Search

A two-dimensional stationary linear model of flows arising in a stably (neutral) stratified medium over a thermally inhomogeneous flat inclined surface is analyzed analytically. Temperature deviations that harmonically depend on the horizontal coordinate transverse to the slope are set at the lower boundary. Explicit analytical solutions allowing one to analyze emerging density flows are obtained. It is shown that these flows can qualitatively differ, depending on the ratio of the slope angle of the lower boundary and the analog of the Rayleigh number. An expression for the latter includes the horizontal scale of the thermal inhomogeneity region as a spatial scale. An appropriate criterion for distinguishing these flows is established. [ABSTRACT FROM AUTHOR]

Consideration has been given to a linear analytical model of perturbations of geostrophic flow of a stratified rotating medium resulting from the action of stationary sources of momentum and/or buoyancy. The problem formulation appears more consistent than the ones considered in the literature. The model makes it possible to evaluate explicitly the amplitudes of such perturbations as a function of the parameters of sources and characteristics of the medium. One example of possible applications is the phenomena occurring during interventions of cold air into a rather warm surface (strong temperature contrasts are, for example, frequent over the water surface in the polar regions). In such cases, the air develops intense penetrating convection which, in rough approximation, acts on the background flux as an intense volume heat source and horizontal momentum outlet (background flux deceleration due to high effective viscosity). [ABSTRACT FROM AUTHOR]

Abstract In this paper, we develop the theory of differential equations with linear perturbations of second type on time scales. An existence theorem for differential equations with linear perturbations of second type on time scales is given under D $\mathscr{D}$ -Lipschitz conditions. Some fundamental differential inequalities on time scales, which are utilized to investigate the existence of extremal solutions, are also presented. The comparison principle on differential equations with linear perturbations of second type on time scales is established. Our results in this paper extend and improve some well-known results.

A system with two degrees of freedom in the case of a double natural frequency is considered. The unperturbed system consists of two independent oscillators. The system coordinates describe an elliptical trajectory with four orbital elements. An analysis of the action of linear perturbations (forces) on the orbital elements is carried out. Perturbations are subdivided into six types of forces, and for each type of forces a system of differential equations for the orbital elements is obtained. For all six types of forces, a general solution of the system of differential equations in elementary functions is found. [ABSTRACT FROM AUTHOR]

We outline the modifications in the numerical Boltzmann code Cosmic Linear Anisotropy Solving System (CLASS) in order to include extra inflationary fields. The functioning of the code is first described, how and where modifications are meant to be done are later explained. In the present study, we focus on the modifications needed for the implementation of a two‐field inflationary model, with canonical kinetic terms and a polynomial potential with no cross terms, presenting preliminary results for the effect of the second field on the spectra. The adaptability of the code is exploited, making use of the classes and structures of C and the generic Runge–Kutta integration tool provided by the program. [ABSTRACT FROM AUTHOR]

We study the stability properties of static, spherically symmetric configurations in k -essence theories with the Lagrangians of the form F (X) , X ≡ ϕ , α ϕ , α . The instability under spherically symmetric perturbations is proved for the two recently obtained exact solutions for F (X) = F 0 X 1 / 3 and for F (X) = F 0 X 1 / 2 − 2 Λ , where F 0 and Λ are constants. The first solution describes a black hole in an asymptotically singular spacetime, the second one contains two horizons of infinite area connected by a wormhole. It is argued that spherically symmetric k -essence configurations with n < 1 / 2 are generically unstable because the perturbation equation is not of hyperbolic type. [ABSTRACT FROM AUTHOR]

We introduce , the inhomogeneous equation suitable to describe the solution of the linearized version of the conformal part of the Riemann tensor connected to the perturbations of the Kerr spacetime far from the origin. Then we find the right decays we have to impose to the source term to obtain the peeling decays for this linearized solution. We explain how these decays are compatible with the ones we need to attack the full nonlinear problem following the Christodoulou-Klainerman approach, see [7, 11]. This result is expressed explicitly in Theorem 1.1 and requires some new detailed estimates for the connection coefficients related to the null cone foliation in Kerr, see [10], which could be considered as a useful result by itself. [ABSTRACT FROM AUTHOR]

We examine the stability of Einstein-Maxwell perfect fluid configurations with a privileged radial direction by means of a $$1+1+2$$ -tetrad formalism. We use this formalism to cast in a quasilinear symmetric hyperbolic form the equations describing the evolution of the system. This hyperbolic reduction is used to discuss the stability of linear perturbations in some special cases. By restricting the analysis to isotropic fluid configurations, we assume a constant electrical conductivity coefficient for the fluid. As a result of this analysis we provide a complete classification and characterization of various stable and unstable configurations. We find, in particular, that in many cases the stability conditions are strongly determined by the constitutive equations and the electric conductivity. A threshold for the emergence of the instability appears in both contracting and expanding systems. [ABSTRACT FROM AUTHOR]

For linear equations in a Banach space, we show that the existence of a nonuniform exponential trichotomy for x ′ = A ( t ) x persists under sufficiently small C 1 perturbations B ( t , λ ) x , in such a way that the stable, unstable and center subspaces are of class C 1 in λ . [ABSTRACT FROM AUTHOR]

Under suitable hypotheses on γ(t), λ(t), q(t) we prove some stability results which relate the asymptotic behavior of the solutions of u" + γ(t)u' + (q(t) + A(t))u = 0 to the asymptotic behavior of the solutions of u" + q(t)u = 0. [ABSTRACT FROM AUTHOR]

