Search results for " solution"
showing 10 items of 3084 documents
Coriolis interaction parameters of the (2100; F2) bands of SiH4 and GeH4. A test of local mode models
1995
Abstract The high-resolution spectra of the (2100; F 2 , N ), N = 1 and 2, bands of SiH 4 and GeH 4 have been recorded and preliminary analyzed. The Coriolis interaction parameter 2 Bζ 3 is obtained; it provides a test of three widely used models: the harmonically coupled anharmonic oscillators model with two different kinds of variables, and the normal mode model with Darling-Dennison resonance included.
Schwarzschild Interior in Conformally Flat Form
2004
A unified conformally flat form of the static Schwarzschild interior space–times is provided. A new parameter that allows us to analyze the symmetry (spherical, plane or hyperbolic) of the three well known classes of metrics is introduced. In the spherically symmetric case, this parameter is related to the historical limit value of the mass to radius ratio found by Schwarzschild for a sphere of incompressible fluid.
Nonlinear anisotropic heat conduction in a transformer magnetic core
1996
In this chapter we deal with a quasilinear elliptic problem whose classical formulation reads: Find \( u \in {C^1}\left( {\bar \Omega } \right) \) such that u|Ω ∈ C 2(Ω) and $$ - div\left( {A\left( { \cdot ,u} \right)grad\;u} \right) = f\quad in\;\Omega $$ (9.1) $$ u = \bar u\quad on\;{\Gamma _1} $$ (9.2) $$ \alpha u + {n^T}A\left( { \cdot ,u} \right)grad\;u = g\quad on\;{\Gamma _2} $$ (9.3) where Ω ∈ L, n = (n 1, ..., n d ) T is the outward unit normal to ∂Ω, d ∈ {1, 2, ...,}, Γ1 and Γ2 are relatively open sets in the boundary ∂Ω, \({\overline \Gamma _1} \cup {\overline \Gamma _2} = \partial \Omega ,\,{\Gamma _1} \cap {\Gamma _2} = \phi\), \( A = \left( {{a_{ij}}} \right)_{i,j = 1}^d \) is…
The exact solution of the diffusion trapping model of defect profiling with variable energy positrons
2013
We report an exact analytical solution of so-called positron diffusion trapping model. This model have been widely used for the treatment of the experimental data for defect profiling of the adjoin surface layer using the variable energy positron (VEP) beam technique. Hovewer, up to now this model could be treated only numerically with so-called VEPFIT program. The explicit form of the solutions is obtained for the realistic cases when defect profile is described by a discreet step-like function and continuous exponential-like function. Our solutions allow to derive the analytical expressions for typical positron annihilation characteristics including the positron lifetime spectrum. Latter …
Quantum knots in Bose-Einstein condensates created by counterdiabatic control
2017
We theoretically study the creation of knot structures in the polar phase of spin-1 BECs using the counterdiabatic protocol in an unusual fashion. We provide an analytic solution to the evolution of the external magnetic field that is used to imprint the knots. As confirmed by our simulations using the full three-dimensional spin-1 Gross-Pitaevskii equation, our method allows for the precise control of the Hopf charge as well as the creation time of the knots. The knots with Hopf charge exceeding unity display multiple nested Hopf links.
Enhanced ferroelectric phase-transition temperature in perovskite-based solid solutions
2004
We explain how the phenomena of ferroelectric phase transition temperature ${T}_{c}$ enhancement beyond the end members in perovskite solid solution such as $\mathrm{Bi}M{\mathrm{O}}_{3}\text{\ensuremath{-}}{\mathrm{PbTiO}}_{3}$ ($M=\mathrm{Sc}$, In, etc.) is related to nonlinear and spatial correlation effects. The explanation is based on the calculation of ${T}_{c}$ in the framework of our random field theory with additional account for nonlinear effects in the above substances. We show that the maximum of ${T}_{c}$ for certain ${\mathrm{PbTiO}}_{3}$ content takes place when coefficient of nonlinearity is positive, the value of this coefficient is found from best fit between theory and ex…
Behavior of one-magnon frequency in antiferromagneticNicMg1−cOsolid solutions
2005
The one-magnon scattering was studied in antiferromagnetic ${\mathrm{Ni}}_{c}{\mathrm{Mg}}_{1\ensuremath{-}c}\mathrm{O}$ solid solutions. We observed unpredicted behavior of both temperature and composition dependences of one-magnon excitation energies. First, the abrupt change of the one-magnon frequency by $7--8\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ occurs between $c=0.98$ and $c=0.9$ in the limit of $T\ensuremath{\rightarrow}0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Second, upon increasing temperature, the one-magnon energy for highly diluted nickel oxide vanishes significantly below the N\'eel temperature.
Test of the semischematic model for a liquid of linear molecules
1998
We apply to a liquid of linear molecules the semischematic mode-coupling model, previously introduced to describe the center of mass (COM) slow dynamics of a network-forming molecular liquid. We compare the theoretical predictions and numerical results from a molecular dynamics simulation, both for the time and the wave-vector dependence of the COM density-density correlation function. We discuss the relationship between the presented analysis and the results from an approximate solution of the equations from molecular mode-coupling theory [R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].
Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator
2003
We use the exact solution for the damped harmonic oscillator to discuss some relevant aspects of its open dynamics often mislead or misunderstood. We compare two different approximations both referred to as Rotating Wave Approximation. Using a specific example, we clarify some issues related to non--Markovian dynamics, non--Lindblad type dynamics, and positivity of the density matrix.
Infrared and broadband dielectric spectroscopy of PZN-PMN-PSN relaxor ferroelectrics: Origin of two-component relaxation
2006
Dielectric spectra of several solid solutions of $\mathrm{Pb}{\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}{\mathrm{O}}_{3}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{Sc}}_{1∕2}{\mathrm{Nb}}_{1∕2}{\mathrm{O}}_{3}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{Zn}}_{1∕3}{\mathrm{Nb}}_{2∕3}{\mathrm{O}}_{3}$ (PMN-PSN-PZN) relaxor ferroelectrics were investigated in a broad frequency range from $20\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ up to $100\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$ by a combination of dielectric spectroscopy $(20\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}\char21{}53\phantom{\rule{0.3em}{0ex}}\mathrm{GHz})$, time-domain terahertz spectroscopy $(0.1\char21{}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{TH…