A Comment on the Light-Cone Vacuum in 1+1 Dimensional Super-Yang–Mills Theory

The discrete light-cone quantization (DLCQ) of a supersymmetric gauge theory in 1+1 dimensions is discussed, with particular attention given to the inclusion of the gauge zero mode. Interestingly, the notorious zero-mode problem is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the nonsupersymmetric case. An analysis of the vacuum structure is provided by deriving the effective quantum mechanical Hamiltonian of the gauge zero mode. It is shown that the inclusion of the zero modes of the adjoint scalars and fermions is crucial for probing the phase properties of the vacua. We find that the ground-state energy is zero and thus consistent with unbroken supersymmetry and conclude that the light-cone Fock vacuum is unchanged with or without the presence of matter fields.     

Eigenfunction Expansions on Geodesic Balls and Rank One Symmetric Spaces of Compact Type

We find sharp conditions for the pointwise convergence ofeigenfunction expansions associated with the Laplace operator and otherrotationally invariant differential operators. Specifically, we considerthis problem for expansions associated with certain radially symmetricoperators and general boundary conditions and the problem in the contextof Jacobi polynomial expansions. The latter has immediate application toFourier series on rank one symmetric spaces of compact type.     

Coupled neutron transport for HZETRN

Exposure estimates inside space vehicles, surface habitats, and high altitude aircrafts exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward–backward (FB) and directionally coupled forward–backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETC-HEDS, FLUKA, and MCNPX, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light ion transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.     

Random Evolutions Are Driven by the Hyperparabolic Operators

We resolve the long-standing problem of describing the multidimensional random evolutions by means of the telegraph equations. This problem was posed by Mark Kac more than 50 years ago and has become the subject of intense discussion among researchers on whether the multidimensional random flights could be described by the telegraph equations similarly to the one-dimensional case. We give the exhaustive answer to this question and show that the multidimensional random evolutions are driven by the hyperparabolic operators composed of the telegraph operators and their integer powers. The only exception is the 2D random flight whose transition density is the fundamental solution to the two-dimensional telegraph equation. The reason of the exceptionality of the 2D-case is explained. We also show that, under the standard Kac’s condition, the governing hyperparabolic operator turns into the generator of the Brownian motion.     

Pointwise fourier inversion: A wave equation approach

Functions of the Laplace operator F(− Δ) can be synthesized from the solution operator to the wave equation. When F is the characteristic function of [0, R ² ], this gives a representation for radial Fourier inversion. A number of topics related to pointwise convergence or divergence of such inversion, as R → ∞, are studied in this article. In some cases, including analysis on Euclidean space, sphers, hyperbolic space, and certain other symmetric spaces, exact formulas for fundamental solutions to wave equations are available. In other cases, parametrices and other tools of microlocal analysis are effective.     

Predicting thermal conductivity of liquid suspensions of nanoparticles (nanofluids) based on rheology

A methodology is proposed for predicting the effective thermal conductivity of dilute suspensions of nanoparticles (nanofluids) based on rheology.The methodology uses the rheological data to infer microstructures of nanoparticles quantitatively,which is then incorporated into the conventional Hamilton-Crosser equation to predict the effective thermal conductivity of nanofluids.The methodology is experimentally validated using four types of nanofluids made of titania nanoparticles and titanate nanotubes dispersed in water and ethylene glycol.And the modified Hamilton-Crosser equation successfully predicted the effective thermal conductivity of the nanofluids.     

Influence of preadsorbed polyelectrolytes on hydrophobic properties of synthetic aluminosilicates

The influence of preadsorbed polyelectrolyte layers on the hydrophilic-hydrophobic properties of synthetic aluminosilicates of a given composition was studied by determining the heat of wetting and considering the respective thermographic data. It was shown that the interactions of polyelectrolytes follow the mechanisms of physical adsorption with the negatively charged sites of the aluminosilicate surface and the mechanism of activated chemisorption with the positively charged sites. It was concluded that cluster mineral-organic structures formed on the modified gels significantly alter physical and chemical properties of their surface, its wettability, and structural-sorption characteristics.     

Asymptotics for the heat equation in the exterior of a shrinking compact set in the plane via Brownian hitting times

Let and let be a continuous, nonincreasing function on satisfying . Consider the heat equation in the exterior of a time-dependent shrinking disk in the plane:

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If there exist constants and a constant 0$"> such that , for sufficiently large , then . The same result is also shown to hold when is replaced by , where . Also, a discrepancy is noted between the asymptotics for the above forward heat equation and the corresponding backward one. The method used is probabilistic.

     

Statistical analysis of the estimation of distance measures

Distance functions serve for quantitative evaluation of the degree of similarity, shape content, symmetry, chirality, and so on. We have developed a general methodology and a general computational tool for the estimation of the value of the distance function and of the error in that estimation, which originates in the experimental uncertainty in the location of the set of points of the studied structure (such as that expressed by the atomic displacement factor in X-ray data analysis).