Onset of instability for a class of nonlinear lagrangian systems

For systems of real and complex (charged) fields derivable from Lorentz-invariant lagrangian densities a general criterion for dynamical instability of lump solutions is presented. This criterion complements the well-known Q-theorem for stability.     

Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.     

Equilibrium and stability of neutrino lumps as TOV solutions

We report about stability conditions for static, spherically symmetric objects that share the essential features of mass varying neutrinos in cosmological scenarios. Compact structures of particles with variable mass are held together preponderantly by an attractive force mediated by a background scalar field. Their corresponding conditions for equilibrium and stability are given in terms of the ratio between the total mass-energy and the spherical lump radius, M/R. We show that the mass varying mechanism leading to lump formation can modify the cosmological predictions for the cosmological neutrino mass limits. Our study comprises Tolman–Oppenheimer–Volkoff solutions of relativistic objects with non-uniform energy densities. The results leave open some questions concerning stable regular solutions that, to an external observer, very closely reproduce the preliminary conditions to form Schwarzschild black holes.     

Point singularities of coupled gauge fields with low energy

Isolated singularities in higher-dimensional Yang-Mills-Higgs fields are considered. The singularities are removable if the energy is smaller than a dimensional constant.This work represents part of the author's doctoral dissertation at Polytechnic University of New YorkResearch partially supported by NSF Grant DMS-8501419     

Masses of nuclei

The study of masses of the different nuclear species is basic to the whole of nuclear physics. Because of the interchangeability of mass and energy the details of energy absorption or release are identical with mass differences or changes in the masses of participating nuclei. The systematic trends in mass value reflect therefore changes in the nuclear binding energy. It is one of the primary tasks of nuclear theory to explain the total binding energy of a lump of nuclear matter. The systematic trends in mass differences are also of basic importance in evolving models to describe the formation of the elements in our galaxy.     

New lump,lump-kink,breather waves and other interaction solutions to the (3+1)-dimensional soliton equation

This study investigates the (3+1)-dimensional soliton equation via the Hirota bilinear approach and symbolic computations. We successfully construct some new lump, lump-kink, breather wave, lump periodic, and some other new interaction solutions. All the reported solutions are verified by inserting them into the original equation with the help of the Wolfram Mathematica package. The solution's visual characteristics are graphically represented in order to shed more light on the results obtained. The findings obtained are useful in understanding the basic nonlinear fluid dynamic scenarios as well as the dynamics of computational physics and engineering sciences in the related nonlinear higher dimensional wave fields.     

Dynamics of mixed lump-soliton for an extended (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov equation

A new (2+1)-dimensional higher-order extended asymmetric Nizhnik–Novikov–Veselov (eANNV) equation is proposed by introducing the additional bilinear terms to the usual ANNV equation. Based on the independent transformation, the bilinear form of the eANNV equation is constructed. The lump wave is guaranteed by introducing a positive constant term in the quadratic function. Meanwhile, different class solutions of the eANNV equation are obtained by mixing the quadratic function with the exponential functions. For the interaction between the lump wave and one-soliton, the energy of the lump wave and one-soliton can transfer to each other at different times. The interaction between a lump and two-soliton can be obtained only by eliminating the sixth-order bilinear term. The dynamics of these solutions are illustrated by selecting the specific parameters in three-dimensional, contour and density plots.     

Response of a Si-diode-based device to fast neutrons

Semiconductor devices based on a Si-detector are frequently used for charged particle's detection; one application being in the investigation of cosmic radiation fields. From the spectra of energy deposition events in such devices, the total energy deposited by the radiation in silicon can be derived. This contribution presents the results of studies concerning the response of this type of detector to fast neutrons. First, the spectrum of energy deposition was established in fast neutron radiation fields with average energies from 0.5 to 50 MeV. It was found that these spectra vary significantly with the neutron energy. The comparison with the spectra registered in photon beams permitted an estimation of the part of energy deposited that could be attributed to neutrons. It was found that this part increases rapidly with neutron energy. The possibilities to use this type of detector for neutron detection and dosimetry for radiation protection are analysed and discussed.     

ON the question of the uniqueness of the energy-momentum complex in the special and general theory of relativity

Modification of the Fock method is used to look systematically for the complexes of energy and momentum which are conserved as a consequence of the vacuum field equations of the second order (real and complex scalar field, real vector field, symmetric tensor field of the linearized and non-linear Einstein theory). In contrast to Fock's results for fields described by equations of the first order, the complexes are not defined uniquely. The non-uniquenesses are eliminated by supplementary conditions.This paper is based on a diploma thesis worked out at the Department of Theoretical Physics, Faculty of Mathematics and Physics, Charles University.     

