394 research outputs found
Representations of solutions of the wave equation based on relativistic wavelets
A representation of solutions of the wave equation with two spatial
coordinates in terms of localized elementary ones is presented. Elementary
solutions are constructed from four solutions with the help of transformations
of the affine Poincar\'e group, i.e., with the help of translations, dilations
in space and time and Lorentz transformations. The representation can be
interpreted in terms of the initial-boundary value problem for the wave
equation in a half-plane. It gives the solution as an integral representation
of two types of solutions: propagating localized solutions running away from
the boundary under different angles and packet-like surface waves running along
the boundary and exponentially decreasing away from the boundary. Properties of
elementary solutions are discussed. A numerical investigation of coefficients
of the decomposition is carried out. An example of the field created by sources
moving along a line with different speeds is considered, and the dependence of
coefficients on speeds of sources is discussed.Comment: submitted to J. Phys. A: Math. Theor., 20 pages, 6 figure
Probabilistic Analysis of Wear of Polymer Material Used in Medical Implants
Probabilistic methods are applied to the study of fatigue wear of sliding surfaces. A variance of time to failure (to occurrence of maximum allowable wear depth) is evaluated as a function of a mean wear rate of normal wear and a size of wear particles. A method of estimating probability of failure-free work during a certain time interval (reliability) is presented. An effect of the bedding-in phase of wear on the reliability is taken into account. Experimental data for Ultra High Molecular Weight Polyethylene (UHMWPE) cups of artificial hip implants is used to make numerical calculations
Localized Solutions of the Non-Linear Klein-Gordon Equation in Many Dimensions
We present a new complex non-stationary particle-like solution of the
non-linear Klein-Gordon equation with several spatial variables. The
construction is based on reduction to an ordinary differential equation.Comment: 4 pages, 1 figur
Transient quantum evolution of 2D electrons under photoexcitation of a deep center
We have considered the ballistic propagation of the 2D electron Wigner
distribution, which is excited by an ultrashort optical pulse from a
short-range impurity into the first quantized subband of a selectively-doped
heterostructure with high mobility. Transient ionization of a deep local state
into a continuum conduction c-band state is described. Since the quantum nature
of the photoexcitation, the Wigner distribution over 2D plane appears to be an
alternating-sign function. Due to a negative contribution to the Wigner
function, the mean values (concentration, energy, and flow) demonstrate an
oscillating transient evolution in contrast to the diffusive classical regime
of propagation.Comment: 8 pages, 6 figures, pape
Collective and static properties of model two-component plasmas
Classical MD data on the charge-charge dynamic structure factor of
two-component plasmas (TCP) modeled in Phys. Rev. A 23, 2041 (1981) are
analyzed using the sum rules and other exact relations. The convergent power
moments of the imaginary part of the model system dielectric function are
expressed in terms of its partial static structure factors, which are computed
by the method of hypernetted chains using the Deutsch effective potential.
High-frequency asymptotic behavior of the dielectric function is specified to
include the effects of inverse bremsstrahlung. The agreement with the MD data
is improved, and important statistical characteristics of the model TCP, such
as the probability to find both electron and ion at one point, are determined.Comment: 25 pages, 6 figures, 5 tables. Published in Physical Review E
http://link.aps.org/abstract/PRE/v76/e02640
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