Search results for "Statistica"
showing 10 items of 5969 documents
Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly.
2011
The internally contracted multireference coupled cluster (icMRCC) method allows a highly accurate description of both static and dynamic correlation with a computational scaling similar to single reference coupled cluster theory. The authors show that the method can lose its orbital invariance and size consistency when no special care is taken in the elimination of redundant excitations. Using the BeH(2) model system, four schemes are compared which differ in their treatment of linear dependencies between excitations of different rank (such as between singles and doubles). While the energy curves agree within tens of μE(h) when truncating the cluster operator at double excitations (icMRCCSD…
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 …
Propagation of uncertainties in the Skyrme energy-density-functional model
2013
Parameters of nuclear energy-density-functionals (EDFs) are always derived by an optimization to experimental data. For the minima of appropriately defined penalty functions, a statistical sensitivity analysis provides the uncertainties of the EDF parameters. To quantify theoretical errors of observables given by the model, we studied the propagation of uncertainties within the UNEDF0 Skyrme-EDF approach. We found that typically the standard errors rapidly increase towards neutron rich nuclei. This can be linked to large uncertainties of the isovector coupling constants of the currently used EDFs.
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)
Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts
2002
The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents $\theta_{s} \approx -0.36$ in 2D and $\theta_{s} \approx +0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than thr…
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.
Energy landscape properties studied using symbolic sequences
2006
We investigate a classical lattice system with $N$ particles. The potential energy $V$ of the scalar displacements is chosen as a $\phi ^4$ on-site potential plus interactions. Its stationary points are solutions of a coupled set of nonlinear equations. Starting with Aubry's anti-continuum limit it is easy to establish a one-to-one correspondence between the stationary points of $V$ and symbolic sequences $\bm{\sigma} = (\sigma_1,...,\sigma_N)$ with $\sigma_n=+,0,-$. We prove that this correspondence remains valid for interactions with a coupling constant $\epsilon$ below a critical value $\epsilon_c$ and that it allows the use of a ''thermodynamic'' formalism to calculate statistical prope…
Modified mode-coupling theory for the collective dynamics of simple liquids
2011
Recently it has been shown that mode-coupling theory, which accounts for the salient features of glassy relaxation near the liquid–glass transition, is also capable of describing the collective excitations of simple liquids away from the glass transition. In order to further improve the agreement between theory and computer simulations on Lennard-Jones argon we modify MCT by taking binary collisions into account. This, in fact, improves the agreement. We also show that multiplying the memory function of the original theory with a reduction factor leads to similar results.
A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system
1996
Using a molecular dynamics computer simulation we determine the temperature dependence of the partial structure factors for a binary Lennard-Jones system. These structure factors are used as input data to solve numerically the wave-vector dependent mode-coupling equations in the long time limit. Using the so determined solutions, we compare the predictions of mode-coupling theory (MCT) with the results of a previously done molecular dynamics computer simulation [Phys. Rev. E 51, 4626 (1995), ibid. 52, 4134 (1995)]. From this comparison we conclude that MCT gives a fair estimate of the critical coupling constant, a good estimate of the exponent parameter, predicts the wave-vector dependence …