Shape selection in non-Euclidean plates

We investigate isometric immersions of disks with constant negative curvature into R³, and the minimizers for the bending energy, i.e. the L² norm of the principal curvatures over the class of W^2,2 isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in H² into R³. In elucidating the connection between these immersions and the non-existence/singularity results of Hilbert and Amsler, we obtain a lower bound for the L^∞ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally W^2,2, and numerically have lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grow approximately exponentially with the radius of the disk. We discuss the implications of our results on recent experiments on the mechanics of non-Euclidean plates.     

Dynamical scaling of the structure factor of some non-Euclidean systems

Predictions of nonlinear theories on dynamics of new phase formation have been examined for the hydration of calcium silicates with light water and heavy water. In the case of hydration with light water, reasonable agreement has been observed with dynamical scaling hypothesis with a new measure of the characteristic length. The characteristic length does not follow a power law relation with time. Hydrating mass is found to be mass fractal throughout hydration, with mass fractal dimension increasing with time. But, in the case of hydration with heavy water, no agreement has been observed with the scaling hypothesis. Hydrating mass undergoes transition from mass fractal to surface fractal and finally again to mass fractal. The qualitative features of the kinetics of hydration, as measured in small-angle scattering experiments, are strikingly different for hydration with light water and heavy water.     

Backscattering coefficients for low energy electrons and positrons impinging on metallic thin films: scaling study

Thin films Backscattering Coefficients (BSCs) for 1 to 4 keV electron and positron normally incident beams are stochastically modeled and calculated by the Monte Carlo method. We suggest a new function BSC(δ) depending only of one free parameter (to be determined) and which can describe very well the variation of the backscattering coefficient versus the film thickness (δ). Moreover, this paper aims at discussing the observed differences between the electron and positron properties impinging on solid targets.     

Single-parameter scaling in thin crystals

Davies, Pepper, and Kaveh in a recent article have reworked some of their previously published g(T) data on Si inversion layers. They show that β versus g curves are not universal, monotonic, smooth; like predicted by Abrahams, Anderson, Licciardello, and Ramakrishnan. We have reworked our previously published data on single crystal films of Bi₂(Te_1?xS_x)₃, x = 0.476; and we find our data to be in good agreement with AALR.     

Pulse energy scaling to 5 microJ from a femtosecond thin disk laser

We report an increase in pulse energy to 5.1 microJ obtained directly from a femtosecond diode-pumped Yb:YAG thin disk laser without external amplification. Stable passive mode locking was obtained with a semiconductor saturable absorber mirror (SESAM). The laser delivers 63 W of average output power in a nearly diffraction-limited beam (M2=1.1) at a center wavelength of 1030 nm. The pulse repetition rate is 12.3 MHz, and the pulses have a duration of 800 fs, which results in a peak power of 5.6 MW. The laser was operated in a box flooded with helium because the nonlinearity of air was found to be a limiting factor for the stability of the pulse formation at increasing pulse energies.     

Microscopic analysis of octupole shape transitions in neutron-rich actinides with relativistic energy density functional

Quadrupole and octupole deformation energy surfaces, low-energy excitation spectra, and electric transition rates in eight neutron-rich isotopic chains – Ra, Th, U, Pu, Cm, Cf, Fm, and No – are systematically analyzed using a quadrupole-octupole collective Hamiltonian model, with parameters determined by constrained reflectionasymmetric and axially-symmetric relativistic mean-field calculations based on the PC-PK1 energy density functional.The theoretical results of low-lying negative-parity bands, odd-even staggering, average octupole deformations β_3,and B(E3;3_1~- →0_1~+) show evidence of a shape transition from nearly spherical to stable octupole-deformed, and finally octupole-soft equilibrium shapes in the neutron-rich actinides. A microscopic mechanism for the onset of stable octupole deformation is also discussed in terms of the evolution of single-nucleon orbitals with deformation.     

The R-function method for the free vibration analysis of thin orthotropic plates of arbitrary shape

Free flexural vibrations of homogeneous, thin, orthotropic plates of an arbitrary shape with mixed boundary conditions are studied using the R-function method. The proposed method is based on the use of the R-function theory and variational methods. In contrast to the widely used methods of the network type (finite differences, finite element, and boundary element methods), in the R-function method all the geometric information given in the boundary value problem statement is represented in an analytical form. This allows one to seek a solution in a form of some formulas called a solution structure. These solution structures contain some indefinite functional components that can be determined by using any variational method. A method of constructing the solution structures satisfying the required mixed boundary conditions for eigenvalue plate bending problems is described. Numerical examples for the vibration analysis of orthotropic plates of complex geometry with mixed boundary conditions for illustrating the aforementioned R-function method and comparison against the other methods are made to demonstrate its merits.     

Rotation-induced shape transitions in Dy nuclei

Lifetimes of states with spins up to 30? have been measured in the nuclei ¹⁵⁶Dy, ¹⁵⁷Dy, and ^ll58Dy using the recoil-distance technique together with inverse reactions of the type $\text{Mg}\text{(}{}^{136}\text{Xe}\text{, x}\text{n}\text{)}$. The applied method, which benefited from the high velocities of the fusion residues as well as from improvements of the recoil-distance technique, allowed us to determine lifetimes and feeding times down to 0.1 ps. Below the first backbending the resultant B(E2) values in the ground-state band of ^{156, 158}Dy increase faster with increasing rotational frequency than expected for rigid rotors, reaching values similar to those observed for the well-deformed neutron-rich Dy isotopes. In contrast to this, the E2-transition probabilities between high-spin states are clearly retarded. The retardation gradually evolves from the rotation alignment of nucléons and indicates deformation changes most likely towards a triaxial shape. From the analysis of the side-feeding times of the high-spin yrast states it could be furthermore deduced that the E2 component of the preyrast γ-decay stems from transitions along highly collective bands.     