The radiation impedance and the energy partition among wave fields generated by a normal force strip radiator on isotropic solid surface

I.IntroductionTheacousticbeams'f0cusingandscanninggeneratedbytransducerarraysonso1idsurfacep1ayaveryimportantroleinacousticimagingandultrasonoc1ectronicdevices.InourpreviouSworkt'-'],weinvestigatcdtheproperties0ftheacousticbeams'focusingandscanninga1ongthesymmetricalaxis,acousticfic1ddistributioninthewho1espaceandnearthefocus.Andwealsogaverigoroustheoretica1ana1ysis,numcrica1simu1ationandexperimenta1obscrvation.Butra-diationimpedanceandenergyofthesurfaceradiatorshavenotbeendiscussedyetbynow.…     

Interaction phenomena between lump and solitary wave of a generalized (3+1)-dimensional variable-coefficient nonlinear-wave equation in liquid with gas bubbles

In this paper, a generalized (3+1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota's bilinear form and symbolic computation, lump and interaction solutions between lump and solitary wave are obtained,which include a periodic-shape lump solution, a parabolic-shape lump solution, a cubic-shape lump solution, interaction solutions between lump and one solitary wave, and between lump and two solitary waves. The spatial structures called the bright lump wave and the bright-dark lump wave are discussed. Interaction behaviors of two bright-dark lump waves and a periodic-shape bright lump wave are also presented. Their interactions are shown in some 3D plots.     

Energy of a wedge-shaped nanotwin calculated in terms of a dislocation mesoscopic model

The total energy of a wedge-shaped micro- and nanotwin is calculated in terms of a dislocation mesoscopic model. The total energy of the twin is represented as a sum of the elastic energy, energy of interaction between twinning dislocations, and stacking-fault energy of partial dislocations of the wedge-shaped twin. It is found that the evolution of the twin is controlled by the energy of interaction between twinning dislocations: in the case of a microtwin, it is five orders of magnitude higher than the elastic energy and six orders of magnitude higher than the stacking-fault energy. In the case of a nanotwin with the number of twinning dislocations at the twin boundary less than 20, all the three energies listed above are of the same order of magnitude. Therefore, all the components of the total energy contribute to the origination of a wedge-shaped twin. As the length of the twin increases with its width and the number of twinning dislocations at twin boundaries fixed, the total energy modulo grows although the density of twinning dislocations at twin boundaries decreases. This indicates that long-range stress fields due to twinning dislocations play an important part in the evolution of a wedge-shaped twin.     

Gravitational collapse of dark energy field configurations and supermassive black hole formation

Dark energy is the dominant component of the total energy density of our Universe. The primary interaction of dark energy with the rest of the Universe is gravitational. It is therefore important to understand the gravitational dynamics of dark energy. Since dark energy is a low-energy phenomenon from the perspective of particle physics and field theory, a fundamental approach based on fields in curved space should be sufficient to understand the current dynamics of dark energy. Here, we take a field theory approach to dark energy. We discuss the evolution equations for a generic dark energy field in curved space-time and then discuss the gravitational collapse for dark energy field configurations. We describe the 3 + 1 BSSN formalism to study the gravitational collapse of fields for any general potential for the fields and apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting equations for the time evolution of field configurations and the dynamics of space-time. Our results show that gravitational collapse of dark energy field configurations occurs and must be considered in any complete picture of our Universe. We also demonstrate the black hole formation as a result of the gravitational collapse of the dark energy field configurations. The black holes produced by the collapse of dark energy fields are in the supermassive black hole category with the masses of these black holes being comparable to the masses of black holes at the centers of galaxies.     

Deviations from hydrodynamics on the nanoscale

This study has examined the decay of an instantaneously imposed heat pulse on an equilibrium model of a dense fluid. The spatial extent of the initial pulse is quite small, of the order of 100 cubic nanometres; the amount of energy added to the system is only 5% of the total system kinetic energy. This small pulse decays quite rapidly, within several picoseconds, but the decay proceeds more slowly than predicted by the hydrodynamic equations. During the first picosecond of the decay, the kinetic energy is not equipartitioned, and a rapid process of energy transfer from kinetic energy to potential energy via interparticle interactions takes place. A new transport theory is developed that includes the ‘pre-hydrodynamic’ stage of evolution of non-equilibrium systems. Formally exact expressions for the local density, velocity, and kinetic energy (temperature) fields are developed in terms of Green's functions that depend on dynamic quantities, such as the mean-square displacement, averaged over the ensemble of initial states. No partial differential equations are involved.     

