Homogeneous Initial Conditions Research Articles

On the Cauchy problem for thermoelastic plates

The Cauchy problem for an infinite thermoelastic plate with a non-homogeneous governing system and homogeneous initial conditions is solved by means of an area potential. This is the first step in the construction of a potential theory for time-dependent problems for thermoelastic plates, enabling the reduction of various initial-boundary value problems to their versions for the homogeneous system of equations with homogeneous initial conditions, which, in turn, may then be solved by means of dynamic potentials. Copyright © 2006 John Wiley & Sons, Ltd.

Gitterrastermethode mit Strohindex zur Bewertung der Stroheinarbeitung

With grid screen scanning the quality of straw incorporation in a cultivator can be rated. However, an exact comparison needs homogeneous initial straw distribution conditions. To compare ratings, which were gathered from different straw masses per unit of area, the straw was developed and included in the evaluation. In the future it will be possible to assess the straw incorporation quality with a single value, the implement index of a stubble cultivation implement.

Two-dimensional dynamic boundary-value problems for curvilinear thermoviscoelastic bodies

A new numerical-analytical method is proposed and demonstrated using an example of dynamic problems of a thermoviscoelastic body. In the general formulation, the thermoviscoelastic problem is split into three simpler problems. In the first problem, boundary functions that should satisfy only boundary conditions are determined. The second problem with homogeneous boundary conditions and inhomogeneous initial conditions is reduced to an eigenvalue problem by introducing special ξ variables and separating time. This problem is solved by organizing integral superpositions with respect to the angular parameter. A linear algebraic system is obtained as a result of satisfaction of the boundary conditions at points that partition the curvilinear boundary of the body into small segments. After the eigenfunctions and eigenvalues are determined, the third problem with homogeneous boundary and initial conditions is solved by spectral decomposition of unknown functions and inhomogeneous terms in a coupled system of ordinary differential equations.

A Method for Solving Partial Differential Equations with Homogeneous Boundary or Initial Conditions

A Method for Solving Partial Differential Equations with Homogeneous Boundary or Initial Conditions

Finite element approximation of field dislocation mechanics

A tool for studying links between continuum plasticity and dislocation theory within a field framework is presented. A finite element implementation of the geometrically linear version of a recently proposed theory of field dislocation mechanics (J. Mech. Phys. Solids 49 (2001) 761; Proc. Roy. Soc. 459 (2003) 1343; J. Mech. Phys. Solids 52 (2004) 301) represents the main idea behind the tool. The constitutive ingredients of the theory under consideration are simply elasticity and a specification of dislocation velocity and nucleation. The set of equations to be approximated are non-standard in the context of solid mechanics applications. It comprises the standard second-order equilibrium equations, a first-order div–curl system for the elastic incompatibility, and a first-order, wave-propagative system for the evolution of dislocation density. The latter two sets of equations require special treatment as the standard Galerkin method is not adequate, and are solved utilizing a least-squares finite element strategy. The implementation is validated against analytical results of the classical elastic theory of dislocations and analytical results of the theory itself. Elastic stress fields of dislocation distributions in generally anisotropic media of finite extent, deviation from elastic response, yield-drop, and back-stress are shown to be natural consequences of the model. The development of inhomogeneity, from homogeneous initial conditions and boundary conditions corresponding to homogeneous deformation in conventional plasticity, is also demonstrated. To our knowledge, this work represents the first computational implementation of a theory of dislocation mechanics where no analytical results, singular solutions in particular, are required to formulate the implementation. In particular, a part of the work is the first finite element implementation of Kröner's linear elastic theory of continuously distributed dislocations in its full generality.

AN ANALYTICAL METHOD FOR CALCULATION OF TRANSIENT TEMPERATURE FIELD IN THE COUNTER-FLOW HEAT EXCHANGERS

We present an analytical solution to the system of partial differential equations with homogeneous initial conditions, describing transient temperature field in countercurrent heat exchangers. The system of partial differential equations is Laplace-transformed and the resultant set of ordinary differential equations is solved analytically. Analytical solution in the original domain is obtained for a special case of the heat exchanger where the thermal capacities and velocities of fluids are equal in both channels. Exemplary calculations are carried out to determine the unsteady response of the heat exchanger to a step change in the inlet temperature of one fluid

Justification of the Fourier method for an inhomogeneous hyperbolic equation with random right-hand side

We consider an inhomogeneous hyperbolic equation with homogeneous initial and boundary conditions and a random right-hand side. In the case where the right-hand side of the equation is a centered sample-continuous Gaussian field, we establish conditions for the existence of a solution of the first boundary-value problem of mathematical physics in the form of a series uniformly convergent in probability.

