Search results for "Scaling"
showing 10 items of 754 documents
Scaling violation in the infinite-momentum frame
1978
The theory of scaling violation is studied in asymptotically free gauge theories formulated in the infinite-momentum frame. The transition probabilities occurring in the equation governing the q/sup 2/ dependence of the parton distributions are calculated directly. The equivalence of this formalism for the longitudinal parton distributions with the usual one based on the operator-product expansion is demonstrated. The assets of our method are calculational simplicity and reference to physical intuition.
The classical statistical mechanics of Frenkel-Kontorova models
1995
The scaling properties of the free energy, specific heat, and mean spacing are calculated for classical Frenkel-Kontorova models at low temperature, in three regimes: near the integrable limit, the anti-integrable limit, and the sliding-pinned transition (“transition by breaking of analyticity”). In particular, the renormalization scheme given in previous work for ground states of Frenkel-Kontorova models is extended to nonzero-temperature Gibbs states, and the hierarchical melting phenomenon of Vallet, Schilling, and Aubry is put on a rigorous footing.
On the Multifractal Character of the Lorenz Attractor
1992
A detailed analysis of the Lorenz attractor in connection with generalized dimensions is presented in this work. Different methods have been employed to estimate these dimensions. Two of them are of standard type. A new method, based on the minimal spanning tree of the point distribution, is extensively tested in this work. It turns out that the Lorenz attractor is very appropriate for being analyzed through this technique, which produces a very clean estimate of the extrema scaling indices α min and α max . The different methods give qualitatively the same result: The Lorenz attractor has a multifractal character
Scaling behavior in the dynamics of a supercooled Lennard-Jones mixture
1994
We present the results of a large scale molecular dynamics computer simulation of a binary, supercooled Lennard-Jones fluid. At low temperatures and intermediate times the time dependence of the intermediate scattering function is well described by a von Schweidler law. The von Schweidler exponent is independent of temperature and depends only weakly on the type of correlator. For long times the correlation functions show a Kohlrausch behavior with an exponent $\beta$ that is independent of temperature. This dynamical behavior is in accordance with the mode-coupling theory of supercooled liquids.
Dynamic fragmentation of a two-dimensional brittle material with quenched disorder
1997
Fragmentation of a two-dimensional brittle material caused by a rapid impact has been analyzed. Computer simulations together with simple arguments are used to obtain a qualitative understanding of crack formation, which is then used to derive an exponential fragment size distribution valid in the large fragment size limit. In the limit of small fragments this distribution is solved numerically, and it is found to obey a scaling law with the exponent {minus}1.5. These results suggest that two different mechanisms are operative in the fragmentation process: branching of propagating cracks determines the small fragment size limit, and merging of the nucleated cracks determines the large size …
Carrier-dependentT c -suppression in Cu-site substituted high-T c cuprates
1996
We studied theTc-suppression by Cu-site substitution in Bi2Sr2Ca1−xYx(Cu1−zMz)2O8+δ (Bi-2212) with M=Fe, Co, Ni, Zn and in Bi2Sr1.6La0.4Cu1−zMzO6+δ (Bi-2201) with M=Co, Zn under variation of the hole concentrationp. We found a distinct behaviour between the underdoped and overdoped side of theTc-p phase diagram. Only in the overdoped regime,Tc is scaling asTc(p,z)=Tc(p,0)g(z) with ap-independent scaling functiong(z). We demonstrate the universality of this distinction in p-type high-Tc cuprates by comparison with publications on the La-214 and Y-123 systems and apply the scaling law to compare Bi2Sr2Ca(Cu1−zCoz)2O8+δ with the intercalation compound IBi2Sr2Ca(Cu1−zCoz)2O8+δ. The results are …
Impact Energy Flux on Earth in the Last 150 Ma as Inferred from the Cratering Records
1998
We have used a compilation of 30 well-dated large impact craters on Earth (i.e., diameters larger than 5 km) younger than 150 Ma, their diameters, geochronologic ages, and the corresponding uncertainties to construct a graph summarizing our current knowledge on the influx of the impact energy onto the Earth as a function of time. From the crater diameters, we estimated the corresponding impact energies through suitable scaling laws. Then to each crater we associated a gaussian (bell) function of time centered at its age. Finally, all the bell functions corresponding to different craters were summed up and the resulting curve was plotted. From this curve, it is apparent that the 65 Ma old Ch…
Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model
2013
AbstractThe singularity of specific heat CV of the three-dimensional Ising model is studied based on Monte Carlo data for lattice sizes L≤1536. Fits of two data sets, one corresponding to certain value of the Binder cumulant and the other — to the maximum of CV, provide consistent values of C0 in the ansatz CV(L)=C0+ALα/ν at large L, if α/ν=0.196(6). However, a direct estimation from our data suggests that α/ν, most probably, has a smaller value (e.g., α/ν= 0.113(30)). Thus, the conventional power-law scaling ansatz can be questioned because of this inconsistency. We have found that the data are well described by certain logarithmic ansatz.
A polymer chain trapped between two parallel repulsive walls: A Monte-Carlo test of scaling behavior
1998
An off-lattice bead-spring model of a polymer chain trapped between two parallel walls a distance D apart is studied by Monte-Carlo methods, using chain lengths N in the range $$32 \le N \le 512$$ and distances D from 4 to 32 (in units of the maximum spring extension). The scaling behavior of the coil linear dimensions parallel to the plates and of the force on the walls is studied and discussed with the help of current theoretical predictions. Also the density profiles of the monomers across the slit are obtained and it is shown that the predicted variation with the distance z from a wall, $$\rho (z) \propto {z^{1/\nu }}$$ , is obtained only when one introduces an extrapolation length λ in…
Multioverlap Simulations of the 3D Edwards-Anderson Ising Spin Glass
1997
We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for the entire $q$-range (multi-overlap) follow by re-weighting. We demonstrate the feasibility of the approach by studying the $3d$ Edwards-Anderson Ising ($J_{ik}=\pm 1$) spin glass in the broken phase ($\beta=1$). For the first time it becomes possible to obtain reliable results about spin glass tunneling barriers. In addition, as do some earlier numerical studies, our results support that Parisi mean field theory is valid down to $3d$.