外电场下CdSe的基态性质和光谱特性研究

采用密度泛函(DFT)B3PW91方法在Lanl2dz基组下优化得到CdSe分子的基态稳定构型, 并研究了外电场对CdSe基态分子的总能量、HOMO能级、LUMO能级、能隙、电偶极矩μ、电荷布居、红外光谱的影响. 在相同的基组下用TD-DFT 方法计算了外电场下CdSe分子的前9个激发态的激发能、激发波长和振子强度. 结果表明: 无电场时CdSe分子的激发波长与实验结果符合较好, 相应的激发能也很接近. 随着电场增加, CdSe基态分子键长、偶极矩、红外谱强度先减小后增大; HOMO能级、LUMO能级、能隙随电场增加而减小; 总能量、谐振频率则是先增大后减小. 此外, 外电场对CdSe分子的激发能, 激发波长和振子强度均有较大影响.     

Radiation of de-excited electrons at large times in a strong electromagnetic plane wave

The late time asymptotics of the physical solutions to the Lorentz–Dirac equation in the electromagnetic external fields of simple configurations–the constant homogeneous field, the linearly polarized plane wave (in particular, the constant uniform crossed field), and the circularly polarized plane wave–are found. The solutions to the Landau–Lifshitz equation for the external electromagnetic fields admitting a two-parametric symmetry group, which include as a particular case the above mentioned field configurations, are obtained. Some general properties of the total radiation power of a charged particle are established. In particular, for a circularly polarized wave and constant uniform crossed fields, the total radiation power in the asymptotic regime is independent of the charge and the external field strength, when expressed in terms of the proper-time, and equals a half the rest energy of a charged particle divided by its proper-time. The spectral densities of the radiation power formed on the late time asymptotics are derived for a charged particle moving in the external electromagnetic fields of the simple configurations pointed above. This provides a simple method to verify experimentally that the charged particle has reached the asymptotic regime.     

Evaluation of the LEP centre-of-mass energy above the W-pair production threshold

Knowledge of the centre-of-mass energy at LEP2 is of primary importance to set the absolute energy scale for the measurement of the W-boson mass. The beam energy above 80 GeV is derived from continuous measurements of the magnetic bending field by 16 NMR probes situated in a number of the LEP dipoles. The relationship between the fields measured by the probes and the beam energy is calibrated against precise measurements of the average beam energy between 41 and 55 GeV made using the resonant depolarisation technique. The linearity of the relationship is tested by comparing the fields measured by the probes with the total bending field measured by a flux loop. This test results in the largest contribution to the systematic uncertainty. Several further corrections are applied to derive the centre-of-mass energies at each interaction point. In addition, the centre-of-mass energy spread is evaluated. The beam energy has been determined with a precision of 25 MeV for the data taken in 1997, corresponding to a relative precision of . This is small in comparison to the present uncertainty on the W mass measurement at LEP. However, the ultimate statistical precision on the W mass with the full LEP2 data sample should be around 25 MeV, and a smaller uncertainty on the beam energy is desirable. Prospects for improvements are outlined. Received: 14 December 1998 / Published online: 3 November 1999     

强外场调控下半导体中浅杂质态的光学吸收特性

理论研究了法拉第位形下强太赫兹激光场、磁场以及压强作用下半导体中浅杂质态非线性光学性质.利用含时非微扰理论——强太赫兹激光场效应被精确包含在激光缀饰库仑势中——和变分法计算出浅杂质态电子能级和波函数,然后基于紧致密度矩阵方法研究强外场和压强对浅杂质态1s→2p_z跃迁的线性、三阶非线性及总的光学吸收系数和折射率变化的影响.研究发现压强和强外场通过激光缀饰库仑势可调控跃迁能和几何因子的增大或减小,所以饱和吸收不但依赖于入射光强和弛豫时间而且还依赖于强外场,在强激光场强度和回旋共振区域附近饱和吸收更容易实现.线性、三阶非线性及总的光学吸收系数和折射率变化的共振峰位置和振幅,在选取合适的外场参数下不但受到强外场的有效调控,而且还受到压强的强烈影响.研究结果为设计强外场调控的新型高效基于杂质电子器件提供了理论支持.     

Interface Polaron Within Parallel Electric and Magnetic Fields

A combinative method of variational wavefunction and harmonic oscillator operator algebra is used to treat the interface polaron in a semi-infinite polar crystal within parallel electric and magnetic fields perpendicular to the interface. Both the bulk longitudinal optical phonon and the interface optical phonon together with the anisotropic mass of the electron are included. The energy level correction up to the second-order perturbation, cyclotron-resonance frequency and cyclotron mass are expressed as functions of the electric and magnetic fields and a parameter characterizing the mean distance of the polaron from the interface. This theory is used to calculate numerically the single heterostructure AlAs/GaAs, when the electron is at the X high-symmetry point of the conduction band of AlAs. The results show that the magnetic field greatly enhances the polaronic correction of the electron energy levels while the electric field only increases the correction of their surface optical phonon part but obviously decreases that of their bulk optical mode part and thus the total energy correction decreases as the electric field increases. The change of red shift due to the electron-phonon interaction with electric and magnetic fields is also obf ained.