Search results for "lattice [space-time]"
showing 10 items of 692 documents
Relative importance of second-order terms in relativistic dissipative fluid dynamics
2014
[Introduction] In Denicol et al. [Phys. Rev. D 85 , 114047 (2012)], the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in the Knudsen number, in the inverse Reynolds number, or their product. Terms of second order in the Knudsen number give rise to nonhyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massl…
Subsecond fluorine-19 MRI of the lung
2006
Minimal scan times in rapid fluorine-19 MRI using sulfur hexafluoride (SF6) have been on the order of 10 s. Because of the very short T1 relaxation time of SF6 (T1 = 1.65 ms), high receiver bandwidths are necessary to allow for a high number of excitations. Since high bandwidths cause high levels of electronic noise, SNR per acquisition has been too low to further reduce scan time. The purpose of this study was to investigate whether scan times could be reduced using hexafluoroethane (C2F6), a gas with a longer T1 (T1 = 7.9 ms) at a relatively low bandwidth of 488 Hz/pixel. Gradient-echo images were acquired during and after completion of the wash-in of a 70% C2F6- 30% O2 mixture. Peak SNR …
13C NMR Spin−Lattice Relaxation and Conformational Dynamics in a 1,4-Polybutadiene Melt
2001
We have performed molecular dynamics (MD) simulations of a melt of 1,4-polybutadiene (PBD, 1622 Da) over the temperature range 400-273 K. 13 C NMR spin-lattice relaxation times (T 1 ) and nuclear Overhauser enhancement (NOE) values have been measured from 357 to 272 K for 12 different resonances. The T 1 and NOE values obtained from simulation C-H vector P 2 (t) orientational autocorrelation functions were in good agreement with experiment over the entire temperature range. Analysis of conformational dynamics from MD simulations revealed that T 1 depends much less strongly on the local chain microstructure than does the mean conformational transition time. Spin-lattice relaxation for a give…
Spatial heterogeneity in glassy polystyrene detected by deuteron NMR relaxation
1999
Using deuteron NMR, the dynamics of supercooled polystyrene-d 3 was investigated near the calorimetric glass transition. At these temperatures non-exponential spin lattice relaxation is found, indicating the presence of spatial heterogeneity. With increasing temperature, structural relaxation becomes fast enough to average efficiently over different spatial environments, leading to exponential magnetization decays. A qualitative comparison with toluene as a representative of a low molecular weight glass former is carried out. Indications are found that in polystyrene the observed averaging process is more effective at T g than it is in toluene.
On the Size Complexity of Deterministic Frequency Automata
2013
Austinat, Diekert, Hertrampf, and Petersen [2] proved that every language L that is (m,n)-recognizable by a deterministic frequency automaton such that m > n/2 can be recognized by a deterministic finite automaton as well. First, the size of deterministic frequency automata and of deterministic finite automata recognizing the same language is compared. Then approximations of a language are considered, where a language L′ is called an approximation of a language L if L′ differs from L in only a finite number of strings. We prove that if a deterministic frequency automaton has k states and (m,n)-recognizes a language L, where m > n/2, then there is a language L′ approximating L such that L′ c…
Dependence of the lattice parameters and the energy gap of zinc-blende-type semiconductors on isotopic masses.
1996
The dependence of the ${\mathit{E}}_{0}$ direct gap of Ge, GaAs, and ZnSe on isotopic masses at low temperatures has been investigated. Contributions of the variation of the lattice parameter to the gap shift of the binary compounds have been evaluated by using a volume-dependent lattice dynamics, while local empirical pseudopotential techniques have been employed to calculate gap shifts due to electron-phonon interaction. The dependence of these terms on the lattice-dynamical model and on the q\ensuremath{\rightarrow}0 extrapolation of the pseudopotential form factors has been investigated. The contributions of the optical and acoustical modes to the isotopic shift are analyzed. The result…
Boundary quotients and ideals of Toeplitz C∗-algebras of Artin groups
2006
We study the quotients of the Toeplitz C*-algebra of a quasi-lattice ordered group (G,P), which we view as crossed products by a partial actions of G on closed invariant subsets of a totally disconnected compact Hausdorff space, the Nica spectrum of (G,P). Our original motivation and our main examples are drawn from right-angled Artin groups, but many of our results are valid for more general quasi-lattice ordered groups. We show that the Nica spectrum has a unique minimal closed invariant subset, which we call the boundary spectrum, and we define the boundary quotient to be the crossed product of the corresponding restricted partial action. The main technical tools used are the results of …
?Almost? mean-field ising model: An algebraic approach
1991
We study the thermodynamic limit of the algebraic dynamics for an "almost" mean-field Ising model, which is a slight generalization of the Ising model in the mean-field approximation. We prove that there exists a family of "relevant" states on which the algebraic dynamics αt can be defined. This αt defines a group of automorphisms of the algebra obtained by completing the standard spin algebra with respect to the quasiuniform topology defined by our states. © 1991 Plenum Publishing Corporation.
Unifying vectors and matrices of different dimensions through nonlinear embeddings
2020
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous parameter $\kappa \in \mathbb{R}$ is being varied, thus allowing the unification of vectors, matrices and tensors in single mathematical structures. This technique is applied to construct warped models in the passage from supergravity in 10 or 11-dimensional spacetimes to 4-dimensional ones. We also show how nonlinear embeddings can be used to connect cellular automata (CAs) to coupled map lattices (CMLs) and to nonlinear partial differential equations, derivi…
Homopolymer adsorption on periodically structured surfaces in systems with incommensurable lengths
2013
Surface-induced selective adsorption of homopolymers on a generic level is numerically analyzed for freely jointed chains (with a fixed bond length) whose monomers are attracted by the sites of regular periodic patterns. In particular, the behavior of the specific heat, the gyration tensor, and the bond order tensor are investigated as functions of the temperature. The properties of the transition are related to the interplay of the characteristic lengths. The adsorption proceeds in two steps for certain incommensurabilities of the bond length and the lattice constant. The corresponding adsorption mechanisms are elucidated by looking at the evolution of the inter bond angle distribution upo…