Search results for "Exponential function"
showing 10 items of 173 documents
18 parameter deformations of the Peregrine breather of order 10 solutions of the NLS equation
2015
We present here new solutions of the focusing one-dimensional nonlinear Schrödinger (NLS) equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric rings as found for the lower-orders.
The glass transition in (KI)0.5(ND4I)0.5 mixed crystals as studied by deuteron spin-lattice relaxation
1993
Abstract Nuclear spin resonance has been used to study the deuteron magnetization recovery in (KI)0.5(ND4I)0.5 mixed crystals. At high temperatures the spin-lattice-relaxation is exponential. For T ⪅ 45 K deviations from this simple behaviour occur, signalling the onset of spatial inhomogeneities due to the formation of an orientational glass. The results demonstrate that the transition of (KI)0.5(ND4I)0.5 into the glassy state is driven by the freezing of random bonds.
Correlations of the nonexponentiality and state dependence of mechanical relaxations with bond connectivity in Ge-As-Se supercooled liquids
1992
We have studied the mechanical responses of supercooled Ge-As-Se liquids to flexural strains and temperature steps. The departures from exponential relaxation correlate well with the variations in connectivity. The structural state dependence of the mechanical relaxation, detected in pure and weakly cross-linked Se, is suppressed completely at the rigidity percolation threshold {l angle}{ital r}{sub {ital c}}{r angle}, where the liquid fragility is a minimum. The shapes of the decay functions of samples with the same {l angle}{ital r}{sub {ital c}}{r angle} but different compositions are not universal at {ital T}{sub {ital g}} probably because of chemical effects near the binary edges of th…
A Monte Carlo study of diffusion in "living polymers"
1996
We report the first numeric experiments on diffusion in living polymers (polymers that can break and recombine reversibly, and are characterized by an exponential molecular weight distribution). In the simulation we use a modification of the bond fluctuation model which is known to reproduce the correct Rouse dynamics of polymer chains. The diffusion coefficient D reveals a Rouse-type behaviour D ∝ 1/L, where L is the average chain length of the polydisperse system. We also find a D ∝ exp [ − V/2kBT] dependence on the bond energy V, whereas at constant temperature the diffusion coefficient turns out to be inversely proportional, D ∝ ρ−1, to the monomer density of the system ρ in agreement w…
Polymer-specific effects of bulk relaxation and stringlike correlated motion in the dynamics of a supercooled polymer melt
2003
We analyze dynamical heterogeneities in a simulated “bead-spring” model of a nonentangled, supercooled polymer melt. We explore the importance of chain connectivity on the spatially heterogeneous motion of the monomers. We find that when monomers move, they tend to follow each other in one-dimensional paths, forming strings as previously reported in atomic liquids and colloidal suspensions. The mean string length is largest at a time close to the peak time of the mean cluster size of mobile monomers. This maximum string length increases, roughly in an exponential fashion, on cooling toward the critical temperature TMCT of the mode-coupling theory, but generally remains small, although large…
Brownian dynamics of grafted polymer chains: time dependent properties
1995
Results of computer simulations of polymer layers consisting of chains grafted by one end on an unpenetrable plane are presented. Characteristics of translational and rotational motion of different chain segments and correlation functions of chain radii were calculated both for single layers at different grafting densities s and for two interacting layers at different distances D between parallel grafting planes. Two values of grafting density were used in the latter case. The behavior of different correlation times as function of s and D and the interplay between the interpenetration of the brushes and rotational and translational motion are discussed. Both relaxation functions and mean sq…
Dynamical heterogeneities in glass-forming materials
1996
ABSTRACTCooperative dynamics around the glass transition leads to complex motional behavior of the individual molecules, resulting in non-exponential relaxation. The nature of this non-exponentiality is clarified theoretically as well as experimentally. The non-exponentiality may be due to heterogeneous relaxation (superposition of exponential processes with different rate constants) or homogeneous relaxation (identical intrinsically non-exponential processes). A precise definition of both limits is given. It is shown that the type of relaxation, i.e. to which degree heterogeneous and homogeneous contributions are present, reflects geometrical properties of the dynamics. The heterogeneous c…
Modeling long-range memory with stationary Markovian processes
2009
In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate transformation of a specific power-law correlated additive process x(t), already known in the literature, whose pdf shows power-law tails 1/x^a. We give analytical and numerical evidence that although the new processes (i) are Markovian and (ii) have gaussian or exponential tails their autocorrelation function still shows a power-law decay =1/T^b where b grows with a with a law which is compatible with b=a/2-c, where c is a numerical constant. When a<2(1+c) th…
A New Feature Selection Methodology for K-mers Representation of DNA Sequences
2015
DNA sequence decomposition into k-mers and their frequency counting, defines a mapping of a sequence into a numerical space by a numerical feature vector of fixed length. This simple process allows to compare sequences in an alignment free way, using common similarities and distance functions on the numerical codomain of the mapping. The most common used decomposition uses all the substrings of a fixed length k making the codomain of exponential dimension. This obviously can affect the time complexity of the similarity computation, and in general of the machine learning algorithm used for the purpose of sequence analysis. Moreover, the presence of possible noisy features can also affect the…
Poincare Inequalities and Spectral Gap, Concentration Phenomenon for G-Measures
2002
We produce a new approach based upon inequalities of Poincare’s type for giving constructive estimates of the mixing rate for a family of mixing stationary processes continuously depending on their past called g-measures. We establish also exponential inequalities of Hoeffding’s type leading to a concentration phenomenon for a large class of observables; this last property permits in particular to give the typical behaviour of the n-orbits of a g-measure.