On the <Emphasis Type="Italic">C</Emphasis>*-Algebra of a Locally Injective Surjection and its KMS States

It is shown that a locally injective surjection on a compact metric space is a factor of a local homeomorphism in such a way that the associated C*-algebras are isomorphic. This is subsequently used to obtain upper and lower bounds for the possible β-values of KMS-states for generalized gauge actions on the C*-algebra.     

Bounds on phase velocities of guided modes in open waveguides

Guiding of waves along cylinders with a surface impedance or along low velocity sound channels lead to eigenvalue problems in unbounded domains. Variational and comparison methods are used to find bounds on the discrete eigenvalues, which are related to the phase velocities of the guided modes. The variational methods yield upper bounds only, but they can be applied systematically to a large class of problems. The comparison methods yield upper and lower bounds, but are restricted to a smaller class of problems.     

Ideal Mixture Approximation of Cluster Size Distributions at Low Density

We consider an interacting particle system in continuous configuration space. The pair interaction has an attractive part. We show that, at low density, the system behaves approximately like an ideal mixture of clusters (droplets): we prove rigorous bounds (a) for the constrained free energy associated with a given cluster size distribution, considered as an order parameter, (b) for the free energy, obtained by minimising over the order parameter, and (c) for the minimising cluster size distributions. It is known that, under suitable assumptions, the ideal mixture has a transition from a gas phase to a condensed phase as the density is varied; our bounds hold both in the gas phase and in the coexistence region of the ideal mixture. The present paper improves our earlier results by taking into account the mixing entropy.     

Universal Bounds for the Littlewood-Paley First-Order Moments of the 3D Navier-Stokes Equations

We derive upper bounds for the infinite-time and space average of the L ¹-norm of the Littlewood-Paley decomposition of weak solutions of the 3D periodic Navier-Stokes equations. The result suggests that the Kolmogorov characteristic velocity scaling, U_k ~ e^1/3 k^-1/3{\mathbf{U}_\kappa\sim\epsilon^{1/3} \kappa^{-1/3}} , holds as an upper bound for a region of wavenumbers near the dissipative cutoff.     

Upper bounds on superpartner masses from upper bounds on the Higgs boson mass

The LHC is putting bounds on the Higgs boson mass. In this Letter we use those bounds to constrain the minimal supersymmetric standard model (MSSM) parameter space using the fact that, in supersymmetry, the Higgs mass is a function of the masses of sparticles, and therefore an upper bound on the Higgs mass translates into an upper bound for the masses for superpartners. We show that, although current bounds do not constrain the MSSM parameter space from above, once the Higgs mass bound improves big regions of this parameter space will be excluded, putting upper bounds on supersymmetry (SUSY) masses. On the other hand, for the case of split-SUSY we show that, for moderate or large tanβ, the present bounds on the Higgs mass imply that the common mass for scalars cannot be greater than 10(11) GeV. We show how these bounds will evolve as LHC continues to improve the limits on the Higgs mass.     

中型tokamak中快离子的约束

利用三个运动常数发展了导心轨道程序GCORBIT. 该程序在计算轴对称tokamak中带电粒子导心轨道的同时，也考虑了纵场纹波和螺距角散射的效应. GCORBIT可以用来计算轴对称tokamak中的导心轨道，计算速度空间的损失区，计算快离子的损失份额. 与已有的工作相比，GCORBIT计算出的速度空间损失区包括了多种效应：偏滤器位形中的非闭合轨道、由于导心轨道与第一壁相交引起的首次轨道损失、纵场纹波局部磁阱俘获、纹波随机扩散以及速度空间不连续约束区导致的螺距角散射效应增强. GCORBIT程序已被用于分析“先进超导托卡马克实验装置”(experimental advanced superconducting tokamak,EAST) tokamak中快离子的约束. 并讨论其中的某些数值计算结果. 关键词： 导心轨道程序 快离子约束 tokamak     

Limits of applicability of Gupta's theory

The applicability of the quantum theory of a weak gravitational field (Gupta's theory) is examined on the basis of the quasiclassical generally relativistic point of view. It is shown that in standard quantum theory the energy of a particle cannot be arbitrary but is bounded both below and above. These bounds arise because it is impossible to treat the region of interaction of elementary particles as a part of flat space. The lower limit depends on the curvature tensor of the external gravitational field, while the upper is determined by the gravitational field of the particle itself.     

Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields

Rigorous upper bounds are derived for large-scale turbulent flame speeds in a prototypical model problem. This model problem consists of a reaction-diffusion equation with KPP chemistry with random advection consisting of a turbulent unidirectional shear flow. When this velocity field is fractal with a Hurst exponentH with 0<H<1, the almost sure upper bounds suggest that there is an accelerating large-scale turbulent flame front with the enhanced anomalous propagation lawy=C _H t ^1+H for large renormalized times. In contrast, a similar rigorous almost sure upper bound for velocity fields with finite energy yields the turbulent flame propagation law within logarithmic corrections. Furthermore, rigorous theorems are developed here which show that upper bounds for turbulent flame speeds with fractal velocity fields are not self-averaging, i.e., bounds for the ensemble-averaged turbulent flame speed can be extremely pessimistic and misleading when compared with the bounds for every realization.     

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.     

The upper bound function of nonadiabatic dynamics in parametric driving quantum systems

The adiabatic control is a powerful technique for many practical applications in quantum state engineering, light-driven chemical reactions and geometrical quantum computations. This paper reveals a speed limit of nonadiabatic transition in a general time-dependent parametric quantum system that leads to an upper bound function which lays down an optimal criteria for the adiabatic controls. The upper bound function of transition rate between instantaneous eigenstates of a time-dependent system is determined by the power fluctuations of the system relative to the minimum gap between the instantaneous levels. In a parametric Hilbert space, the driving power corresponds to the quantum work done by the parametric force multiplying the parametric velocity along the parametric driving path. The general two-state time-dependent models are investigated as examples to calculate the bound functions in some general driving schemes with one and two driving parameters. The calculations show that the upper bound function provides a tighter real-time estimation of nonadiabatic transition and is closely dependent on the driving frequencies and the energy gap of the system. The deviations of the real phase from Berry phase on different closed paths are induced by the nonadiabatic transitions and can be efficiently controlled by the upper bound functions. When the upper bound is adiabatically controlled, the Berry phases of the electronic spin exhibit nonlinear step-like behaviors and it is closely related to topological structures of the complicated parametric paths on Bloch sphere.     

Two-sided bounds on the free energy from local states in Monte Carlo simulations

We show that a precise assessment of free energy estimates in Monte Carlo simulations of lattice models is possible by using cluster variation approximations in conjunction with the local states approximations proposed by Meirovitch. The local states method (LSM) utilizes entropy expressions which recently have been shown to correspond to a converging sequence of upper bounds on the thermodynamic limit entropy density (i.e., entropy per lattice site), whereas the cluster variation method (CVM) supplies formulas that in some cases have been proven to be, and in other cases are believed to be, lower bounds. We have investigated CVM-LSM combinations numerically in Monte Carlo simulations of the two-dimensional Ising model and the two-dimensional five-states ferromagnetic Potts model. Even in the critical region the combination of upper and lower bounds enables an accurate and reliable estimation of the free energy from data of a single run. CVM entropy approximations are therefore useful in Monte Carlo simulation studies and in establishing the reliability of results from local states methods.     

Decay rate of an excited atom in a moving medium

The effect of a uniformly moving medium on the decay rate of an excited atom is calculated. When the local field effects are neglected, the free space decay rate is modified by a factor which is a complicated function of refractive index, permeability, and velocity of the medium. It is shown that the decay rate vanishes if the velocity of the medium exceeds the phase velocity of light in the stationary medium.     

INSTABILITY OF A BOGIE MOVING ON A FLEXIBLY SUPPORTED TIMOSHENKO BEAM

The stability of vibration of a bogie uniformly moving along a Timoshenko beam on a viscoelastic foundation has been studied. The bogie has been modelled by a rigid bar of a finite length on two identical supports. Each support consists of a spring and a dashpot connected in parallel. The upper ends of the supports are attached to the bar, whilst the lower ends are mounted onto concentrated masses through which the supports interact with the beam. It is assumed that the masses and the beam are always in contact. It is shown that when the velocity of the bogie exceeds the minimum phase velocity of waves in the beam, the vibration of the system may become unstable. The instability region is found in the space of the system parameters with the help of the D-decomposition method and the principle of the argument. An extended analysis of the effect of the bogie parameters on the model stability has been carried out.     

