milestone model. In particular, the model features task hierarchy, concurrency, and richer artifact data. It also allows database key and foreign key dependencies, as well as arithmetic constraints. The results show decidability of verification and establish its complexity, making use of novel techniques including a hierarchy of Vector Addition Systems and a variant of quantifier elimination tailored to our context.Comment: Full version of the accepted PODS pape

Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals

In this communication, the convergence of the 1/t and Wang - Landau algorithms in the calculation of multidimensional numerical integrals is analyzed. Both simulation methods are applied to a wide variety of integrals without restrictions in one, two and higher dimensions. The errors between the exact and the calculated values of the integral are obtained and the efficiency and accuracy of the methods are determined by their dynamical behavior. The comparison between both methods and the simple sampling Monte Carlo method is also reported. It is observed that the time dependence of the errors calculated with 1/t algorithm goes as N^{-1/2} (with N the MC trials) in quantitative agreement with the simple sampling Monte Carlo method. It is also showed that the error for the Wang - Landau algorithm saturates in time evidencing the non-convergence of the methods. The sources for the error are also determined.Comment: 8 pages, 5 figure

805-1 Theophylline Reverses Myocardial Infarction-Related Brady and Tachy Arrhythmias: Role of Adenosine

Brady and tachyarrhythmias often complicate the early management of acute myocardial infarction (MI). Endogenously released adenosine (ADO) from ischemic cardiac cells has been proposed as a potential mediator of these arrhythmias. In order to test this hypothesis, theophylline (THEO), a competitive ADO receptor antagonist, was administered to nine patients who developed sustained or hemodynamically significant brady or tachyarrhythmias immediately following an acute inferior MI.MethodsOnce such an arrhythmia was detected, continuous ECG monitoring was begun. THEO was then administered i.v. at a rate of 100mg/min until the arrhythmia resolved or a maximum of 250mg THEO was infused. Patients were then monitored for 24 hours for recurrent arrhythmias.ResultsBradyarrhythmias were detected in 5 patients (3 with 3° AV block, 2 with 2° AV block). Tachyarrhythmias were detected in four patients (2 with atrial fibrillation, 2 with accelerated idioventricular rhythm). All patients converted to normal sinus rhythm within five minutes of the administration of THEO (178±57mg). No recurrent arrhythmia occurred in the follow-up period.ConclusionsMany of the brady and tachyarrhythmias which occur early after inferior MI are ADO-mediated. ADO receptor antagonism appears effective in converting these arrhythmias to normal sinus rhythm and may be considered as primary therapy

Thermal fluctuations of an interface near a contact line

The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random variables, we explore the equilibrium properties of the corresponding fluctuating contact line problem based on an interfacial Hamiltonian involving a "contact" binding potential. To facilitate an analytical treatment we consider the case of a one-dimensional interface. The effective boundary condition at the contact line is determined by a dimensionless parameter that encodes the relative importance of thermal energy and substrate energy at the microscopic scale. We find that this parameter controls the transition from a partially wetting to a pseudo-partial wetting state, the latter being characterized by a thin prewetting film of fixed thickness. In the partial wetting regime, instead, the profile typically approaches the substrate via an exponentially thinning prewetting film. We show that, independently of the physics at the microscopic scale, Young's angle is recovered sufficiently far from the substrate. The fluctuations of the interface and of the contact line give rise to an effective disjoining pressure, exponentially decreasing with height. Fluctuations therefore provide a regularization of the singular contact forces occurring in the corresponding deterministic problem.Comment: 40 Pages, 12 Figure