Probability of boundary conditions in quantum cosmology

One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler–DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler–DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.     

Application of audience-seats characteristics to the sound field analysis for large enclosures

The analysis of the sound field of a hall including the effect of audience seats has difficulties in computing time and memory. Although extensive investigations have been conducted for analyzing sound fields, there is scarcely any report dealing with the sound field including this effect. The main cause may be the complex shape and amount of materials of the audience seats. However, there is a possibility that periodical grooved structures like seat rows can be replaced by an appropriate imaginary boundary with an impedance of quasi-local reaction at the top of seats. The purpose of this research is to reduce the calculation load of acoustical analysis by treating the seat rows as an imaginary-impedance boundary which is almost equivalent to the characteristics of audience seats. The SDE filter, which can express excess attenuation caused by seat rows, is proposed and some applications to both the geometrical and wave theoretical methods are presented. To examine the validity of this method, some numerical examples calculated using an image method are discussed in comparison with the measured data. Furthermore, the numerical results of its application to the boundary element method are presented and discussed in terms of its effectiveness and validity.     

Mixed boundary value problems for the stationary magnetohydrodynamics model of a viscous heat-conducting fluid

The boundary value problem for the stationary magnetohydrodynamics model of a viscous heatconducting fluid considered under inhomogeneous mixed boundary conditions for an electromagnetic field and the temperature and Dirichlet condition for the velocity is investigated. This problem describes the flow of an electricaland heat-conducting liquid in a bounded three-dimensional domain the boundary of which consists of several parts with different thermoand electrophysical properties. Sufficient conditions imposed on the initial data to provide for global solvability of the problem and local uniqueness of its solution are established.     

Gutzwiller study of spin-1 bosons in an optical lattice under a magnetic field

We study spin-1 bosons in an optical lattice under a magnetic field with the Gutzwiller approximation for the Bose-Hubbard model. Phase boundary curves between superfluids and Mott insulators depend continuously on the magnetic field, and this provides better results than those obtained with the perturbative mean-field approximation. The phase boundary curve as a function of magnetic field has a sharp cusp structure under certain circumstances. In superfluid phases, both the spin magnetizations and fluctuations in the total number of bosons show strong magnetic field dependence, which is related to the fact that both first-and second-order transitions appear on the phase boundary curve according to the magnetic field.     

Continuation of acoustic near-fields

This paper deals with the analytic continuation of a coherent pressure field specified on a finite sheet located close to and conformal to the surface of a vibrator. This analytic continuation is an extension or extrapolation of the given (measured) field into a region outside and tangential to the original finite sheet, and is based on the Green's function (the transfer function) relating acoustic quantities on the two conformal surfaces. The continuation of the measured pressure field is an inverse problem that requires the use or regularization theory, especially when noise is present in the data. An iteration algorithm is presented that is successful in continuing the pressure field into the tangential sheet. The results are accurate close to the original boundary and taper (decay) toward zero with distance away from it. The algorithm is tested on numerical and experimental data from a point-driven rectangular plate. Results show the successful extrapolation (continuation) of this data into an area nearly double that of the original pressure field. This algorithm is not limited to planar surfaces and can be applied to arbitrarily shaped surfaces.     

Structure and stationary dynamics of the interphase boundary in an La2CuO4 antiferromagnet

The structure of an interphase boundary is studied theoretically. The external magnetic field normal to the Cu-O layers at which an interphase boundary is formed in the La₂CuO₄-type four-sublattice antiferromagnet is determined. The effect of interplanar interactions on the structure of the interphase boundary is analyzed. The dependence of the stationary dynamics of this boundary on the external magnetic field is investigated.     

Boundary conditions as Dirac constraints

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints, which is a new feature in the context of constrained systems. Constructing the Dirac brackets and the reduced phase space structure for different boundary conditions, we show why mode expanding and then quantizing a field theory with boundary conditions is the proper way. We also show that in a quantized field theory subjected to the mixed boundary conditions, the field components are non-commutative. Received: 16 October 2000 / Revised version: 8 January 2001 / Published online: 23 February 2001     

The Solutions for the Boundary Layer Problem of Boltzmann Equation in a Half-Space

We study the half space boundary layer problem for Boltzmann equation with cut-off potentials in all the cases −3<γ≤1, while the boundary condition is imposed on the incoming particles of Dirichlet type, and the solution is assumed to approach to a global Maxwellian at the far field. The same as for cut-off hard sphere model, there is an implicit solvability condition on the boundary data which gives the co-dimensions of the boundary data in terms of positive characteristic speeds.     

Numerical Simulation on a Possible Formation Mechanism of Interplanetary Magnetic Cloud Boundaries

The formation mechanism of the interplanetary magnetic cloud (MC) boundaries is numerically investigatedby simulating the interactions between an MC of some initial momentum and a local interplanetary current sheet.The compressible 2.5D MHD equations are solved. Results show that the magnetic reconnection process is a possibleformation mechanism when an MC interacts with a surrounding current sheet. A number of interesting features arefound. For instance, the front boundary of the MCs is a magnetic reconnection boundary that could be caused by adriven reconnection ahead of the cloud, and the tail boundary might be caused by the driving of the entrained flowas a result of the Bernoulli principle. Analysis of the magnetic field and plasma data demonstrates that at these twoboundaries appear large value of the plasma parameterβ, clear increase of plasma temperature and density, distinctdecrease of magnetic magnitude, and a transition of magnetic field direction of about 180 degrees. The outcome of thepresent simulation agrees qualitatively with the observational results on MC boundary inferred from IMP-8, etc.     

