On triangular subalgebras of groupoidC*-algebras

Let ℬ be an AFC*-algebra with Stratila-Voiculescu masaD and letU be a maximal triangular subalgebra of ℬ with diagonalD. Peters, Poon and Wagner showed thatU need not be aC*-subdiagonal subalgebra of ℬ in the sense of Kawamura and Tomiyama. We investigate and explain this phenomena here from the perspective of groupoidC*-algebras by representing257-7 as the “incidence algebra” associated with a topological partial order. A number of examples are given showing what can keep a maximal triangular algebra from beingC*-subdiagonal. Supported by a grant from the National Science Foundation.     

Shape distortion of space structures,postulates and controversy

An attempt to resolve the controversy connected with the definition of shape distortion of space structures is proposed by generalization of the different approaches. A generalization of the criterion for shape control robustness of space structures is also proposed.On leave from Department of Aerospace Engineering, Technion, Haifa, Israel.     

Asymptotic stability of a mechanical robotics model with damping and delay

In this paper we study the asymptotic stability of a mechanical robotics model with damping and delay. This model yields a certain linear third order delay differential equation. In proving our results we make use of Pontryagin's theory for quasi-polynomials.     

Safe solution of a car-following problem

A system of nonlinear car-following equations with random delay times is considered. Conditions which ensure a safe response (according to a natural safety criterion) are given.     

Numerical methods for discontinuous linear two point boundary value problems

Numerical methods for the solution of discontinuous two point boundary value problems are developed.     

Efficient stochastic simulations of complex reaction networks on surfaces

Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations, which are based on the mean-field approximation. However, in case that the surface is partitioned into a large number of disconnected microscopic domains, the number of reactants in each domain becomes small and it strongly fluctuates. This is, in fact, the situation in the interstellar medium, where some crucial reactions take place on the surfaces of microscopic dust grains. In this case rate equations fail and the simulation of surface reactions requires stochastic methods such as the master equation. However, in the case of complex reaction networks, the master equation becomes infeasible because the number of equations proliferates exponentially. To solve this problem, we introduce a stochastic method based on moment equations. In this method the number of equations is dramatically reduced to just one equation for each reactive species and one equation for each reaction. Moreover, the equations can be easily constructed using a diagrammatic approach. We demonstrate the method for a set of astrophysically relevant networks of increasing complexity. It is expected to be applicable in many other contexts in which problems that exhibit analogous structure appear, such as surface catalysis in nanoscale systems, aerosol chemistry in stratospheric clouds, and genetic networks in cells.     

A cryostat design for radiation damage experiments at low temperature

Abstract

A cryostat for electron irradiations at liquid hydrogen or helium temperatures is described. The cryostat uses two concentric liquid coolant containers, of which the inner reservoir is sealed and acts as a heat exchanger through ebullition and recondensation of the coolant gas. This allows irradiations with a power input from the beam of up to a few watts, and when the sample is thermally isolated allows it to be annealed up to room temperature.     

Gauge fields,ripples and wrinkles in graphene layers

We analyze elastic deformations of graphene sheets which lead to effective gauge fields acting on the charge carriers. Corrugations in the substrate induce stresses which, in turn, can give rise to mechanical instabilities and the formation of wrinkles. Similar effects may take place in suspended graphene samples under tension.     

Experimental study of parametric autoresonance in Faraday waves

The excitation of large amplitude nonlinear waves is achieved via parametric autoresonance of Faraday waves. We experimentally demonstrate that phase locking to low amplitude driving can generate persistent high-amplitude growth of nonlinear waves in a dissipative system. The experiments presented are in excellent agreement with theory.