Different Types Of Initial Conditions Research Articles

T→0mean-field population dynamics approach for the random3-satisfiability problem

During the past decade, phase-transition phenomena in the random 3-satisfiability ( 3 -SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random 3 -SAT problem by the mean-field first-step replica-symmetry-broken cavity theory at the limit of temperature T-->0 . The reweighting parameter y of the cavity theory is allowed to approach infinity together with the inverse temperature beta with fixed ratio r=ybeta . Focusing on the system's space of satisfiable configurations, we carry out extensive population dynamics simulations using the technique of importance sampling, and we obtain the entropy density s(r) and complexity Sigma(r) of zero-energy clusters at different r values. We demonstrate that the population dynamics may reach different fixed points with different types of initial conditions. By knowing the trends of s(r) and Sigma(r) with r , we can judge whether a certain type of initial condition is appropriate at a given r value. This work complements and confirms the results of several other very recent theoretical studies.

Free vibration of a Jeffcott rotor with pure cubic non-linear elastic property of the shaft

The paper considers the free vibration of a Jeffcott rotor whose shaft has a strong non-linear elastic property. The mathematical model of the Jeffcott rotor is a second-order non-linear differential equation with a complex deflection function. An analytic procedure based on the Krylov–Bogolubov method is developed to solve this differential equation. Two different types of initial conditions are considered. The obtained solution describes the oscillatory motion of the rotor center. The influence of the damping, hydrodynamic and gyroscopic force and the variation of the mass of the rotor on the vibrations of the rotor is then analyzed.

Short-time decay of the Loschmidt echo.

The Loschmidt echo measures the sensitivity to perturbations of quantum evolutions. We study its short-time decay in classically chaotic systems. Using perturbation theory and throwing out all correlation imposed by the initial state and the perturbation, we show that the characteristic time of this regime is well described by the inverse of the width of the local density of states. This result is illustrated and discussed in a numerical study in a two-dimensional chaotic billiard system perturbed by various contour deformations and using different types of initial conditions. Moreover, the influence to the short-time decay of sub-Planck structures developed by time evolution is also investigated.

Riesz bases of solutions of Sturm-Liouville equations

This article concerns the stability of orthogonal bases of solutions of Sturm-Liouville equations with different types of initial conditions. The investigation is based on the stability of Riesz bases of cosines and sines in the Hibert space L2[0,π].

Consistent initial conditions for the DNS of compressible turbulence

Relationships between diverse thermodynamic quantities appropriate to weakly compressible turbulence are derived. It is shown that for turbulence of a finite turbulent Mach number there is a finite effect of compressibility. A methodology for generating initial conditions, consistent with finite Mach number, for the fluctuating pressure, density, and dilatational velocity is given. Use of these initial conditions gives rise to a smooth development of the flow, in contrast to cases in which these fields are specified arbitrarily or set to zero. Comparisons of the effect of different types of initial conditions are made using direct numerical simulation of decaying isotropic turbulence.

Synchronicity in coupled sine circle maps; some numerical results

We study the spatially synchronised and temporally periodic orbits of a 1-d lattice of coupled sine circle maps. A numerical study of the synchronised solutions reveals synchronisation over large regions of parameter space. The entire devil's staircase of periodic orbits as seen for the single circle map is observed for the synchronised coupled sine circle map lattice. The parameter regions for which the synchronised solution is obtained are investigated for different types of initial conditions. These reveal interesting structures in the parameter space and appear to be symmetric about Ω = 0.5.

Spectral properties of inviscid solutions of the burgers equation with random initial conditions

The Burgers equation with random self-similar initial conditions is investigated numerically in the inviscid limit by a parallel fast Legendre transform algorithm, using Connection Machine CM-200. The use of this equation for solving the problem of nervous impulse propagation through axons is discussed. An attempt is made to simulate recent experiments where the form of the density of propagated nerve impulses, which initially had a power spectrum close to a white noise distribution, appeared similar to the triangular pulses that arise in the inviscid Burgers equation and where the 1/f power law was observed on scales larger than the typical time interval between pulses. It is shown that in the inviscid Burgers equation model the power spectra for different types of initial conditions in the developed “Burgers turbulence” regime (i.e., at a sufficiently large time) consists of two parts with a rather sharp transition between them: The spectrum virtually coincides with the initial spectra for low wavenumbers, and the 1/f2 law holds for high wavenumbers. There is no interval with an intermediate power law dependence such as 1/f. It is inferred that the true 1/f spectrum of nerve impulses propagating through axons cannot be explained in terms of the Burgers equation model and that other mechanisms must be taken into account.

