Exact solution of a coagulation equation with a product kernel in the multicomponent case

In this paper, we obtain the general solution for the continuous Smoluchowski equation in the multicomponent case with a product kernel as a series expansion. The solution of the problem involves the Laplace transform in several dimensions. We obtain a nonlinear partial differential equation (PDE) of the advective kind generalizing the one previously given by other authors for the mono-component case.As in its relative mono-component case, gelation is produced at some point, the conditions for its occurrence being the same as those for the mono-component case, though substituting a sum of derivatives by a derivative in the Laplace transform field. We demonstrate that for a multicomponent particle size distribution (PSD) of multiplicative form, it is sufficient for one of the marginal PSDs to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent PSD.The general solution is applied to several specific cases, a discrete case that recovers a previously known solution, and another two continuous cases which can be used to check numerical methods designed to directly solve the Smoluchowski equation in more general cases.We have compared the solutions for the multicomponent PSD for constant, additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono-component and the multicomponent case.Finally, we have analysed the shape of the solutions for multicomponent PSD for constant, additive and product kernels for very small masses of components, obtaining a qualitatively different behaviour for the product kernel. This has effects in the mixing state of the sol phase as time passes.     

Structural and Thermodynamic Peculiarities of Core-Shell Particles at Fluid Interfaces from Triangular Lattice Models

A triangular lattice model for pattern formation by core-shell particles at fluid interfaces is introduced and studied for the particle to core diameter ratio equal to 3. Repulsion for overlapping shells and attraction at larger distances due to capillary forces are assumed. Ground states and thermodynamic properties are determined analytically and by Monte Carlo simulations for soft outer- and stiffer inner shells, with different decay rates of the interparticle repulsion. We find that thermodynamic properties are qualitatively the same for slow and for fast decay of the repulsive potential, but the ordered phases are stable for temperature ranges, depending strongly on the shape of the repulsive potential. More importantly, there are two types of patterns formed for fixed chemical potential—one for a slow and another one for a fast decay of the repulsion at small distances. In the first case, two different patterns—for example clusters or stripes—occur with the same probability for some range of the chemical potential. For a fixed concentration, an interface is formed between two ordered phases with the closest concentration, and the surface tension takes the same value for all stable interfaces. In the case of degeneracy, a stable interface cannot be formed for one out of four combinations of the coexisting phases, because of a larger surface tension. Our results show that by tuning the architecture of a thick polymeric shell, many different patterns can be obtained for a sufficiently low temperature.     

Modelling of a closed two-dimensional reactor bounded by a wavy wall

In this paper, we propose a model for a two-dimensional closed reactor bounded by a wavy wall. The left, right and top walls of the reactor are assumed to be flat surfaces while the bottom wall is a wavy surface. In order to formulate a model for such a reactor, we introduce a coordinate transformation into the dimensionless equations of a rectangular closed domain. Then the resulting equations illustrate the phenomena for a closed reactor bounded by a wavy wall. We solve these equations using the finite difference method. The astonishing results are that the intensity of streamlines and the maximum temperature within the reactor significantly increase with an increase of the number of waves in the bottom wall, the amplitude of waves and the Frank-Kamenetskii number. Converse characteristics are observed for higher values of the enlargement of a wave. Moreover, larger Rayleigh number induces stronger vortices in the flow field and reduces the maximum temperature. The Nusselt number at the bottom wavy wall is found to increase for higher values of the Frank-Kamenetskii number and the amplitude of a wave. A transition from the steady-state to the oscillatory convection is identified for a certain value of the Frank-Kamenetskii number. However, for a low value of the Rayleigh number, there occurs a transition from the steady-state to an explosion for increasing value of the Frank-Kamenetskii number. Results also demonstrate that the critical value of the Frank-Kamenetskii number, for which a transition from the steady-state to the oscillatory convection occurs, is higher for increasing values of the number of waves, the enlargement of a wave and the amplitude of a wave.     

Stopping time of a one-dimensional bounded quantum walk

The stopping time of a one-dimensional bounded classical random walk(RW) is defined as the number of steps taken by a random walker to arrive at a fixed boundary for the first time.A quantum walk(QW) is a non-trivial generalization of RW,and has attracted a great deal of interest from researchers working in quantum physics and quantum information.In this paper,we develop a method to calculate the stopping time for a one-dimensional QW.Using our method,we further compare the properties of stopping time for QW and RW.We find that the mean value of the stopping time is the same for both of these problems.However,for short times,the probability for a walker performing a QW to arrive at the boundary is larger than that for a RW.This means that,although the mean stopping time of a quantum and classical walker are the same,the quantum walker has a greater probability of arriving at the boundary earlier than the classical walker.     

Second quantized reduced Bloch equations and the exact solutions for pairing Hamiltonian

In this article, we present a set of hierarchy Bloch equations for the reduced density operators in either canonical or grand canonical ensembles in the occupation number representation. They provide a convenient tool for studying the equilibrium quantum statistical mechanics for some model systems. As an example of their applications, we solve the equations for the model system with a pairing Hamiltonian. With the aid of its symplectic group symmetry, we obtain the statistical reduced density matrices with different orders. As a special instance for the solutions, we also get the reduced density matrices of the ground state for a superconductor.     