Formation of saucer-shaped sills

Abstract We have developed a coupled model for sill emplacement in sedimentary basins. The intruded sedimentary strata are approximated as an elastic material modelled using a discrete element method. A non-viscous fluid is used to approximate the intruding magmatic sill. The model has been used to study quasi-static sill emplacement in simple basin geometries. The simulations show that saucer-shaped sill complexes are formed in the simplest basin configurations defined as having homogeneous infill and initial isotropic stress conditions. Anisotropic stress fields are formed around the sill tips during the emplacement due to uplift of the overburden. The introduction of this stress asymmetry leads to the formation of transgressive sill segments when the length of the horizontal segment exceeds two to three times the overburden thickness. New field and seismic observations corroborate the results obtained from the modelling. Recent fieldwork in undeformed parts of the Karoo Basin, South Africa, shows that saucer-shaped sills are common in the middle and upper parts of the basin. Similar saucer shaped sill complexes are also mapped on new two- and three-dimensional seismic data offshore of Mid-Norway and on the NW Australian shelf, whereas planar and segmented sheet intrusions are more common in structured and deep basin provinces.

The decay of homogeneous anisotropic turbulence

We present the results of a numerical investigation of three-dimensional decaying turbulence with statistically homogeneous and anisotropic initial conditions. We show that at large times, in the inertial range of scales: (i) isotropic velocity fluctuations decay self-similarly at an algebraic rate which can be obtained by dimensional arguments; (ii) the ratio of anisotropic to isotropic fluctuations of a given intensity falls off in time as a power law, with an exponent approximately independent of the strength of the fluctuation; (iii) the decay of anisotropic fluctuations is not self-similar, their statistics becoming more and more intermittent as time elapses. We also investigate the early stages of the decay. The different short-time behavior observed in two experiments differing by the phase organization of their initial conditions gives a new hunch on the degree of universality of small-scale turbulence statistics, i.e., its independence of the conditions at large scales.

The equivalence of weak solutions and entropy solutions of nonlinear degenerate second-order equations

We prove the equivalence of weak solutions and entropy solutions of an elliptic–parabolic–hyperbolic degenerate equation g(t) t− Δb(u)+ div φ(u)=f with homogeneous Dirichlet conditions and initial conditions. As a result of the equivalence, we obtain the L 1-contraction principle and uniqueness of weak solutions of elliptic–parabolic degenerate equations.

Linear Evolution of Error Covariances in a Quasigeostrophic Model

The characteristics of forecast-error covariances, which are of central interest in both data assimilation and ensemble forecasting, are poorly known. This paper considers the linear dynamics of these covariances and examines their evolution from (nearly) homogeneous and isotropic initial conditions in a turbulent quasigeostrophic flow qualitatively similar to that of the midlatitude troposphere. The experiments use ensembles of 100 solutions to estimate the error covariances. The error covariances evolve on a timescale of O(1 day), comparable to the advective timescale of the reference flow. This timescale also defines an initial period over which the errors develop characteristic features that are insensitive to the chosen initial statistics. These include 1) scales comparable to those of the reference flow, 2) potential vorticity (PV) concentrated where the gradient of the reference-flow PV is large, particularly at the surface and tropopause, and 3) little structure in the interior of the troposphere. In the error covariances, these characteristics are manifest as a strong spatial correlation between the PV variance and the magnitude of the reference-flow PV gradient and as a pronounced enhancement of the error correlations along reference-flow PV contours. The dynamical processes that result in such structure are also explored; the key is the advection of reference-flow PV by the error velocity, rather than the passive advection of the errors by the reference flow.

Recent Trident single hot spot experiments: Evidence for kinetic effects, and observation of Langmuir decay instability cascade

Single hot spot experiments offer several unique opportunities for developing a quantitative understanding of laser-plasma instabilities. These include the ability to perform direct numerical simulations of the experiment due to the finite interaction volume, isolation of instabilities due to the nearly ideal laser intensity distribution, and observation of fine structure due to the homogeneous plasma initial conditions. Experiments performed at Trident in the single hot spot regime have focused on the following issues. First, the intensity scaling of stimulated Raman scattering (SRS) for classically large damping regimes (kλD=0.35) was examined, and compared to classical SRS theory. SRS onset was observed at intensities much lower than expected (2×1015 W/cm2), from which nonclassical damping is inferred. Second, Thomson scattering was used to probe plasma waves driven by SRS, and structure was observed in the scattered spectra consistent with multiple steps of the Langmuir decay instability. Finally, scattering from a plasma wave was observed whose frequency and phase velocity are between an ion acoustic wave and an electron plasma wave. The presence of this wave cannot be explained by linear Landau theory, and it is shown to be consistent with a BGK-type mode due to electron trapping.

Ensemble Cloud Model Applications to Forecasting Thunderstorms

Abstract A cloud model ensemble forecasting approach is developed to create forecasts that describe the range and distribution of thunderstorm lifetimes that may be expected to occur on a particular day. Such forecasts are crucial for anticipating severe weather, because long-lasting storms tend to produce more significant weather and have a greater impact on public safety than do storms with brief lifetimes. Eighteen days distributed over two warm seasons with 1481 observed thunderstorms are used to assess the ensemble approach. Forecast soundings valid at 1800, 2100, and 0000 UTC provided by the 0300 UTC run of the operational Meso Eta Model from the National Centers for Environmental Prediction are used to provide horizontally homogeneous initial conditions for a cloud model ensemble made up from separate runs of the fully three-dimensional Collaborative Model for Mesoscale Atmospheric Simulation. These soundings are acquired from a 160 km × 160 km square centered over the location of interest; they ar...

