Is there the radion in the RS2 model?

We analyse the physical boundary conditions at infinity for metric fluctuations and gauge functions in the RS2 model with matter on the brane. We argue that due to these boundary conditions the radion field cannot be gauged out in this case. Thus, it represents a physical degree of freedom of the model.     

Exact diffusion constant of a one-dimensional asymmetric exclusion model with open boundaries

For the 1D fully asymmetric exclusion model with open boundary conditions, we calculate exactly the fluctuations of the current of particles. The method used is an extension of a matrix technique developed recently to describe the equatime steady-state properties for open boundary conditions and the diffusion constant for particles on a ring. We show how the fluctuations of the current are related to non-equal-time correlations. In the thermodynamic limit, our results agree with recent results of Ferrari and Fontes obtained by working directly in the infinite system. We also show that the fluctuations of the current become singular when the system undergoes a phase transition with discontinuities along the first-order transition line.     

From Alternating Sign Matrices to the Gaussian Unitary Ensemble

The aim of this note is to prove that fluctuations of uniformly random alternating sign matrices (equivalently, configurations of the 6-vertex model with domain wall boundary conditions) near the boundary are described by the Gaussian Unitary Ensemble and the GUE-corners process.     

Controlling density fluctuations in wall-bounded dissipative particle dynamics systems

Dissipative Particle Dynamics (DPD) simulations of wall-bounded flows exhibit density fluctuations that depend strongly on the no-slip boundary condition and increase with the level of coarse graining. We develop an adaptive model for wall-particle interactions that eliminates such oscillations and can target prescribed density profiles. Comparisons are made with ideal no-slip boundary conditions and molecular dynamics simulations. The new model is general and can be used in other coarse-grained particle methods.     

Fluctuations in the Bose Gas with Attractive Boundary Conditions

In this paper limiting distribution functions of field and density fluctuations are explicitly and rigorously computed for the different phases of the Bose gas. Several Gaussian and non-Gaussian distribution functions are obtained and the dependence on boundary conditions is explicitly derived. The model under consideration is the free Bose gas subjected to attractive boundary conditions, such boundary conditions yield a gap in the spectrum. The presence of a spectral gap and the method of the coupled thermodynamic limits are the new aspects of this work, leading to new scaling exponents and new fluctuation distribution functions.     

Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under periodic boundary conditions. Thus the spatial inhomogeneity of the statistical state arises through spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations. (c) 1996 American Institute of Physics.     

Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum

Using a recently developed theory of scintillation that is valid under all fluctuation conditions, including the focussing and saturation regimes, we develop general models for predicting power fluctuations (or aperture averaging) over finite-size collecting apertures. Inner-scale effects are introduced using a modified atmospheric spectrum for refractive-index fluctuations that includes a high-wavenumber bump. Where comparisons can be made, these models of aperture averaging are in good agreement with previous asymptotic models and experimental data. In addition to the aperture-averaging factor, we calculate the temporal spectrum associated with power fluctuations over various aperture sizes and conditions of turbulence. These later results clearly show the transfer of power distribution from high to low frequencies as the size of the collecting aperture is increased. The transfer of power is more pronounced in the saturation regime where high frequencies (fastest fluctuations) can be averaged out even for relatively small apertures.     

Boundary from Bulk Integrability in Three Dimensions: 3D Reflection Maps from Tetrahedron Maps

We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process on the Sierpinski gasket in the presence of a variable speed boundary. We obtain, at the hydrodynamics level, the heat equation evolving on the Sierpinski gasket with either Dirichlet or Neumann boundary conditions, depending on whether the reservoirs are fast or slow. For a particular strength of the boundary dynamics we obtain linear Robin boundary conditions. As for the fluctuations, we prove that, when starting from the stationary measure, namely the product Bernoulli measure in the equilibrium setting, they are governed by Ornstein-Uhlenbeck processes with the respective boundary conditions.

     

正交偶极声波测井换能器有限元分析*

三叠片型换能器是正交偶极声波测井仪器的重要组成部分。换能器的性能直接影响声波测井数据的质量。本文在前人工作基础上,针对三叠片型声波测井发射换能器长度方向的一阶弯曲振动工作模式,利用有限元方法,模拟了换能器结构尺寸和边界条件变化对换能器性能的影响。结果显示,结构尺寸和边界条件对换能器的谐振频率和电导值均有不同程度的影响。参考数值模拟结果,选取合适的结构尺寸参数和边界固定方式,可以调整和选择正交偶极声波测井仪器发射换能器工作频率和最大发射效率。本文研究结果对三叠片型换能器的优化设计有较好的指导意义。     

Self-organized critical earthquake model with moving boundary

A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center of the boundary. As a result, all avalanches grow in equivalent conditions and the avalanche size distribution obeys excellent finite size scaling. Though the recurrence time distribution of the time series of avalanche sizes obeys well both the scaling forms recently observed in analysis of the real data of earthquakes, it is found that the scaling function decays only exponentially in contrast to a generalized gamma distribution observed in the real data analysis. The non-conservative version of the model shows periodicity even with open boundary.     

