Straight Theta Research Articles

Anomalous scaling of a passive scalar in the presence of strong anisotropy.

Field theoretic renormalization group and the operator product expansion are applied to a model of a passive scalar quantity straight theta(t,x), advected by the Gaussian strongly anisotropic velocity field with the covariance infinity delta(t-t('))/x-x(')/(epsilon). Inertial-range anomalous scaling behavior is established, and explicit asymptotic expressions for the structure functions S(n)(r) identical with<[straight theta(t,x+r)-straight theta(t,x)](n)> are obtained. They are represented by superpositions of power laws; the corresponding anomalous exponents, which depend explicitly on the anisotropy parameters, are calculated to the first order in epsilon in any space dimension d. In the limit of vanishing anisotropy, the exponents are associated with tensor composite operators built of the scalar gradients, and exhibit a kind of hierarchy related to the degree of anisotropy: the less is the rank, the less is the dimension and, consequently, the more important is the contribution to the inertial-range behavior. The leading terms of the even (odd) structure functions are given by the scalar (vector) operators. For the finite anisotropy, the exponents cannot be associated with individual operators (which are essentially "mixed" in renormalization), but the aforementioned hierarchy survives for all the cases studied. The second-order structure function S2 is studied in more detail using the renormalization group and zero-mode techniques; the corresponding exponents and amplitudes are calculated within the perturbation theories in epsilon, 1/d, and in the anisotropy parameters. If the anisotropy of the velocity is strong enough, the skewness factor S(3)/S(3/2)(2) increases going down towards the depth of the inertial range; the higher-order odd ratios increase even if the anisotropy is weak.

Segregation transitions in wet granular matter

We report the effect of interstitial fluid on the extent of segregation by imaging the pile that results after bidisperse color-coded particles are poured into a silo. Segregation is sharply reduced and preferential clumping of small particles is observed when a small volume fraction of fluid V(f) is added. We find that viscous forces in addition to capillary forces have an important effect on the extent of segregation s and the angle of repose straight theta. We show that the sharp initial change and the subsequent saturation in s and straight theta occurs over similar V(f). We also find that a transition back to segregation can occur when the particles are completely immersed in a fluid at low viscosities.

Evidence for genetic heterogeneity in families with congenital motor nystagmus (CN)

Congenital motor nystagmus (CN) is a relatively common genetic disorder (approximately 1 in 1500) characterized by bilateral involuntary ocular oscillations, with onset occurring within the first six months of life. To date, three loci associated with CN have been mapped to chromosomes 6p12, Xp11.4-p11.3, and Xq26-q27. We analyzed five pedigrees segregating for CN. Mapping studies using markers in these three regions showed that only one pedigree exhibited suggestive linkage with a lod score of 2.08, straight theta=0.0, at chromosome Xp11. This pedigree had both affected male and female members, with two unaffected obligate female carriers. The remaining four pedigrees did not exhibit evidence of linkage for any of the three chromosome locations. Three of the pedigrees, Pedigrees 2, 4, and 5, exhibited several instances of male-to-male transmission, excluding X-linkage, and exhibited a lod score of -3.82, straight theta=0.0, for marker D6S459 located at 6p12, thus excluding the chromosome 6 locus. This provides evidence for at least a fourth locus associated with CN.

Autosomal dominant cone-rod dystrophy due to a missense mutation (R838C) in the guanylate cyclase 2D gene (GUCY2D) with preserved rod function in one branch of the family

We present the clinical and molecular genetic features of a large multi-generation Norwegian family with dominant cone-rod dystrophy. Ophthalmological evaluation including electroretinography showed cone dysfunction in younger patients, with rod dysfunction becoming apparent at more advanced stages of the disease. In one branch of the family, cone degeneration remained the only manifestation despite advancing age. Linkage analysis mapped the disease gene in this family to 17p12-p13, a chromosome region previously linked to cone-rod dystrophy in a Swedish family (CORD5). A maximum LOD score of 3.25 (straight theta = 0.00) for marker D17S1844 was obtained. Mutation analysis of the guanylate cyclase 2D gene (GUCY2D, MIM 600179, previously called RETGC1), located at 17p12-p13, showed a missense mutation (R838C) in exon 13, that co-segregated with the eye disease in the family. Our suspicion of the possibility of an interrelationship between the Swedish CORD5 family and the present family, both originating from Northern Scandinavia, initiated the linkage analysis in the Norwegian family. The R838C missense mutation was not, however, detected in the Swedish patients, strongly suggesting no relationship between these two families. The long-term ophthalmological evaluation in this large four-generation family, combined with the identification of the disease-causing mutation, provide critical information for refining the classification, prognosis, and genetic counselling of patients with cone-rod dystrophies.