Computation of Current Cumulants for Small Nonequilibrium Systems

We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrödinger perturbation expansion for the generating function. Here it is derived from a simple path-distribution identity and extended to the joint statistics of multiple currents. For a possible thermodynamical interpretation, we compare this approach to a generalized Onsager-Machlup formalism. We present calculations for a boundary driven Kawasaki dynamics on a one-dimensional chain, both for attractive and repulsive particle interactions.     

Photorefractive Four-Wave Mixing Switches Utilizing Pockels Effect -Longitudinal and Lateral Switches-

We carried out detailed calculations for photorefractive wave-mixing switches based on one of three crystals with high electro-optic coefficients, namely, BaTiO₃, Strontium Barium Niobate (SBN (0.75)), and Potasium Sodium Strontium Barium Niobate (KNSBN). A comparison of results for the three crystals shows that a 0_-cut BaTiO³ crystal is suitable for a longitudinal switch and requires a voltage of about 80 for a 2-mm-thick crystal to induce sufficient phase mismatch. The electrodes must be transparent for the incident and diffracted beams. A 45_-cut SBN (0.75) crystal, however, is suitable for a lateral switch and requires a voltage of about 150 for a 1-mm-wide crystal. The electrodes do not need to be transparent.     

The Explicit Density Functional and Its Connection with Entropy Maximization

The intrinsic Helmholtz free energy, commonly used as a basis for density functional theories, is here given explicitly as a cluster diagram expansion with density field points. Also given are explicit variational procedures for determining the chemical potential for a given density, the pair potential for a given pair correlation function, and the pair correlation function for a given pair potential. The physical meaning of the density functional is established within the context of a new derivation of statistical mechanics based on entropy that supplies a variational principle for equilibrium by generalizing the thermodynamic potential to nonequlibrium states. This shows that the conventional density functional determines not only the equilibrium density, but also the probability of fluctuations about that density.     

Molecular model for the VLE p- T-x relationships of binary mixtures

An analytical expression for the pressure-temperature-composition relations in the vapour - liquid equilibrium of non-polar binary mixtures is proposed. The model is based on a simple analytical expression for the vapour pressure of pure non-polar fluids, which, for a given temperature, requires as input only the Lennard- Jones molecular parameters and the acentric factor of the substance. The equilibrium mixture pressure is then expressed as a function of the vapour pressure of each component and of a mixture contribution. The molecular parameters required for this mixture contribution are related to the molecular parameters of the pure component through a modified Lorentz-Berthelot mixing rule, where the interaction parameters are given as simple functions of the temperature and composition, with eight appropriate constants for each binary mixture. We show that the model permits one to reproduce or predict in a simple way the pressure (for a given liquid mole fraction) or the liquid composition (for a given pressure).     

Sound radiation from rectangular baffled and unbaffled plates

The radiation efficiency of a flat rectangular plate is often used as a basis on which to represent the sound radiation from more complex plate-like structures. The solution for a plate set in a rigid baffle is well known, including the radiation efficiency for multi-modal response of the plate. In this case the assumption is usually made that each mode within a given frequency band has equal modal vibration energy. This paper explores a number of limitations of this simple result. First, the extent to which the radiation efficiency for a particular forcing point deviates from the modal-average result is investigated. Second, the difference is shown between the results for a baffled plate and an unbaffled plate. For a multi-modal response, an empirical formula is also presented which allows the radiation efficiency to be estimated for the unbaffled case. Finally, the effect of different boundary conditions on both baffled and unbaffled results is demonstrated by comparing the results for guided boundaries with those for simply supported boundaries.     

Anti-diffusion method for interface steepening in two-phase incompressible flow

In this paper, we present a method for obtaining sharp interfaces in two-phase incompressible flows by an anti-diffusion correction, that is applicable in a straight-forward fashion for the improvement of two-phase flow solution schemes typically employed in practical applications. The underlying discretization is based on the volume-of-fluid (VOF) interface-capturing method on unstructured meshes. The key idea is to steepen the interface, independently of the underlying volume-fraction transport equation, by solving a diffusion equation with reverse time, i.e. an anti-diffusion equation, after each advection time step of the volume fraction. As the solution of the anti-diffusion equation requires regularization, a limiter based on the directional derivative is developed for calculating the gradient of the volume fraction. This limiter ensures the boundedness of the volume fraction. In order to control the amount of anti-diffusion introduced by the correction algorithm we propose a suitable stopping criterion for interface steepening. The formulation of the limiter and the algorithm for solving the anti-diffusion equation are applicable to 3-dimensional unstructured meshes. Validation computations are performed for passive advection of an interface, for 2-dimensional and 3-dimensional rising-bubbles, and for a rising drop in a periodically constricted channel. The results demonstrate that sharp interfaces can be recovered reliably. They show that the accuracy is similar to or even better than that of level-set methods using comparable discretizations for the flow and the level-set evolution. Also, we observe a good agreement with experimental results for the rising drop where proper interface evolution requires accurate mass conservation.     