Numerical Simulation on a Possible Formation Mechanism of Interplanetary Magnetic Cloud Boundaries

The formation med2aniRm of the interplanetary magnetic cloud (MC) boundaries is numerically investigated by simulating the interactions between an MC of some initial momentum and a local interplanetary current sheet.The compressible 2.51:) MHD equations are solved. R~sults show that the magnetic reconnection process is a possible formation mechanism when an MC interacts with a surrounding current sheet. A number of interesting features are found. For instance, the front boundary of the MCs is a magnetic reconnection boundary that could be caused by a driven reconnection ahead of the cloud, and the tail boundary might be caused by the driving of the entrained flow as a result of the Bernoulli principle. Analysis of the magnetic field and plasma data demonstrates that at these two boundaries appear large value of the plasma parameter β, clear increase of plasma temperature and density, distinct decrease of magnetic magnitude, and a transition of maguetic field direction of about 180 degrees. The outcome of the present simulation agrees qualitatively with the observational results on MC boundary inferred from IMP-8, etc.     

On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments

This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem.     

Vibrations of an elastic strip with a rough boundary

A plane problem of steady-state forced vibrations of an elastic strip whose lower boundary contains a rough segment is considered. Using Green’s functions for a strip, the problem is reduced to a system of integral equations with integrals over the rough boundary, which is solved by the boundary-element method. The inverse problem of determining the shape of the rough boundary segment from the data on the displacement field of a certain part of the upper boundary is formulated. By the linearization procedure, the inverse problem is reduced to a Fredholm integral equation of the first kind with a smooth kernel, which is solved by Tikhonov’s regularization method.     

Sound source reconstruction using inverse boundary element calculations

Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularization is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov regularization and parameter-choice methods not requiring an error-norm estimate for choosing the right amount of regularization. Several parameter-choice strategies have been presented lately, but it still remains to be seen how well these can handle industrial applications with real measurement data. In the present work it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation (GCV) approach for the present tire noise studies.     

Lunar tides in the electric field of the atmospheric boundary layer

Investigations are aimed at a search for and an estimation of a correlation between the electric field in the atmospheric boundary layer (ABL) and the lunar tides. The lunar tides and their correlation with the electric field in the ABL can be studied either by accumulation of a large experimental data arrays or by the method of signal reception at spatially separated points. The problem of investigating lunar tide manifestations in the electric field in the ABL is solved using a network of stations for monitoring the vertical electric field strength component, specially constructed models and their consequences, and procedures developed for experimental data processing.     

Microscopic derivation of fluctuation formulas for calculating dielectric constants by simulation

A microscopic derivation using the average Maxwell electric field is given for fluctuation formulas for the dielectric constant of a simulation sample for both periodic and reaction field boundary conditions. The reaction field case is for a spherical cavity reaction field. The derivations put both boundary conditions on an equal footing of microscopic theory and the only nonrigorous part of the derivation is the assumption that the region used to average the electric field is large enough. The fluctuation formula for reaction field boundary conditions is rather different from that used heretofore. The method is applied to a subregion of an isolated spherical system.     

基于区域分解算法的叶顶间隙流场的数值模拟

本文采用Marini－Quarteroni的不重叠区域分解算法和“镶嵌”式间隙网格技术,开发了可计算叶项间隙流场的N－S方程求解程序。通过计算结果同实验显示结果的比较表明,本文的计算方法不仅可以很好地描述叶顶间隙流动的细节,而且在复杂区域流场计算中是非常有效的。本文指出在叶栅存在间隙时,前缘产生什么样的拓扑结构不仅取决于相对间隙的大小,同时也取决于叶栅的负荷情况。     

Computational simulation of wave propagation problems in infinite domains

This paper deals with the computational simulation of both scalar wave and vector wave propagation problems in infinite domains. Due to its advantages in simulating complicated geometry and complex material properties, the finite element method is used to simulate the near field of a wave propagation problem involving an infinite domain. To avoid wave reflection and refraction at the common boundary between the near field and the far field of an infinite domain, we have to use some special treatments to this boundary. For a wave radiation problem, a wave absorbing boundary can be applied to the common boundary between the near field and the far field of an infinite domain, while for a wave scattering problem, the dynamic infinite element can be used to propagate the incident wave from the near field to the far field of the infinite domain. For the sake of illustrating how these two different approaches are used to simulate the effect of the far field, a mathematical expression for a wave absorbing boundary of high-order accuracy is derived from a two-dimensional scalar wave radiation problem in an infinite domain, while the detailed mathematical formulation of the dynamic infinite element is derived from a two-dimensional vector wave scattering problem in an infinite domain. Finally, the coupled method of finite elements and dynamic infinite elements is used to investigate the effects of topographical conditions on the free field motion along the surface of a canyon.     

Casimir Effect in Hemisphere Capped Tubes

In this paper we investigate the vacuum densities for a massive scalar field with general curvature coupling in background of a (2 + 1)-dimensional spacetime corresponding to a cylindrical tube with a hemispherical cap. A complete set of mode functions is constructed and the positive-frequency Wightman function is evaluated for both the cylindrical and hemispherical subspaces. On the base of this, the vacuum expectation values of the field squared and energy-momentum tensor are investigated. The mean field squared and the normal stress are finite on the boundary separating two subspaces, whereas the energy density and the parallel stress diverge as the inverse power of the distance from the boundary. For a conformally coupled field, the vacuum energy density is negative on the cylindrical part of the space. On the hemisphere, it is negative near the top and positive close to the boundary. In the case of minimal coupling the energy density on the cup is negative. On the tube it is positive near the boundary and negative at large distances. Though the geometries of the subspaces are different, the Casimir pressures on the separate sides of the boundary are equal and the net Casimir force vanishes. The results obtained may be applied to capped carbon nanotubes described by an effective field theory in the long-wavelength approximation.