Optical Formation and Transport of a Local Region with an Increased Content of a Neutral Component in a Photopolymerizable Composite Layer

It has been shown that a local region with an increased concentration of a nonpolymerizable component can be formed in a photopolymerizable composite layer via a diffusion process stimulated by the motion of the area of initiating illumination. Furthermore, it has been demonstrated that this region can be transferred to a given place of the polymerized material. The dependences of the formation path, width, and amplitude of the local inhomogeneity of the nonpolymerizable component on the velocity of the boundary of illumination area along the polymerized layer have been determined by numerical simulation. The results of the experiment have been presented.     

Euclidean quantum gravity on a lattice

We construct a number of related euclidean lattice formulations of quantum gravity. The first version incorporates a path integral over discrete manifolds built out of four-cubes embedded in a higher dimensional flat hypercubic lattice. We show this expression is equal to a corresponding path integral in a local lattice field theory. The field theoretic path integral diverges and lacks a satisfactory vacuum state. This divergence can be interpreted as a consequence of a divergent phase space available for topological fluctuations in the four-manifolds of the original path integral. A modified version of the path integral over manifolds converges. We construct a Schrödinger equation and hamiltonian for the modified theory. The hamiltonian is self-adjoint, but as a result of the large phase space available for topological fluctuations, the hamiltonian's spectrum is probably not bounded from below. We show briefly how the flat enveloping space—time can be removed from most of the theories we present and how matter fields can be included.     

Fracture of a viscous liquid

When a viscous liquid hits a pool of liquid of the same nature, the impact region is hollowed by the shock. Its bottom becomes extremely sharp if increasing the impact velocity, and we report that the curvature at that place increases exponentially with the flow velocity, in agreement with a theory by Jeong and Moffatt. Such a law defines a characteristic velocity for the collapse of the tip, which explains both the cusplike shape of this region, and the instability of the cusp if increasing (slightly) the impact velocity. Then, a film of the upper phase is entrained inside the pool. We characterize the critical velocity of entrainment of this phase and compare our results with recent predictions by Eggers.     

Path sums for Brownian motion and quantum mechanics

A treatment is given of classical Brownian motion in phase space based on path summation. It treats efficiently the usual exactly solvable cases when the external force is linear in momentum or position. The method might be useful for generating approximations for more complicated external forces. A path sum formalism is given to generate the Wigner propagator in the Wigner-Weyl phase space formulation of quantum mechanics. The short-time Brownian and Wigner propagators bear a generic similarity.     

Bounding the set of quantum correlations

We introduce a hierarchy of conditions necessarily satisfied by any distribution P_{alphabeta} representing the probabilities for two separate observers to obtain outcomes alpha and beta when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Among other applications, our approach can be used to obtain upper bounds on the quantum violation of an arbitrary Bell inequality. It yields, for instance, tight bounds for the violations of the Collins et al. inequalities.     

On Measuring and Modeling Local Average Particle Velocities for particle ensembles in classifying systems

In most multi-phase flow problems, the particulate phase is exposed to an external field which causes dispersion. Therefore, local velocity measurements of the disperse phase are no longer equivalent with respect to averaging in time and averaging in volume. While the local time-averaged velocity still characterizes the transport of the ensemble in the Eulerian sense, one has to be be careful in modeling this velocity average by considering the ensemble's composition. It is shown for different particle ensembles that the conventional particle velocity average M_1,0 calculated with respect to the dispersion relationship and a particle size number density distribution is far below the measured ensemble average; the deviation depends on the width of the particle size distribution. It is deduced that Eulerian particle velocity values referring to a certain time interval can be modeled by a ratio of velocity moments M_2,0/M_1,0 calculated with particle size number distributions referring to a certain probe volume. This relationship was confirmed by measurements.     

Supercooling across first-order phase transitions in vortex matter

Hysteresis in cycling through first-order phase transitions in vortex matter, akin to the well-studied phenomenon of supercooling of water, has been discussed in literature. Hysteresis can be seen while varying either temperature T or magnetic field H (and thus the density of vortices). Our recent work on phase transitions with two control variables shows that the observable region of metastability of the supercooled phase would depend on the path followed in H-T space, and will be larger when T is lowered at constant H compared to the case when H is lowered at constant T. We discuss the effect of isothermal field variations on metastable supercooled states produced by field-cooling. This path dependence is not a priori applicable to metastability caused by reduced diffusivity or hindered kinetics.