Nonlinear rheological models for structured interfaces

The GENERIC formalism is a formulation of nonequilibrium thermodynamics ideally suited to develop nonlinear constitutive equations for the stress-deformation behavior of complex interfaces. Here we develop a GENERIC model for multiphase systems with interfaces displaying nonlinear viscoelastic stress-deformation behavior. The link of this behavior to the microstructure of the interface is described by including a scalar and a tensorial structural variable in the set of independent surface variables. We derive an expression for the surface stress tensor in terms of these structural variables, and a set of general nonlinear time evolution equations for these variables, coupling them to the deformation field. We use these general equations to develop a number of specific models, valid for application near equilibrium, or valid for application far beyond equilibrium.     

基于一组Kalman滤波器信息融合的故障诊断

为了能及时准确地诊断发动机的传感器和执行机构故障,本文提出了基于一组Kalman滤波器信息融合的方法进行故障诊断。首先根据传感器特性设计了一组滤波器用于传感器故障诊断、隔离,每个滤波器针对一个传感器进行设计;其次根据执行机构故障特性设计了一组Kalman滤波器进行执行机构偏差估计,从而对执行机构进行故障诊断、隔离;接着给出了传感器、执行机构信息融合的诊断方案;最后分别给传感器、执行机构添加故障进行方案验证,仿真结果得出在传感器或者执行机构任意部件出故障的情况下,该融合方法可以有效地诊断并隔离出有故障的传感器或者执行机构。     

Ground State and Single Vortex for Bose-Einstein Condensates in Anisotropic Traps

For Bose-Einstein condensation of neutral atoms in anisotropic traps at zero temperature, we present simple analytical methods for computing the properties of ground state and single vortex of Bose-Einstein condensates, and compare those results to extensive numerical simulations. The critical angular velocity for production of vortices is calculated for both positive and negative scattering lengths a, and find an analytical expression for the large-N limit of the vortex critical angular velocity for a 〉0, and the critical number for condensate population approaches the point of collapse for a 〈 0, by using approximate variational method.     

The influence of connectivity on the firing rate in a neuronal network with electrical and chemical synapses

We study the firing rate properties of a cellular automaton model for a neuronal network with chemical synapses. We propose a simple mechanism in which the nonlocal connections are included, through electrical and chemical synapses. In the latter case, we introduce a time delay which produces self-sustained activity. Nonlocal connections, or shortcuts, are randomly introduced according to a specified connection probability. There is a range of connection probabilities for which neuron firing occurs, as well as a critical probability for which the firing ceases in the absence of time delay. The critical probability for nonlocal shortcuts depends on the network size according to a power-law. We also compute the firing rate amplification factor by varying both the connection probability and the time delay for different network sizes.     

Investigation of Simulated Trading — A multi agent based trading system for optimization purposes

Some years ago, Bachem, Hochstättler, and Malich proposed a heuristic algorithm called Simulated Trading for the optimization of vehicle routing problems. Computational agents place buy-orders and sell-orders for customers to be handled at a virtual financial market, the prices of the orders depending on the costs of inserting the customer in the tour or for his removal. According to a proposed rule set, the financial market creates a buy-and-sell graph for the various orders in the order book, intending to optimize the overall system. Here I present a thorough investigation for the application of this algorithm to the traveling salesman problem.     

Respiratory and laryngeal contributions to maximum phonation duration

Maximum phonation duration (MPD) is a common assessment procedure in speech-language pathology. However, the specific contributions of the respiratory and phonatory components of the speech-production mechanism to this task are not typically assessed. Six women and 6 men with normal speech and voice were monitored for lung volume during a standard MPD task, and for laryngeal airway resistance (Rlaw) during a modified MPD (slow syllable-repetition) task. On average, subjects used 90% of their vital capacity (VC) for their best MPD trial. There was no systematic relation between MPD and VC for these subjects. Rlaw was strongly correlated with MPD for the men (r(s) = 0.886 for /a/; r(s) = 0.829 for /i/), but not for the women. Rlaw increased linearly as lung volume decreased (slope > 0.15) for a subset of trials (32%). This was a common pattern for four of the subjects. The clinical utility of MPD to assess breathing for speech is questioned because of the lack of association between MPD and VC, and some atypical laryngeal-valving strategies.     

The Steady State Fluctuation Relation for the Dissipation Function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.     

制冷剂饱和热力性质的隐式拟合方法

１前言准确、快速、稳定地计算制冷剂热力性质是计算机辅助设计和工程计算的要求。但目前流行的多项式类简化拟合函数在总体计算精度、外推以及求反计算等方面都有待改进［１－３］。本文从函数展开的角度剖析了现有多项式类拟合函数的不足,提出了一种低次的隐函数形式的...