Search results for "Linear"
showing 10 items of 7165 documents
1H and13C NMR spectroscopy of brominated diphenyl ethers. A multiple linear regression analysis
2000
The 1H and 13C NMR chemical shifts and 1H, 1H coupling constants of 27 brominated diphenyl ethers are reported. The increment models for the bromine substituent effects on the 1H and 13C NMR chemical shifts were constructed based on a multiple linear regression analysis. In addition to the single substituent effects, two particle increments and corrective terms for conformational effects are included in these models in order to obtain a reliable prediction of chemical shifts. Copyright © 2000 John Wiley & Sons, Ltd.
COMMUNICATION. OBSERVATIONS ON THE 121-Sb MÖSSBAUER PARAMETERS OF ANTIMONY (III) COMPOUNDS FEATURING A PYRAMIDAL SbS3SKELETAL UNIT
1991
Abstract A linear correlation between the chemical isomer shift and the quadrupole coupling constant for a number of antimony tris-thiolates has been evidenced. This behaviour can be rationalized on considering a modulation of the s/p character of the lone pair of electrons from the influence of secondary bonds.
Scaling behaviour of non-hyperbolic coupled map lattices
2006
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order which exhibit strongest possible chaotic behaviour for small coupling constants a. We prove that the expectations of arbitrary observables scale with \sqrt{a} in the low-coupling limit, contrasting the hyperbolic case which is known to scale with a. Moreover we prove that there are log-periodic oscillations of period \log N^2 modulating the \sqrt{a}-dependence of a given expectation value.…
Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation
2000
We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling constants collapse of the particle density occurs for $Dn\ge 2$ and typically to a $\delta$-function centered at the origin of the trap. By introducing a new dynamical variable for the spherically symmetric solutions we show that all such solutions are self-similar close to the center of the trap. Exact self-similar solutions occur if, and only if, $Dn=2$, and for this case of $Dn=2$ we exhibit an exact but rather special D=1 analytical self-similar solution collapsing to a $\delta$-function which …
Statistical Mechanics of the Integrable Models
1987
There is an infinity of classically integrable models. The only ones we can consider here, and these only briefly, are: the sine-Gordon (s-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sin \phi ,$$ (1.1) the sinh-Gordon (sinh-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sinh \phi ,$$ (1.2) and the repulsive and attractive non-linear Schrodinger (NLS) models $${}^ - {\rm{i}}{\phi _{\rm{t}}} = {\phi _{{\rm{xx}}}}{}^ - 2{\rm{c}}\phi {\left| \phi \right|^2}.$$ (1.3) The “attractive” NLS has real coupling constant c 0; φ is complex. In (1.1) and (1.2) m is a mass (ħ = c = 1) and φ is real. These 4 integrable models are in one space and one time …
Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms II: Charge Exchange
2019
International audience; We present the formalism of linear response theory both at zero and finite temperature in the case of asymmetric nuclear matter excited by an isospin flip probe. The particle-hole interaction is derived from a general Skyrme functional that includes spin-orbit and tensor terms. Response functions are obtained by solving a closed algebraic system of equations. Spin strength functions are analyzed for typical values of density, momentum transfer, asymmetry, and temperature. We evaluate the role of statistical errors related to the uncertainties of the coupling constants of the Skyrme functional and thus determine the confidence interval of the resulting response functi…
Quantum and Classical Statistical Mechanics of the Non-Linear Schrödinger, Sinh-Gordon and Sine-Gordon Equations
1985
We are going to describe our work on the quantum and classical statistical mechanics of some exactly integrable non-linear one dimensional systems. The simplest is the non-linear Schrodinger equation (NLS) $$i{\psi _t} = - {\psi _{XX}} + 2c{\psi ^ + }\psi \psi $$ (1) where c, the coupling constant, is positive. The others are the sine- and sinh-Gordon equations (sG and shG) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi $$ (1.2) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sinh \phi $$ (1.3)
Three-state Landau-Zener model in the presence of dissipation
2019
A population transfer based on adiabatic evolutions in a three-state system undergoing an avoided crossing is considered. The efficiency of the process is analyzed in connection with the relevant parameters, bringing to light an important role of the phases of the coupling constants. The role of dissipation is also taken into account, focusing on external decays that can be described by effective non-Hermitian Hamiltonians. Though the population transfer turns out to be quite sensitive to the decay processes, for very large decay rates the occurrence of a Zeno-phenomenon allows for restoring a very high efficiency.
Enhancement of charm quark production due to nonlinear corrections to the DGLAP equations
2004
We have studied how parton distributions based on the inclusion of nonlinear scale evolution and constraints from HERA data affect charm production in $pp$ collisions at center-of-mass energies of 5.5, 8.8 and 14 TeV. We find that, while the resulting enhancement can be substantial, it is very sensitive to the charm quark mass and the scale entering the parton densities and the strong coupling constant.
Role of Disorder on the Dynamics of a Nonlinear Model for DNA Thermal Denaturation
1992
The dynamics of thermal denaturation of DNA is a good example in which nonlinearity coexits with disorder. The amplitude of the motions is so high that bonds break and the base sequence is inhomogeneous since it contains the genetic code. Using a simple nonlinear model, we study the role of local inhomogeneities or of extended disorder on the dynamics of the localized excitations and on the denaturation rate by numerical simulations at constrained temperature. Approximate analytical results are obtained for the trapping of the breatherlike excitations by isolated defects and the statistical mechanics of the disordered molecule.