M theory solution to the hierarchy problem

An old idea for explaining the hierarchy is strong gauge dynamics. We show that such dynamics also stabilizes the moduli in M theory compactifications on manifolds of G2 holonomy without fluxes. This gives stable vacua with softly broken supersymmetry, grand unification, and a distinctive spectrum of TeV and sub-TeV sparticle masses.     

Resolution of the out-of-zone solution problem in envelope-function theory

Envelope-function equations are widely used to model electron states in microstructures where single-band effective mass models are inappropriate. However, the presence of spurious out-of-zone solutions poses a serious problem for the method: the out-of-zone solutions appear unphysical yet including them is necessary to satisfy all the boundary conditions implied by the envelope-function equations. In an earlier publication, the author has suggested that the mathematically correct procedure is to use all solutions, including out-of-zone solutions, of the envelope-function equations and to apply all the boundary conditions implied by those equations at abrupt interfaces. This procedure is applied to a simple one-dimensional model and it is shown that it generates the correct wavefunction and the role of the out-of-zone solutions is clarified. As a result of this work there is now a straightforward unambiguous procedure for applying the envelope-function method to microstructures, a procedure that removes uncertainty, but retains the simplicity of the envelope-function\break approach.     

On the theory of nonlinear dopplerons in metals

The possibility of the nonlinear wave propagation occurring in metals, such as cadmium, in the geometry where a constant magnetic field H is directed at an angle with respect to the hexagonal axis of the crystal has been investigated theoretically. In the linear regime in this geometry, there is a significant magnetic Landau damping, which prevents propagation of waves. It has been shown that the electron trapping by the magnetic field of a wave can substantially decrease the efficiency of this damping. As a result, the propagation of a doppleron, i.e., the mode related to the Doppler-shifted cyclotron resonance of electrons, becomes possible. It has been noted that a similar “bleaching” effect should also take place in some other metals.     

On the theory of nonlinear thermal conductivity

A nonlinear differential equation of thermal conductivity is derived phenomenologically from the general principles of construction of functional Q invariant to the inversion operation I(r →–r), and the temperature evolution dynamics is analyzed in the nonstationary case. The proposed method makes it possible to reveal some general regularities in the physical behavior of such systems for describing irreversible phenomena in self-organization processes. It is noted that an analogous situation may take place, for example, in strongly inhomogeneous structures with stochastic internal heat fluxes.     

On the problem of macrocausality in field theory

After a critical discussion of some definitions of macrocausality we propose a definition for causal propagation of observables, in particular of energy. This definition, which was already given in a preceding paper by Gerlach, Petzold, Rosenthal, and the author, is applied to various examples of local and nonlocal theories. Finally, we deal with the question of signals, a question, which needs some further consideration. The propagation of signals is discussed for local and nonlocal theories, including tachyon fields.     

Initial value problem solution of nonlinear shallow water-wave equations

The initial value problem solution of the nonlinear shallow water-wave equations is developed under initial waveforms with and without velocity. We present a solution method based on a hodograph-type transformation to reduce the nonlinear shallow water-wave equations into a second-order linear partial differential equation and we solve its initial value problem. The proposed solution method overcomes earlier limitation of small waveheights when the initial velocity is nonzero, and the definition of the initial conditions in the physical and transform spaces is consistent. Our solution not only allows for evaluation of differences in predictions when specifying an exact initial velocity based on nonlinear theory and its linear approximation, which has been controversial in geophysical practice, but also helps clarify the differences in runup observed during the 2004 and 2005 Sumatran tsunamigenic earthquakes.     

一个非线性力学问题的解析解

研究质点相对旋转光滑圆环的运动,通过椭圆积分,利用特殊函数得出了系统的解析解,并对质点的运动情况进行了定性分析。     

On the theory of nonlinear response in a nonideal plasma

A theory of nonlinear response is developed for studying nonlinear phenomena and nonlinear transport processes in nonideal Coulomb systems. Temporal plasma echo and transformation of waves in a nonideal Coulomb system are studied on the basis of the theory of nonlinear response to mechanical perturbations. General constraints imposed on nonlinear response functions are considered, and the model for determining quadratic response functions is formulated. The conditions for the emergence of temporal plasma echo and wave transformation are determined. It is shown that these nonlinear effects in a nonideal plasma can be initiated by ultrashort field pulses. A theory of transport is developed for determining the Burnett transport properties of a nonideal multielement plasma. A procedure is proposed for comparing the phenomenological conservation equations for a charged continuous medium and equations of motion for the operators of corresponding dynamic variables. The Mori algorithm is used for deriving the equations of motion for operators of dynamic variables in the form of generalized Langevin equations. The linearized Burnett approximation is considered in detail. The properties of the matrices of coefficients of higher-order derivatives in the system of conservation equations in the linearized Burnett approximation, which are important for hydrodynamic applications, are discussed. Various versions of the theory of nonlinear response are compared.     

