Hitting times with taboo for a random walk

For a symmetric homogeneous and irreducible random walk on the d-dimensional integer lattice, which have a finite variance of jumps, we study passage times (taking values in [0,??]) determined by a starting point x, a hitting state y, and a taboo state z. We find the probability that these passage times are finite, and study the distribution tail. In particular, it turns out that, for the above-mentioned random walks on ? ^d except for a simple random walk on ?, the order of the distribution tail decrease is specified by dimension d only. In contrast, for a simple random walk on ?, the asymptotic properties of hitting times with taboo essentially depend on mutual location of the points x, y, and z. These problems originated in recent study of a branching random walk on ? ^d with a single source of branching.     

Truncated Trust Region Methods Based on Preconditioned Iterative Subalgorithms for Large Sparse Systems of Nonlinear Equations

This paper is devoted to globally convergent methods for solving large sparse systems of nonlinear equations with an inexact approximation of the Jacobian matrix. These methods include difference versions of the Newton method and various quasi-Newton methods. We propose a class of trust region methods together with a proof of their global convergence and describe an implementable globally convergent algorithm which can be used as a realization of these methods. Considerable attention is concentrated on the application of conjugate gradient-type iterative methods to the solution of linear subproblems. We prove that both the GMRES and the smoothed COS well-preconditioned methods can be used for the construction of globally convergent trust region methods. The efficiency of our algorithm is demonstrated computationally by using a large collection of sparse test problems.     

Nonlinear instability during the isothermal draw of optical fibers

The nonlinear instability of the isothermal draw of optical fibers from cylindric preforms is studied. The unsteady model of the process is solved numerically, accounting for the effects of inertia, gravity and surface forces. The effect of viscosity and gravity on the nonlinear stability of the process is studied. The possibility of draw resonance occurring is shown for a rate ratio much lower than the critical one, obtained when solving the simplified model. The proposed solution can be used to study technological stability and to model the draw of fibers of other materials which behave as Newtonian fluids.     

From realistic to simple models of fluids. III. Primitive models of carbon dioxide,hydrogen sulphide and acetone,and their properties

Recently developed methodology to construct primitive models of associating fluids as direct descendants of complex realistic intermolecular potential functions [L. Vl?ek, I. Nezbeda. Molec. Phys., 102, 485 (2004).] is extended to polar fluids and applied to three substances of practical importance: quadrupolar carbon dioxide, and dipolar hydrogen sulphide and acetone. It is shown that the structural properties (in terms of the site–site correlation functions) of the primitive models of polar fluids reproduce very well those of their parent realistic models but, nonetheless, they perform worse than in the case of associating fluids. A number of thermodynamic properties of the developed models obtained by computer simulations is also reported (for their later use in theoretical investigation) and discussed.     

Experimental study of the dynamics of penetration of a solid body into a soil medium

An experimental system is developed to determine the main parameters of the impact and penetration of a solid deformable body into a soft soil medium. This system is based on the technique of an inverse experiment with a measuring rod and the technique of a direct experiment with photo recording and the application of a shadow picture of the interaction of a striker with a soil target. To verify these techniques, the collision of a solid body with soil is studied by a numerical calculation and the time intervals in which the change of the resistance force is proportional to the penetration velocity squared are determined. The penetration resistance coefficients determined in direct and inverse experiments are shown to agree with each other in the collision velocity range 80–400 m/s, which supports the validity of the techniques and the reliability of measuring the total load.