Optimal pruning in neural networks

We study pruning strategies in simple perceptrons subjected to supervised learning. Our analytical results, obtained through the statistical mechanics approach to learning theory, are independent of the learning algorithm used in the training process. We calculate the post-training distribution P(J) of synaptic weights, which depends only on the overlap rho(0) achieved by the learning algorithm before pruning and the fraction kappa of relevant weights in the teacher network. From this distribution, we calculate the optimal pruning strategy for deleting small weights. The optimal pruning threshold grows from zero as straight theta(opt)(rho(0), kappa) approximately [rho(0)-rho(c)(kappa)](1/2) above some critical value rho(c)(kappa). Thus, the elimination of weak synapses enhances the network performance only after a critical learning period. Possible implications for biological pruning phenomena are discussed.

Self-collimation in an atomic beam evaporated from a superfluid 4He film

Using a scaling Monte Carlo method, we have simulated the scattering in a pulsed atomic beam evaporated from a superfluid 4He film. The simulation assumes that the atoms leaving the surface have the equilibrium Maxwellian distribution at the temperature of the film T. This means that the initial particle flux varies as cos straight theta (Lambert's law). We find that the effect of atomic scattering just above the film is to bias the flux in favor of the forward (small straight theta) direction, in agreement with the experiment of Eckardt et al. The simulation predicts that the deviation from Lambert's law grows rapidly with increasing heat input Q and decreasing pulse length. At the same time, the average kinetic energy per particle in the forward direction is enhanced relative to the global average, 2k(B)T. The distribution with respect to speed is narrower than Maxwellian in the forward direction but broader at large angles. We find that a beam that has passed through a slit is slightly narrower than in a ballistic calculation with no collisions. This effect seems to saturate at values of Q that correspond to 30 or 40 collisions per atom.

Convective rolls and heat transfer in finite-length Rayleigh-Bénard convection: A two-dimensional numerical study

A two-dimensional (2D) numerical study using a single-point algebraic k-straight theta;(2)-varepsilon-varepsilon(straight theta) turbulence closure was performed to detect the existence, origin, creation and behavior of convective rolls and associated wall Nusselt (Nu) number variation in thermal convection in 2D horizontal slender enclosures heated from below. The study covered the Rayleigh (Ra) numbers from 10(5) to 10(12) and aspect ratios from 4:1 to 32:1. The time evolution of the convective rolls and the formation of the corner vortices were analyzed using numerical flow visualization, and the correlation between roll structures and heat transfer established. A major consequence of the imposed two dimensionality appeared in the persistence of regular roll structures at higher Ra numbers that approach a steady state for all configurations considered. This finding contradicts the full three-dimensional direct numerical simulations (DNS), large eddy simulations (LES), and three-dimensional transient Reynolds-averaged Navier-Stokes (TRANS) computations, which all show continuously changing unsteady patterns. However, the final-stage roll structures, long-term averaged mean temperature and turbulence moments, and the Nusselt number (both local and integral), are all reproduced in good agreement with the ensemble-averaged 3D DNS, TRANS, and several recent experimental results. These findings justified the 2D approach as an acceptable method for ensemble average analysis of fully 3D flows with at least one homogeneous direction. Based on our 2D computations and adopting the low and high Ra number asymptotic power laws of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)], new prefactors in the Nu-Ra correlation for Pr=O(1) were proposed that fit better several sets of data over a wide range of Ra numbers and aspect ratios: Nu=0.1Ra(1/4)+0.05Ra(1/3). Even better agreement of our computations was achieved with the new correlation Nu=0.124 Ra0.309 proposed recently by Niemela et al. [Nature (London) 404, 837 (2000)] for 10(6)</=Ra</=10(17).

Optical spatial shock waves in photorefractive media

We show that the evolution equations describing the two-wave mixing interaction between two codirectional optical beams in photorefractive media can allow spatial shock-wave solutions. Our analysis indicates that these kink-type wavefronts move together at an angle that falls outside the initial +/-straight theta sector of propagation. The apparent direction of propagation and the spatial widths of these optical shock-wave beams are directly related to their relative intensity.

Interface scaling in the contact process

A correspondence between lattice models with absorbing states and models of pinned interfaces in random media can be established by defining local height variables h(x,t) as integrals of the activity at point x up to time t. Within this context we study the interface representation of a prototypical model with absorbing states, the contact process, in dimensions 1-3. Simulations confirm the scaling relation beta(W)=1-straight theta between the interface-width growth exponent beta(W) and the exponent straight theta governing the decay of the order parameter. A scaling property of the height distribution, which serves as the basis for this relation, is also verified. The height-height correlation function shows clear signs of anomalous scaling, in accord with Lopez' analysis [Phys. Rev. Lett. 83, 4594 (1999)], but no evidence of multiscaling.