Non-standard fractal spectrum of a 1D gravitating model

A one-dimensional (1D) system obeying the Hubble expansion is studied numerically using an N-body code. The rescaling of both space and time changes the dynamics which, in the rescaled frame, is analogous to the dynamics of a 1D one-component plasma with the addition of a friction term. We start from a homogeneous initial condition but, because of Jeans’ instability, the system enters a non-linear regime and builds a hierarchical structure. Applying a multi-fractal analysis, we show that the density reveals a non-standard fractal spectrum related to a bifractal geometry.

Spatial decay bounds for the Forchheimer equations

This paper establishes exponential decay bounds for solutions of the Forchheimer equations in semi-infinite pipe flow through a porous medium when homogeneous initial and lateral surface boundary conditions are applied. We investigate the decay for zero net flow and for nonzero net flow separately.

SPATIAL DECAY IN THE PIPE FLOW OF A VISCOUS FLUID INTERFACING A POROUS MEDIUM

This paper establishes exponential decay of weighted energy in the pipe flow of a slowly moving viscous fluid interfacing with a porous medium when homogeneous initial and lateral surface boundary conditions and appropriate interface conditions are applied. This decay requires that the net flow across the intake section of the semi-infinite pipe be zero.

Controlled nonperturbative dynamics of quantum fields out of equilibrium

We compute the nonequilibrium real-time evolution of an O( N)-symmetric scalar quantum field theory from a systematic 1/ N expansion of the 2PI effective action to next-to-leading order, which includes scattering and memory effects. In contrast to the standard 1/ N expansion of the 1PI effective action, the next-to-leading-order expansion in presence of a possible expectation value for the composite operator leads to a bounded-time evolution where the truncation error may be controlled by higher powers in 1/ N. We present a detailed comparison with the leading-order results and determine the range of validity of standard mean-field-type approximations. We investigate “quench” and “tsunami” initial conditions frequently used to mimic idealized far-from-equilibrium pion dynamics in the context of heavy-ion collisions. For spatially homogeneous initial conditions, we find three generic regimes, characterized by an early-time exponential damping, a parametrically slow (power-law) behavior at intermediate times, and a late-time exponential approach to thermal equilibrium. The different time scales are obtained from a numerical solution of the time-reversal invariant equations in 1+1 dimensions without further approximations. We discuss in detail the out-of-equilibrium behavior of the nontrivial n-point correlation functions as well as the evolution of a particle number distribution and inverse slope parameter.

Persistence in the one-dimensional A+B--> Ø reaction-diffusion model.

The persistence properties of a set of random walkers obeying the A+B--> Ø reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability P(t) that an annihilation process has not occurred at a given site has the asymptotic form P(t) approximately const+t(-straight theta), where straight theta is the persistence exponent (type I persistence). We argue that, for a density of particles rho>>1, this nontrivial exponent is identical to that governing the persistence properties of the one-dimensional diffusion equation, partial differential(t)straight phi= partial differential(xx)straight phi, where straight theta approximately 0.1207 [S. N. Majumdar, C. Sire, A. J. Bray, and S. J. Cornell, Phys. Rev. Lett. 77, 2867 (1996)]. In the case of an initial low density, rho(0)<<1, we find straight theta approximately 1/4 asymptotically. The probability that a site remains unvisited by any random walker (type II persistence) is also investigated and found to decay with a stretched exponential form, P(t) approximately exp(-constxrho(1/2)(0)t(1/4)), provided rho(0)<<1. A heuristic argument for this behavior, based on an exactly solvable toy model, is presented.

Reproductive pair correlations and the clustering of organisms.

Clustering of organisms can be a consequence of social behaviour, or of the response of individuals to chemical and physical cues. Environmental variability can also cause clustering: for example, marine turbulence transports plankton and produces chlorophyll concentration patterns in the upper ocean. Even in a homogeneous environment, nonlinear interactions between species can result in spontaneous pattern formation. Here we show that a population of independent, random-walking organisms ('brownian bugs'), reproducing by binary division and dying at constant rates, spontaneously aggregates. Using an individual-based model, we show that clusters form out of spatially homogeneous initial conditions without environmental variability, predator-prey interactions, kinesis or taxis. The clustering mechanism is reproductively driven-birth must always be adjacent to a living organism. This clustering can overwhelm diffusion and create non-poissonian correlations between pairs (parent and offspring) or organisms, leading to the emergence of patterns.

Thermalization in a Hartree ensemble approximation to quantum field dynamics

For homogeneous initial conditions, Hartree (gaussian) dynamical approximations are known to have problems with thermalization, because of insufficient scattering. We attempt to improve on this by writing an arbitrary density matrix as a superposition of gaussian pure states and applying the Hartree approximation to each member of such an ensemble. Particles can then scatter via their back-reaction on the typically inhomogeneous mean fields. Starting from initial states which are far from equilibrium we numerically compute the time evolution of particle distribution functions and observe that they indeed display approximate thermalization on intermediate time scales by approaching a Bose-Einstein form. However, for very large times the distributions drift towards classical-like equipartition.