Stochastic void coarsening

The random nature of diffusing jumps and cascade occurrence produce stochastic fluctuations of the point-defect fluxes. The effect of such fluctuations on the kinetics of void growth is investigated in the present paper. It is found that the non-linear coupling between the stochastic fluctuations and the void sizes may lead to the instability of void evolution within the mean-field theory, when the sizes of voids and their growth rates are both relatively small. The growth rate of voids becomes dominated by the stochastic component, causing the smaller voids to shrink away. This effect is investigated in terms of a non-equilibrium phase transition induced by a purely random stochastic noise. The derived conditions for this non-equilibrium transition are compared favourably with experimental observations. Received: 5 June 2000 / Accepted: 9 October 2000 / Published online: 21 March 2001     

High-Reynolds-number turbulent-boundary-layer wall pressure fluctuations with skin-friction reduction by air injection

The hydrodynamic pressure fluctuations that occur on the solid surface beneath a turbulent boundary layer are a common source of flow noise. This paper reports multipoint surface pressure fluctuation measurements in water beneath a high-Reynolds-number turbulent boundary layer with wall injection of air to reduce skin-friction drag. The experiments were conducted in the U.S. Navy's Large Cavitation Channel on a 12.9-m-long, 3.05-m-wide hydrodynamically smooth flat plate at freestream speeds up to 20 ms and downstream-distance-based Reynolds numbers exceeding 200 x 10(6). Air was injected from one of two spanwise slots through flush-mounted porous stainless steel frits (approximately 40 microm mean pore diameter) at volume flow rates from 17.8 to 142.5 l/s per meter span. The two injectors were located 1.32 and 9.78 m from the model's leading edge and spanned the center 87% of the test model. Surface pressure measurements were made with 16 flush-mounted transducers in an "L-shaped" array located 10.7 m from the plate's leading edge. When compared to no-injection conditions, the observed wall-pressure variance was reduced by as much as 87% with air injection. In addition, air injection altered the inferred convection speed of pressure fluctuation sources and the streamwise coherence of pressure fluctuations.     

Stokes Flows under Random Boundary Velocity Excitations

A viscous Stokes flow over a disc under random fluctuations of the velocity on the boundary is studied. We give exact Karhunen-Loève (K-L) expansions for the velocity components, pressure, stress, and vorticity, and the series representations for the corresponding correlation tensors. Both the white noise fluctuations, and general homogeneous random excitations of the velocities prescribed on the boundary are studied. We analyze the decay of correlation functions in angular and radial directions, both for exterior and interior Stokes problems. Numerical experiments show the fast convergence of the K-L expansions. The results indicate that ignoring the stochastic fluctuations in boundary conditions dramatically underestimates the variance of the velocity and pressure in the interior/exterior of the domain. The support of the RFBR Grant N 06-01-00498 is kindly acknowledged.     

Model experiments for the Czochralski crystal growth technique

A lot of the physical and the numerical modeling of Czochralski crystal growth is done on the generic Rayleigh-Bénard system. To better approximate the conditions in a Czochralski puller, the influences of a rounded crucible bottom, deviations of the thermal boundary conditions from the generic case, crucible and/or crystal rotation, and the influence of magnetic fields are often studied separately. The present contribution reviews some of these topics while concentrating on studies of the flow and related temperature fluctuations in systems where a rotating magnetic field (RMF) was applied. The three-dimensional convective patterns and the resulting temperature fluctuations will be discussed both for the mere buoyant case and for the application of an RMF. It is shown that a system between a Rayleigh-Bénard and a more realistic configuration, which is still cylindrical but whose surface is partially covered by a crystal model, behaves much the same as a Rayleigh-Bénard system. An RMF can be used to damp the temperature fluctuations. Secondly, a more Czochralski-like system is examined. It turns out that the RMF does not provide the desired damping of the temperature fluctutions in the parameter range considered.     

Repulsive and attractive critical Casimir forces

When confining vacuum fluctuations between two identical walls, the Casimir force manifests itself as a mutual attraction of the walls. When confining concentration fluctuations of a binary liquid mixture, an analogous force should exist near the critical temperature T_C; it is called the critical Casimir force. Here we show experimentally that this purely entropic force can be either attractive or repulsive, depending on the boundary conditions for the fluctuations. For symmetrical boundary conditions an attractive force is found while asymmetrical ones lead to a repulsive force. This is observed directly by confining the fluctuations in a thin wetting film. Depending on the boundary conditions either a thinning or a thickening of the film is observed when T→T_C.     

Computer simulation of the non-local dielectric function of polar liquids: boundary conditions revisited

For the calculation of ε(k) via the correlation function of the bound charge density fluctuations or the ratio of the bound charge density to an external charge density, a generalized form of the fluctuation dissipation theorem is derived which accounts for different types of boundary conditions through a modified Green's function. It is demonstrated for the case of an interaction site model of water that it is possible to obtain consistent results for the non-local dielectric function with different types of boundary conditions. This is shown by calculating ε(k) both from the correlation function 〈ρ_b(k)ρ_b(-k)〉 and from the dielectric response to an external electric field.     

Symmetry breaking in de Sitter spacetime by antipodal symmetric and antisymmetric fields

The symmetry behaviour of a ϵø⁴ model in the identified de Sitter space is considered. The different boundary conditions imposed on the quantum field correspond to antipodally symmetric and antisymmetric cases. For both cases, the variance of the quantum fluctuations around a constant background field is evaluated using a result on the conformal transformation of the effective action.     

The phase separation line in the two-dimensional Ising model

We prove that, at low temperature, the line of separation between the two pure phases shows large fluctuations in shape. This implies the translation invariance of the correlation functions associated with some non translation invariant boundary conditions and should be a peculiarity of the dimensionality of the model.This work has been partially supported by the Consiglio Nazionale delle Ricerche (Gruppo Nazionale per l'Analisi Funzionale): CNR(GNAFA).