Vacuum Cherenkov effect in logarithmic nonlinear quantum theory

We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics - cone angle, flash duration, radiation yield and spectral distribution - are computed. It turns out that the radiation yield is proportional to the square of the proper energy scale of the vacuum which serves also as the vacuum instability threshold and the natural ultraviolet cutoff. While the analysis is mainly based on the theory engaging the logarithmic nonlinear quantum wave equation, some of the obtained results must be valid for any Lorentz-invariance violating theory describing the vacuum by (effectively) continuous medium in the long-wavelength approximation.     

零维气候系统非线性模式的周期解问题

运用重合度理论探讨了一个非线性问题的周期解, 然后将其应用于零维气候系统模式的周期解问题的研究, 获得了该模式存在周期解的结果. 关键词： 非线性 零维气候系统 周期解     

On the problem of nonlinear distortions of the maximum-entropy method

We consider the problem of nonlinear distortions resulting from noise in the input data in the reconstruction of images from incomplete Fourier spectra using nonlinear information-theoretic methods, in particular, the maximum-entropy method. Comparison of traditional and generalized maximum-entropy methods shows that generalized methods, which operate in the space of complex functions, provide the best agreement of the solution with the data and, therefore, a minimal level of nonlinear distortions. Recommendations for processing of real nonnegative images of incoherent radio sources are given.Institute of Applied Astronomy, Russian Academy of Sciencies St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1267–1277, December, 1995.     

On Arthur Fine's solution to the measurement problem

Arthur Fine has recently proposed a novel solution to the measurement problem. Fine's innovation is to exploit the idea that a measurement is a selective interaction in which the apparatus responds to a probability distribution. I develop Fine's solution in some detail, responding to various potential objections along the way. In the end, however, I suggest that Fine needs to tell us more before we can declare the measurement problem solved.     

On the two-component Benard problem a numerical solution

A numerical solution for the two-component Bénard problem is presented, taking into account the contribution of thermal diffusion to the total density gradient. The results are compared with the approximate solution obtained by the variational technique of the local potential introduced some years ago by Glansdorff and Prigogine. The results calculated by the two methods are in agreement when the Soret coefficient is not too large. But when the gradients become important, the exact numerical solution presented here shows a small divergence from the variational method.The critical Rayleigh number is also compared with the one extrapolated from the analytical solution obtained for free boundary conditions.     

On the problem of spacetime symmetries in the theory of supergravity

In the framework of the simple (N=1) supergravity, a definition of a spacetime symmetry is discussed. It is shown to have a smooth relativistic limit. As an application, the problem of the plane wave in supergravity is studied.Research Fellow at the Belgian National Fund for Scientific Research (FNRS).     

On vacuum oscillations solution of the solar neutrino problem

Experimental signatures of vacuum oscillations solution of the solar neutrino problem are considered. This solution predicts a strict correlation between a distortion of the neutrino energy spectrum and an amplitude of seasonal variations of the neutrino flux. The slope parameter which characterizes a distortion of the recoil electron energy spectrum in the Super-Kamiokande experiment and the seasonal asymmetry of the signal have been calculated in a wide range of oscillation parameters. The correlation of the slope and asymmetry gives crucial criteria for identification or exclusion of this solution. For the positive slope indicated by preliminary Super-Kamiokande data we predict (40 – 60) % enhancement of the seasonal variations.     

A solution to the problem of the skin effect with a bias current in the Maxwell plasma by the method of expansion in eigenfunctions

A problem of the skin effect in the Maxwell plasma is solved analytically by the method of expansion in eigenfunctions based on the Vlasov–Maxwell kinetic equation with a self-consistent electric field. Specular electron reflection from the boundary is used as a boundary condition. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 33–38, February, 2009.     

On asymptotics of the solution of the moving oscillator problem

Asymptotic behavior of the solution of the moving oscillator problem is examined for large and small values of the spring stiffness for the general case of non-zero beam initial conditions. In the limiting case of infinite spring stiffness, it is shown that the moving oscillator problem for a simply supported beam is not equivalent, in a strict sense, to the moving mass problem. The two problems are shown to be equivalent in terms of the beam displacements but are not equivalent in terms of stresses (the higher order derivatives of the two solutions differ). In the general case, the force acting on the beam from the oscillator is shown to contain a high-frequency component , which does not vanish and can even grow when the spring coefficient tends to infinity. The magnitude of this force and its dependence on the oscillator parameters can be estimated by considering the asymptotics of the solution for the initial stage of the oscillator motion. It is shown that, for the case of a simply supported beam, the magnitude of the high-frequency force depends linearly on the oscillator eigenfrequency and velocity. The deficiency of the moving mass model is principally that it fails to predict stresses in the supporting structure. For small values of the spring stiffness, the moving oscillator problem is shown to be equivalent to the moving force problem. The discussion is amply illustrated by results of numerical experiments.     

On the theory of the Buckingham effect

We apply general arguments (based on spatial transformation properties, intrinsic symmetry and dimensional analysis) to the theory of the Buckingham effect (electric-field–gradient-induced birefringence in a gas). These yield, in a simple manner, the temperature-dependent and temperature-independent terms in the birefringence (each to within a numerical factor), and also the expression, derived by Buckingham and Longuet-Higgins, for the effective quadrupole centre of a molecule. We show in addition how the calculation of the two numerical factors can be simplified in our approach.