First-order transitions in spherical models: Finite-size scaling

Finite-size behavior near the first-order phase boundary of ferromagnetic spherical models is investigated for block- and cylinder-shaped systems ind dimensions. The bulk thermodynamic singularities are rounded and, asymptotically for large size, obey appropriate scaling laws. Both short-range interactions and long-range couplings, decaying like 1/r^d+ with >0, are analyzed: the short-range results agree precisely with a recently developed scaling theory forO(n) symmetric systems in the limitn. More generally, the scaling functions are universal, depending only on . Explicit aspects of the shape and interactions enter only in the spin wave or Goldstone mode contributions which appear, technically, as corrections to scaling. An appendix analyzes the truncation error in the approximation, by many-fold sums, of multivariate integrals with integrands diverging like [_ja_{j j} ² ]^- as 0.     

Experimental study of isotope scaling of ion thermal transport

The wide divergence between most theoretical predictions of isotopic mass scaling of transport and tokamak experimental results motivated a basic physics experiment in the Columbia Linear Machine [R. Scarmozzino, A. K. Sen, and G. A. Navratil, Phys. Rev. Lett. 57, 1729 (1986)]]. The experiments on ion thermal conductivity due to ion temperature gradient-driven slab modes are performed using two different gases: hydrogen and deuterium. The results indicate inverse dependence of ion thermal conductivity on the isotope mass close to K(radially) approximately A(-0.5)(i). This is similar to the tokamak results, but in stark contradiction to most present theoretical models.     

连续相位板远场焦斑能量集中度实验研究

在惯性约束聚变（ICF）研究过程中,焦面上聚焦光斑形态要求极为苛刻。基于离线测试平台,从实验上研究了各种应用误差对连续相位板（CPP）远场焦斑能量集中度的影响。得出光束旋转误差、口径误差、平移误差和倾斜误差在可控范围内CPP远场焦斑能量集中度均高于95%,其波动范围小于0.5%,CPP的容忍度较强。而实验畸变波前属于空间频率小于0.02 mm-1的低频波前,严重影响了CPP的整形能力,波前畸变是影响能量集中度高于90%的主要因素。     

Charge transport transitions and scaling in disordered arrays of metallic dots

We examine the charge transport through disordered arrays of metallic dots using numerical simulations. We find power law scaling in the current-voltage curves for arrays containing no voids, while for void-filled arrays charge bottlenecks form and a single scaling is absent, in agreement with recent experiments. In the void-free case we also show that the scaling exponent depends on the effective dimensionality of the system. For increasing applied drives we find a transition from 2D disordered filamentary flow near threshold to a 1D smectic flow which can be identified experimentally using characteristics in the transport curves and conduction noise.     

Glass transitions in thin polymer films

Freely standing polystyrene films show an anomalous drop of the glass temperature when the molecular weight is high and the thickness smaller than the coil size R₀. We present here a tentative explanation for these features, where two types of motions compete: a) standard motions, controlled by the free volume, and independent of chain length, b) collective motions along the chain, which require a weaker free volume (except for the end groups). For bulk systems, the standard motion always wins because of the end group hindrance. But for films thinner than the coil size, the dominant process may be the collective motion of a “loop” which does not involve the chain ends. What matters then is not the overall polymerisation index (N), but the length g of a typical loop starting from the surface (which is a more fluid region) and reaching deep into the film. With these ingredients, some surprising aspects of may possibly be understood. Received 7 December 1999     

Developable modes in vibrated thin plates

We investigate the normal modes of a developable cone singularity as observed in a circular sheet supported by a rigid circular frame and pushed at its center. When the center of the sheet is in addition submitted to a sinusoidal forcing, two types of bending modes, named here rolling and tilt modes, are parametrically excited. The rolling mode is an angular oscillation of the concave sector of the developable cone structure. If the amplitude of vibration is high enough, the rolling mode amplitude increases dramatically giving rise to both a continuous rotation of the concave sector and a material angular displacement of the sheet, similar to that produced by a moving wrinkle in a carpet.     

Terahertz spectroscopy of quantum phase transitions and the temperature-frequency scaling

In the last few decades, significant progress has been achieved in the development of generators and detectors of terahertz radiation (at frequencies in the range from ≈300 GHz to ≈3 THz). Different terahertz spectroscopic techniques have been widely used now in investigating semiconductors, superconductors, molecular magnets, multiferroics, metamaterials, and other promising objects. It has been demonstrated that terahertz spectroscopy offers wide but not completely realized possibilities for studying quantum phase transitions in electron-correlated systems.     

First-order magnetic phase transitions in thin films

Using the simple Landau model, we discuss near-surface magnetic effects for thin films corresponding to first-order phase transitions. The size effects observed in ultrathin ferroelectric films are in agreement with this theoretical interpretation. The presence of a weak external field is also formulated. The text was submitted by the authors in English.