Genetic Linkage of Bietti Crystallin Corneoretinal Dystrophy to Chromosome 4q35

Bietti crystalline corneoretinal dystrophy (BCD) is an autosomal recessive retinal degeneration characterized by multiple glistening intraretinal dots scattered over the fundus, degeneration of the retina, and sclerosis of the choroidal vessels, ultimately resulting in progressive night blindness and constriction of the visual field. Although BCD has been associated with abnormalities in fatty-acid metabolism and absence of fatty-acid binding by two cytosolic proteins, the genetic basis of BCD is unknown. We report linkage of the BCD locus to D4S426 (maximum LOD score [Z(max)] 4.81; recombination fraction [straight theta] 0), D4S2688 (Zmax=3.97; straight theta=0), and D4S2299 (Zmax=5.31; straight theta=0), on chromosome 4q35-4qtel. Multipoint analysis confirmed linkage to the region telomeric of D4S1652 with a Z(max) of 5.3 located 4 cM telomeric of marker D4S2930.

Interlayer interactions in enantiomeric anticlinic liquid crystalline mixtures

The interlayer interaction coefficient U in the anticlinic phase of enantiomeric binary mixtures was determined by measuring the threshold electric field for the onset of solitary waves. U was found to increase with decreasing temperature in the anticlinic phase for a given enantiomer excess X. The ratio U(X,straight theta)/U(X=1,straight theta), where straight theta is the polar angle, was found to be significantly smaller for mixtures with low enantiomer excess than for the optically pure material. The observed behavior is analyzed using a mean-field model for dipole-dipole interactions in adjacent layers.

Deviations from linear theory for fluctuations below the supercritical primary bifurcation to electroconvection

Over two decades ago it was predicted that nonlinear interactions between thermally driven fluctuations in dissipative nonlinear nonequilibrium systems lead to deviations from mean-field theory. Here we report experimental observations of such deviations as a supercritical primary bifurcation is approached. We measured the mean-square director-angle fluctuations <straight theta(2)> below the bifurcation to electroconvection of two different nematic liquid crystals. For epsilon(mf) identical withV2/V(2)(c,mf)-1 less, similar-0.1 ( V is the applied voltage) we find <straight theta(2)> approximately |epsilon(mf)|(-gamma) with gamma given by linear theory (LT). Closer to the bifurcation there are deviations from LT with a smaller gamma and with V(2)(c)>V(2)(c,mf).

A Gene for Pyridoxine-Dependent Epilepsy Maps to Chromosome 5q31

Pyridoxine-dependent epilepsy (PDE) is a rare autosomal recessive disorder characterized by generalized seizures in the first hours of life and responding only to pyridoxine hydrochloride. The pathogenesis of PDE is unknown, but an alteration in the binding of pyridoxal 5-phosphate to glutamic acid decarboxylase (GAD) has been postulated in patients with PDE. Results are reported for genetic linkage analyses in four families with consanguineous parents and in one family with nonconsanguineous parents. The GAD1 (2q31) and GAD2 genes (10p23) were tested and excluded. A genomewide search was subsequently performed, using microsatellite markers at an average distance of 10 cM, and the search revealed linkage of the disease-causing gene to markers on chromosome 5q31.2-q31.3 (maximum LOD score [Z(max)] 8.43 at recombination fraction [theta] 0 and Zmax=7.58 at straight theta=0 at loci D5S2017 and D5S1972, respectively). A recombination event, between loci D5S638 and D5S463, in one family defined the distal boundary, and a second recombination event between loci D5S2011 and D5S2017 in another family defined the proximal boundary of the genetic interval encompassing the PDE gene (5.1 cM). Ongoing studies may lead to the identification of the disease-causing gene.

Spiraling spin structure in an exchange-coupled antiferromagnetic layer

Using trilayers of permalloy/FeMn/Co with various thicknesses t(AF) of the antiferromagnetic FeMn, we have observed evidence of a spiraling spin structure within FeMn. For t(AF)<90 A, the turn angle straight theta of the spiral varies as straight theta = (1.76 degrees /A)t(AF).

New constraints from haverah park data on the photon and iron fluxes of ultrahigh-energy cosmic rays

Using data from inclined events ( 60 degrees <straight theta<80 degrees ) recorded by the Haverah Park shower detector, we show that above 10(19) eV less than 41% ( 54%) of the primary cosmic rays can be photons (iron nuclei) at the 95% confidence level. Above 4x10(19) eV less than 65% of the cosmic rays can be photonic at the same confidence level. These limits place important constraints on some models of the origin of ultrahigh-energy cosmic rays. Details of two new events above 10(20) eV are reported.

