Conditions for blow-up of solutions of some nonlinear Volterra integral equations

In this paper we give necessary and sufficient conditions for blow-up of solutions for a particular class of nonlinear Volterra equations. We also give some examples.     

On a Lp-estimate for the linearized compressible Navier-Stokes equations with the Dirichlet boundary conditions

In this paper a special L_p-estimate for the linearized compressible Navier-Stokes in the Lagrangian coordinates for the Dirichlet boundary conditions is obtained. The constant in the estimate does not depend on the length of time interval [0,T]. The result is essential to obtain an existence for regular solutions for the nonlinear problem with the lowest class of regularity in L_p-spaces.     

A scheduling policy with maximal stability region for ring networks with spatial reuse

A slotted ring that allows simultaneous transmissions of messages by different users is considered. Such a ring network is commonly called ring withspatial reuse. It can achieve significantly higher throughput than standard token rings but it also raises the issue of fairness since some nodes may be prevented from accessing the ring for long time intervals. Policies that operate in cycles and guarantee that a certain number (quota) of packets will be transmitted by every node in every cycle have been considered before to deal with the fairness issue. In this paper we address the problem of designing a policy that results in a stable system whenever the end-to-end arrival rates are within the stability region of the ring with spatial reuse (the stability region of the ring is defined as the set of end-to-end arrival rates for which there is a policy that makes the ring stable). We provide such a policy, which does not require knowledge of end-to-end arrival rates. The policy is an adaptive version of the quota policies and can be implemented with the same distributed mechanism. We use the Lyapunov test function technique together with methods from the theory of regenerative processes to derive our main results.This research was primarily done while the author was visiting INRIA in Rocquencourt, France. The author wishes to thank INRIA (projects ALGO, MEVAL and REFLECS) for a generous support. Additional support was provided by NSF Grants NCR-9206315 and CCR-9201078 and INT-8912631, and by Grant AFOSR-90-0107, and in part by NATO Grant 0057/89.The research of this author was supported in part by NSF under Grants NCR-9211417 and NCR-9406415, and by the New York State Center for Advanced Technology in Telecommunications, Polytechnic University.     

Navier-stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case

We consider the equations which describe the motion of a viscous compressible fluid, taking into consideration the case of inflow and/or outflow through the boundary. By means of some a priori estimates we prove the existence of a global (in time) solution. Moreover, as a consequence of a stability result, we show that there exist a periodic solution and a stationary solution.     

Origin of the optical contrast in phase-change materials

Several chalcogenide alloys exhibit a pronounced contrast between the optical absorption in the metastable rocksalt and in the amorphous phase. This phenomenon is the basis for their application in optical data storage. Here we present ab initio calculations of the optical properties of GeTe and Ge1Sb2Te4 in the two phases. The analysis of our computations and experimental data reveal the correlation between local structural changes and optical properties as well as the origin of the optical contrast in these materials. We find that the change in optical properties cannot be attributed to a smearing of transition energies as commonly assumed for amorphous semiconductors: the optical contrast between the two phases can only be explained by significant changes in the transition matrix elements.     

Continua with self-rotation nuclei: evolution of asymmetric fields

We present a consistent theory of continua with defect distribution including the density of rotation nuclei. The elastic and self-fields of stresses and strains become asymmetric; the tensor of incompatibility also becomes asymmetric. We derive the dislocation–stress relations and the equations of motion related to the momentum and moment of momentum. Some applications important for earthquake engineering are presented.     

Thermodynamical evaluation of usefulness of future hydrocarbon fuels for use in compression ignition engines

The paper discusses the issues of the influence of the fuel spray formation on the generation of self-ignition spots and the development of pre-flame processes in the cylinder of a model diesel engine. The investigations were carried out for a standard diesel fuel and two other types of fuel that were mixtures of ethanol, butanol, and diethylether in a variety of proportions. By applying optical methods of analysis, the authors determined the geometrical indexes of the injected fuel spray as well as fuel mass distribution in the longitudinal and transverse cross section of the fuel spray during the injection process. The location and number of the self-ignition spots in the combustion chamber were evaluated on the basis of a comparison under various conditions: in presence of the charge swirl and at the lack of it. Research conducted for the single-cylinder engine confirmed the possibility of the use of diesel-like fuels for compression ignition engines.

     

Hydrogen Storage Materials: Room‐Temperature Wet‐Chemistry Approach toward Mixed‐Metal Borohydrides

The poor kinetics of hydrogen evolution and the irreversibility of the hydrogen discharge hamper the use of transition metal borohydrides as hydrogen storage materials, and the drawbacks of current synthetic methods obstruct the exploration of these systems. A wet‐chemistry approach, which is based on solvent‐mediated metathesis reactions of precursors containing bulky organic cations and weakly coordinating anions, leads to mixed‐metal borohydrides that contain only a small amount of “dead mass”. The applicability of this method is exemplified by Li[Zn₂(BH₄)₅] and M[Zn(BH₄)₃] salts (M=Na, K), and its extension to other systems is discussed.     

Development of zinc alkyl/air systems as radical initiators for organic reactions

This paper reports a series of comparative experiments on the activity of carbon- and oxygen-centred radical species in a model reaction of the radical addition of THF to imines mediated by a series of zinc alkyl/air reaction systems. The study strongly contradicts the notion that generally R˙ radicals are the initiating species in organic reactions mediated by R_nM/air systems, and simultaneously demonstrates that oxygen-centred radical species are the key intermediates responsible for the initiation process. In addition, a new efficient RZn(L)/air initiating system for radical organic reactions exampled by a model reaction of radical addition of THF to imines is developed. Moreover, the isolation and structural characterization of the first zinc alkylperoxide supported by a carboxylate ligand, [Zn₄(μ₃-OOtBu)₃(μ₄-O)(O₂CEt)₃]₂, as well as the novel octanuclear zinc oxo(alkoxide) aggregate with entrapped O–THF species, [Zn₄(μ₄-O)(μ₃-2-O–THF)(O₂CEt)₅]₂, provide clear mechanistic signatures for the mode of function of the RZn(O₂CR′)/air system.