Abstract: We show that the determinant objective function introduced in Ejov et al. [V. Ejov, J. A. Filar, W. Murray, G.T. Nguyen, Determinants and longest cycles of graph, SIAM J. Discrete Math. 22 (33) (2008) 1215–1225] performs well under a certain symmetric linear perturbation. That means sub-graphs corresponding to Hamiltonian cycles of a given graph are maximizers over the hull of all sub-graphs with perturbation parameter . Note that in other optimization formulations (see, for example [V.S. Borkar, V. Ejov, J.A. Filar, Directed graphs, Hamiltonicity and doubly stochastic matrices, Random Structures Algorithms 25 (2004) 376–395; V. Ejov, J.A. Filar, M. Nguyen, Hamiltonian cycles and singularly perturbed Markov chains, Math. Oper. Res. 29 (1) (2004) 114–131; J.A. Filar, K. Liu, Hamiltonian cycle problem and singularly perturbed Markov decision process, in: Statistics, Probability and Game Theory: Papers in Honor of David Blackwell, IMS Lecture Notes – Monograph Series, USA, 1996]), in the corresponding perturbation was required to be significantly small. [Copyright &y& Elsevier]

The stability of a unipolarly charged electrohydrodynamic boundary layer on a flat dielectric plate along which an electric current flows between electrodes located on the plate is investigated within the framework of the linear theory. The solution of the steady-state problem is obtained on the basis of methods developed earlier for conditions typical of aerodynamical experiments and various electric currents and electrode voltages. The effect of the interaction between perturbations of the electric and hydrodynamic flow parameters on the flow stability is estimated within the framework of the locally homogeneous approximation. This effect turns out to be insignificant under the conditions considered. It is shown that steady-state electrohydrodynamic action on the main flow makes it possible to obtain “accelerating” velocity profiles with increased absolute values of the second derivative in the transverse direction. This ensures a significant increase in the critical Reynolds numbers of loss of stability and a narrowing of the growing perturbation wavenumber range. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the linear perturbations of the spherically symmetric space–times with kinematic self-similarity of the second kind. The massless scalar field equations are solved which yield the background and an exact solutions for the perturbed equations. We discuss the boundary conditions of the resulting perturbed solutions. The possible perturbation modes turn out to be stable as well as unstable. The analysis leads to the conclusion that there does not exist any critical solution. [ABSTRACT FROM AUTHOR]

It is well known that the solution map of a quadratic program where only the linear part of the data is subject to perturbation is an upper Lipschitz multifunction. This paper characterizes the continuity and lower semicontinuity of that solution map. [ABSTRACT FROM AUTHOR]

We apply the method of linear perturbations to the case of Spin (7) -structures, showing that the only nontrivial perturbations are those determined by a rank one nilpotent matrix. We consider linear perturbations of the Bryant-Salamon metric on the spin bundle over S 4 that retain invariance under the action of Sp (2) , showing that the metrics obtained in this way are isometric. [ABSTRACT FROM AUTHOR]

This paper builds upon the relationship between the objective function of a semi-infinite linear program and its constraints to identify a class of semi-infinite linear programs which do not have a duality gap. The key idea is to guarantee the approximation of the primal program by a sequence of linear programs where the nth approximating program is to minimize the objective function subject to the first n constraints. The paper goes on to show that any program not in the identified class can be linearly perturbed into it with the optimal value of the perturbed program converging to the optimal value of the original program. The results are then extended to the case when an uncountable number of constraints are present by reducing this case to the countable case. [ABSTRACT FROM AUTHOR]

A straight-line 160-Gb/s 1000-km differential phase-shift keying transmission was successfully demonstrated with time-domain optical Fourier transformation (OFT) without employing polarization multiplexing or Raman amplification. The OFT greatly reduced the transmission impairments caused by linear perturbations, and transmission performance close to the amplified spontaneous emission limit was achieved. [ABSTRACT FROM PUBLISHER]

We demonstrate a new adaptive equalization scheme at 160 Gb/s using time-domain optical Fourier transformation. In this technique, we take advantage of the fact that the spectral profile does not change even when the transmission fiber has linear perturbations such as jitter, polarization-mode dispersion, and higher order dispersions. The unchanged spectral profile is then converted into the time-domain waveform at the output, resulting in the reconstruction of the original undistorted waveform. With the present scheme, a 160-Gb/s optical time-division-multiplexing signal was successfully transmitted over 120 km by simultaneously equalizing both second- and third-order dispersions even when they varied with time. [ABSTRACT FROM PUBLISHER]

We investigate the cosmological perturbations in the context of a Scalar-Tensor-Vector theory of Gravity known as MOG in the literature. Recent investigations show that MOG reproduces a viable background cosmological evolution comparable to ΛCDM. However, the matter dominated era is slightly different. In this paper, we study the linear matter perturbations and estimate the relevant modified gravity parameters. We show that MOG reduces the growth rate of the perturbations and comparing with the RSD data reveals that MOG suggests a higher value for σ 8 , compare to ΛCDM. This point, constitute a powerful challenge to the cosmological viability of MOG. [ABSTRACT FROM AUTHOR]

In this paper, we develop the theory of differential equations with linear perturbations of second type on time scales. An existence theorem for differential equations with linear perturbations of second type on time scales is given under D -Lipschitz conditions. Some fundamental differential inequalities on time scales, which are utilized to investigate the existence of extremal solutions, are also presented. The comparison principle on differential equations with linear perturbations of second type on time scales is established. Our results in this paper extend and improve some well-known results. [ABSTRACT FROM AUTHOR]