A complex systems approach to metallic fracture surface characterization

The physical scale of observation and the mathematical formalism of description are important choices for the modeling of physical phenomena. The role of local interactions in relating complex features at different scales in inelastic material fracture is important since material damage has local origins while fracture is a large scale event. In this investigation, the relationship between large scale and small continuum scale fracture surface features are quantified in terms of local, small scale interactions. Experimental measurements of local fracture surface orientation were obtained from processing video images of the fracture surface under different illumination directions. The image processing mapped pixel intensities into a set of three local fracture surface inclination classes defined with respect to the macroscopic surface normal and crack growth direction. Stochastic cellular automaton parameters were identified from the processed image of local inclination classes for use in subsequent simulation. Physical consistency of the parameters with respect to symmetry under spatial reflection was demonstrated. Synthetic processed images were generated using two different types of initial conditions. The processed and synthetic processed images contained similar proportions and features of self-organization, as compared to random images, yet were relatively insensitive to initial conditions of the simulations. This is consistent with the local uniqueness and global reproducibility associated with the mechanics of fracture. Through this approach, the ability to determine the dominant local interaction scale and the global scale of self-organization from experiment should complement analytical modeling of the fracture process. This method of analysis serves to identify features on the fracture surface for additional scrutiny by higher resolution experimental methods.

Solitary excitations in an electron-phonon system

In a one-dimensional quantum mechanical model we numerically show that the coupling of acoustic phonons with local, non-interacting electronic two-level centers can lead to the formation of solitons. Inclusion of non-resonant interaction results in very narrow solitons. Despite of the lattice discreteness the solitons show extreme stability. The complex scattering behaviour is studied for different types of initial conditions.

A Case Study of the Sensitivity of Numerical Simulation of Mesoscale Convective Systems to Varying Initial Conditions

Abstract A 12 h nested-grid numerical simulation of a warm-season mesoscale convective weather system (Zhang and Fritsch, 1986) is utilized as a control run in order to 1) test the sensitivity of the numerical simulation to different types of initial conditions; 2) examine the need for an observing system that would resolve mesoscale features; and 3) determine which meteorological variables need to be most carefully considered in observing system design and preprocessing analysis. It is found that improved observational capabilities are likely to have an important impact on the successful prediction of the timing and location of summertime mesoscale convective weather systems if mesoscale features can be resolved. In particular, the resolution of the moisture field significantly affects the prediction of the evolution of the convective weather systems. Correspondingly, the mesoscale distribution of precipitation is substantially affected, especially the location of the areas of heavy rain. It is also foun...

Time-dependent solutions of mean-field equations with applications for mantle convection

The set of time-dependent, single-mode, mean-field equations appropriate for mantle convection has been converted by means of the method of lines formulation to a set of non-linear ordinary differential equations. The resulting system has been integrated in time t to steady-state by means of differential/algebraic system F(t, y , d y dt ) = 0 , in which the solution vector y consists of the vertical velocity, the thermal perturbation and the mean temperature and the spatial operators are finite differenced by high order schemes (up to 4th order). This large differential system—up to 500 equations—can be solved conveniently and economically by employing variable step-size, variable order (up to 5th order) stiff method such as backward differentiation formulas. We have studied thermal convection of infinite Prandtl number fluids with constant viscosity for both base heated and constant internally heated configurations. Both stress-free and rigid boundaries have been examined for these two modes of heating. Solutions for Rayleigh numbers up to 10 4 times of the critical value have been obtained. Heat transfer coefficients in the relationship between the Nusselt and Rayleigh number of the form Nu = aRa b are derived from the steady-state solutions. In general, the exponent b is ∼ 10% higher than the corresponding value obtained from asymptotic or numerical solutions of the full set of 2-dimensional equations. We have also examined the effects of time-dependent heating and different types of initial conditions on the subsequent thermal evolution. The role of time-dependent heating from radioactive sources is to lengthen substantially the period of time during which the system is still influenced by the initial conditions. This time of thermal equilibration is found to vary as c Ra − d , where d = 0.24 and is related to the heat-transfer coefficient. The constant c depends on the decay time of the heat sources. For Ra between 10 6 and 10 7 this time of readjustment is one-tenth of the thermal diffusion time of the entire layer and is 0(10 9 y) for upper-mantle convection, thus suggesting that modeling thermal history in the Archean may depend on earlier primeval events of the Earth.