Unusual dynamical scaling in the spatial distribution of persistent sites in one-dimensional potts models

The distribution n(k,t) of the interval sizes k between clusters of persistent sites in the dynamical evolution of the one-dimensional q-state Potts model is studied using a combination of numerical simulations, scaling arguments, and exact analysis. It is shown to have the scaling form n(k,t)=t(-2z)f(k/t(z)), with z=max(1/2, straight theta), where straight theta(q) is the persistence exponent which describes the fraction P(t) approximately t(-straight theta) of sites which have not changed their state up to time t. When straight theta>1/2, the scaling length t(straight theta) for the interval-size distribution is larger than the coarsening length scale t(1/2) that characterizes spatial correlations of the Potts variables.

Structure of charged colloids under a wedge confinement

Monte Carlo simulations have been performed to study the influence of a wedge confinement by hard walls on the ordering of charged colloidal particles interacting through screened Coulomb repulsive potential in an aqueous medium. The density distribution of particles for a fixed wedge angle straight theta(0) is studied for different suspension parameters, viz., bulk volume fraction straight phi, salt concentration C(s), and charge Ze on the particles. The density distribution rho(straight theta) along the angular direction and that along the radial direction, rho(r), have been analyzed in different regions of the wedge. Simulations show the formation of layered structure along the angular direction and a large gathering of particles along the wall. The number of layers as well as the density of particles within the layer are found to change as the strength and range of the interaction are varied, whereas the density profiles calculated close to the vertex region showed no significant variation in the density. The radial density profiles rho(r) corresponding to the vertex region show one-dimensional (1D) ordering of particles parallel to the vertex at a distance that is close to a wedge height, h equal to diameter of the particle. This 1D ordering is found to be destroyed upon the addition of salt or lowering the straight phi. The reported experimental observations on the "vacuum phase" are discussed in the light of the present results.

Atomic scattering factors for K-shell and L-shell ionization by fast electrons

Atomic scattering factors have been calculated for K-shell ionization for elements in the range Z = 6 (carbon) to Z = 50 (tin) and for L-shell ionization in the range Z = 20 (calcium) to Z = 60 (neodymium). The calculations are based on relativistic Hartree-Fock wave functions for the atomic bound states and Hartree-Slater wave functions for the continuum wave functions. The results are presented in tabular form such that accurate values of the scattering factors can be obtained by cubic spline interpolation for incident electron energies between 50 and 400 keV and for scattering vectors with magnitude s = sin straight theta / lambda up to 2.5 A(-1) (2straight theta is the scattering angle and lambda the wavelength of the incident electrons). A separate parameterization of the form factors is given for 2.5 </= s </= 20 A(-1), where they are small. In addition, a simpler but less accurate parameterization of the atomic scattering factors in an exponential form has been obtained by fitting the calculated form factors in the region s </= 2.5 A(-1). The scattering factors are suitable for the calculation of ionization cross sections for use in atom location by channelling-enhanced microanalysis (ALCHEMI).

Four-dimensional polymer collapse: pseudo-first-order transition in interacting self-avoiding walks

In an earlier work we provided the first evidence that the collapse, or coil-globule transition of an isolated polymer in solution can be seen in a four-dimensional model. Here we investigate, via Monte Carlo simulations, the canonical lattice model of polymer collapse, namely, interacting self-avoiding walks, to show that it not only has a distinct collapse transition at finite temperature but that for any finite polymer length this collapse has many characteristics of a rounded first-order phase transition. However, we also show that there exists a "straight theta point" where the polymer behaves in a simple Gaussian manner (which is a critical state), to which these finite-size transition temperatures approach as the polymer length is increased. The resolution of these seemingly incompatible conclusions involves the argument that the first-order-like rounded transition is scaled away in the thermodynamic limit to leave a mean-field second-order transition. Essentially this happens because the finite-size shift of the transition is asymptotically much larger than the width of the pseudotransition and the latent heat decays to zero (algebraically) with polymer length. This scenario can be inferred from the application of the theory of Lifshitz, Grosberg, and Khokhlov (based upon the framework of Lifshitz) to four dimensions: the conclusions of which were written down some time ago by Khokhlov. In fact it is precisely above the upper critical dimension, which is 3 for this problem, that the theory of Lifshitz may be quantitatively applicable to polymer collapse.

Quasifree compton scattering from the deuteron and nucleon polarizabilities

Cross sections for quasifree Compton scattering from the deuteron were measured for incident energies of E(gamma) = 236-260 MeV at the laboratory angle straight theta(gamma(')) = -135 degrees. The recoil nucleons were detected in a liquid-scintillator array situated at straight theta(N) = 20 degrees. The measured differential cross sections were used, with the calculations of Levchuk et al., to determine the polarizabilities of the bound nucleons. For the bound proton, the extracted values were consistent with the accepted value for the free proton. Combining our results for the bound neutron with those from Rose et al., we obtain 1-sigma constraints of alpha;(n) = 7.6-14.0 and beta;(n) = 1.2-7.6.