Sharp Crossover Research Articles

Transients and asymptotics in granular phase space

The dynamics of dissipative dynamical systems can be described by the sequential appearance of two different regimes. From a given initial condition, one first observes transient behavior characterized by a high degree of contraction of volumes in phase space. This is followed by an asymptotic regime with one or several attractors into which trajectories inject after long times. There is however, no sharp crossover between these two regimes and the identification of either one depends on the precision of measurement. In order to investigate these issues, we studied the dynamics of contracting integer maps. We found out that for the cases which in the continuum limit correspond to bifurcations, transients consists of two regimes sharply separated by a crossover point which displays universal scaling with the size of the set. Moreover, their average lengths display power law dependence on the accuracy of their measurement. This behavior persists away from bifurcation but with a different scaling law. In addition, we studied deterministic diffusion on finite sets and obtained analytic expressions for the mean square displacement in the long time limit.

Fractal shape of hail clouds.

We present a fractal analysis of severe convective storms using data collected during a recent hail suppression experiment ``Grossversuch IV'' in Switzerland. For larger clouds, a fractal shape is observed and from an analysis of the perimeter-to-area relation the fractal (i.e., Hausdorff) dimension is found to be ${\mathrm{D}}_{\mathrm{s}}$=1.36\ifmmode\pm\else\textpm\fi{}0.1 in agreement with the value 1.35 from the theory of relative turbulent diffusion and an earlier analysis of cloud shapes. Moreover, a particle drift, present in strong lateral winds as well as in the center of hail clouds, is presumably responsible for a rather sharp crossover to a smooth behavior (${\mathrm{D}}_{\mathrm{s}}$=1) showing the existence of an apparent characteristic length.

Correlations between adjoint polyakov loops

We consider 4D SU(2) lattice gauge theory and report a high statistics MC investigation of correlations between Polyakov loops in the adjoint SU(2) representation. For large β-values and on lattices with small sized spatial volumes these correlations allow glueball estimates improving results of the literature by several orders of magnitude. Our data for the mass gap and the string tension exhibit a very sharp crossover between the small-volume limit and the infinite-volume limit. This is prohibitive to extracting physics from Lüscher's weak coupling expansion by matching it with numerical data.

Order of the deconfining transition for finite-temperature QCD in the presence of dynamical quarks.

We present a high-statistics computation of finite-temperature QCD: The effects of dynamical quarks are included by the pseudofermion method. We concentrate only on one value of the bare quark mass and try to determine the order of the transition. The metastability observed in a previ- ous preliminary study of ours is confirmed also by this new set of data. Ordered start. did not allo~ us to study the properties of the transi- tion in detail. We decided, therefore, to consolidate our computation by improving the statistics and the density of the measurements around P, . The outcome of this work is presented here. Let us briefly review the results of Ref. 1 to justify our choice of parameters. We performed Monte Carlo simulations including dynamical quarks by the pseudo- fermion method. We used two different lattice volumes, 63&&4 and 83x4. For all the values of the bare quark masses that we studied (m = 0.1, 0.2, 0.5, 1, 2) we always observed a sharp crossover until values of m for which P, was compatible with the pure gauge value. The quantities we measured were 8'and The results were pretty much independent of the dimension of the lattice and also stable with respect to

Analysis of light-scattering measurements near a cloud point.

An anlysis is reported of earlier light-scattering measurements by Wong and Knobler on a liquid mixture undergoing phase separation. When the system was quenched into the two-phase region to a temperature near the cloud point, the growth of intensity with time displayed two characteristic regions: an initial rapid rise followed by a sharp crossover to slower growth. It is shown that such behavior is consistent with the predictions of the Langer-Schwartz description of the homogeneous nucleation and growth of droplets.

Pseudospin approach for planar ferromagnets

A pseudospin approach is developed for the study of quantum spin systems. The method is based on generalized coherent states in the symmetric representations of the unitary algebra U(2 s+1), where s is the total spin at each site, and on the associated Holstein-Primakoff theory. A systematic 1/ n éxpansion is derived which enables one to study magnets with weak as well as strong single-site anisotropies. While the method applies to a variety of quantum spin systems in arbitrary lattice dimensions, particular emphasis is placed here on the spin-1 planar ferromagnetic chain observed in CsNiF 3. The 1/ n expansion for that system yields a twofold spectrum of elementary excitations, the usual magnon and a collective mode. It is also found that a sharp crossover transition occurs for intermediate couplings in analogy with the Gross-Witten third-order transition in the large- n limit of simple gauge models.

Hydrodynamic crossover in two‐polymer mixtures from viscosity measurements

AbstractA very sharp crossover is observed in the variation of the reduced viscosity ηsp/c as a function of the concentration c for mixtures of 1:1 by weight mixtures of polystyrene and poly(methylmethacrylate) in benzene at 20°C and a 1:1 by weight mixture of poly(ethylene glycol) and polystyrene in benzene at 20°C. The crossover is attributed to the critical to the concentration of the two respective polymers in the solution and its sharpness is due to the incompatibility between the two different polymers.

Specific heat near the nematic-smectic-Atransition of octyloxycyanobiphenyl

High-resolution ac microcalorimetry studies of octyloxycyanobiphenyl, 80CB, reveal a nematic-smetic-$A$ transition consistent with the superfluid analogy as regards the specific-heat exponents, namely $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\lesssim}O(log)$. However, the amplitude ratio, $\frac{A}{{A}^{\ensuremath{'}}}=1.35$, is inconsistent with the superfluid analogy. This may be related to two complicating features of the nematic-smectic-$A$ transition of the 80CB studied. First, the transition appears to be weakly first order and slightly broadened by impurities. The two-phase region is \ensuremath{\sim}0.04 K wide and an analysis of it based on weak-solution theory gives a transition entropy in the range $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{R}_{o}l\ensuremath{\Delta}Sl3.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{R}_{o}$. Secondly, the specific-heat exponent exhibits sharp crossover above ${T}_{c}$ from $\ensuremath{\alpha}\ensuremath{\gtrsim}0.3$ to $\ensuremath{\alpha}\ensuremath{\sim}O(log)$ as the asymptotic limit is approached.

Detailed crossover studies of transition metal ions

The complete ligand field, interelectronic repulsion, and spin-orbit interaction matrices were solved for the octahedral and tetrahedrald4 andd6 electron configurations. The results are employed in a detailed study of the crossover region. It is demonstrated that, close to the crossover, complicated mixing and interaction patterns may arise. A sharp crossover is encountered in the octahedrald6 system exclusively whereΓ1 andΓ5 levels are involved. In all situations where the two ground levels transform according to the same irreducible representation, the crossover is redefined by that value of 10Dq where both ground terms participate in the lowest level to equal amounts.

Frequency Stabilization of a Gas Laser

The frequency of a gas laser was stabilized by making use of the competition between the oppositely circularly polarized components of a single cavity mode of a laser in an axial magnetic field. For appropriate transitions the coupling between the polarizations leads to a sharp crossover in their intensities as the cavity is tuned across the center of the atomic line. The difference of the intensities of the two polarizations is used as the discriminant for a feedback loop which keeps the cavity tuned to the atomic line center. This discriminant is at least an order of magnitude more sensitive than those previously reported. Two identical lasers and control systems were constructed utilizing the 1.52-microm transition of Ne (2s(2) ? 2p(1), J = 1 ? J = 0), and their relative stability was determined by measurements of their difference frequency. The very short term frequency fluctuations were essentially determined by the free-running stability of the laser and were of the order of +/-2 parts in 10(9) per laser. The longterm fluctuations were considerably reduced by the control loop, and over times of the order of 10 min, the average frequencies (10-sec averages) had standard deviations of 1 part in 10(10) per laser.

Hall Effect Determination of Planar Stress in Ferromagnetic Films

Hall effect measurements on a ferromagnetic film can be used to examine the normal anisotropy and the distribution of stresses in the plane of the film. The measured Hall voltage exhibits a smooth transition from low to high field regions rather than the sharp crossover, at technical saturation, which is expected of a single domain. Since the ferromagnetic Hall effect depends upon the component of magnetization perpendicular to the plane one can attribute this difference of behavior to a domain structure describable by a distribution of normal anisotropies. The difference between the single and multi-domain Hall plots depends upon the nature of this distribution and from certain features of the experimentally obtained difference curve one can infer the type and extent of the distribution. If the anisotropy distribution is due to a corresponding range of strains superimposed on the geometric anisotropy of the film one can also estimate the form and extent of the function describing the planar stresses. It is shown that the existence of the anisotropy distribution results in a difference between the field at which the Hall measurements indicate technical saturation and that at which the normal anisotropy distribution is peaked.