Brownian motion of a classical particle through potential barriers. Application to the helix-coil transitions of heteropolymers

We discuss some properties of the one-dimensional Fokker-Planck equation, and in particular the time required to go through a potential barrier of arbitrary size and shape. We apply the resulting formulas to the melting of helical polymers made of two types of monomers (A and B) with different melting temperatures: We consider a restricted problem in irreversible melting, where onesingle boundary (separating a coil region from a helical region) moves through the chemical sequence. In a crude approximation the distribution function for the boundary point is then ruled by a simple Fokker-Planck equation. When the temperatureT is equal to or higher than the average melting point¯T, the boundary tends to move over macroscopic distances, thus extending the size of the coil regions. In an interval¯T ^* the progression is predicted to be slow (logarithmic). At higher temperatureT>T ^* essentially all barriers are overcome and the progression is fast.     

Influence of structural defects on magnetic properties of the submicrometer ceramic Mn3O4

A high-density single-phase submicrometer ceramic Mn₃O₄ with a grain size d ≥ 0.06 μm has been obtained by using spherically converging shock waves. The action of shock waves reduces the unit cell volume and increases the Curie temperature T _C . The shape of the temperature dependences of reciprocal susceptibility x ^?1 of a polycrystal and the submicrometer ceramic at T > T _C is hyperbolic, which is typical of ferrimagnets. It is shown that the susceptibility of the ceramic in the region of short-range order at 78 K ≤ T ≤ 300 K is larger than that of the polycrystal, while the field dependences of the magnetization are nonlinear. The bombardment by electrons with a small dose of Φ = 0.8 × 10¹⁸ cm^?2 increases the susceptibility of the submicrometer ceramic as well as that of the polycrystal. When the fluence increases to Φ = 5 × 10¹⁸ cm^?2, the susceptibility decreases, which can be explained by radiation-induced disordering and a change in the “local” exchange interactions.     

The boundary condition approach to nucleon-nucleon potentials and the calculation of the T- and K-matrices

It has been shown that the off-shell T- and K-matrices can be obtained by means of boundary conditions imposed upon the off-shell wave function only. When there is a potential outside the boundary condition radius the method proposed permits to deduce in a rather simple way a renormalized Lippmann-Schwinger equation. The S-components of the T- and K-matrices are considered in detail using a potential of the exponential type in the exterior region. For such types of potentials a rather effective method for factorizing the K-matrix is given. Parameter fits to the ¹S₀ and ³S₁ phases are presented.     

Crystallization and melting of spin-polarized<Superscript>3</Superscript>He

The melting and growth of³He crystals, spin-polarized by an external magnetic field, are different in nature depending on whether the temperature is higher or lower than the characteristic ordering temperatures in the crystal (the Neel temperatureT _N ) and in the liquid (the superfluid transition temperatureT _c ). In the high-temperature region (T≥T _N ,T _c ) the liquid which appears upon melting has a high nonequilibrium spin density. In the low-temperature region (T?T _N ,T _c ) the melting and growth are accompanied by spin supercurrents both in the liquid and in the crystal in addition to mass supercurrents in the liquid. The crystallization waves at the liquid-solid interface should exist in the low-temperature region. With increasing magnetic field the waves change in nature, because the spin currents begin to play a dominant role. The wave spectrum becomes linear with a velocity inversely proportional to the magnetic field. The attenuation of the waves at low enough temperatures is mainly due to the interaction of the moving crystal-liquid interface with thermal spin waves in the crystal. The waves could be weakly damped at temperatures below a few hundreds microkelvins.     

Magnetic Excitations in the antiferromagnet CoCl2

Magnetic neutron inelastic scattering has been used to investigate the non degenerate spim waves propagating in the [00.1] direction in CoCl₂. The neutron results are explicable in terms of a model containing isotropic exchange as proposed by Lines [12, 13] with the addition of a small “in plane” anisotropy. At zero wave vector the anisotropy produces an energy gap in the lower magnon branch which is observed by AFMR to be 70 GHz. Since the maximum spin wave frequency at the zone centre and boundary is 0.56 THz and 0.42 THz respectively the calculations were made within the ground doublet of the ⁴T_1g term. The derived exchange parameters are consistent with those obtained from susceptibility and light scattering. Finally there was no direct evidence to suggest the presence of a strong magnon-phonon hybridization in the [00.1] direction of CoCl₂.     

Ultrasonic attenuation anomalies at the two transitions in antiferromagnetic FeGe2

The attenuation of longitudinal and shear sound waves is measured through the Néel temperature, T_N≈286 K, and the lower transition temperature, T_K≈265 K, of FeGe₂. Longitudinal sound with wavevector q along the [100] axis of this tetragonal antiferromagnetic metal shows an attenuation peak at T_N, which is reversibly suppressed by compressive uniaxial stress σ along [010]. The estimated pressure dependence of T_N is dT_N/dp=(?2.8±0.3) mK bar^?1. The peak at T_N shows thermal and stress hysteresis, which suggests that it is associated with domain wall motion and that this transition is first order.     

Critical current behavior in locally illuminated superconducting lead strips

We have used guided optical waves to locally illuminate superconducting thin lead strips and measured the critical current as a function of optical power. The measured results resemble the predictions of a simple heating model more closely than the Parker T¹ model in the temperature range investigated (5.5 K to T_c) and several possible reasons for this behavior are discussed.     

Spin waves in MnO; from 4°K to temperatures close to TN

Spin waves have been measured in MnO by inelastic scattering of neutrons from 4 °K to a temperature 0·25 °K below T_N. The 4 °K spectrum is interpreted in the frame of linear spin wave theory with effective exchange integrals J₁^? = 0·321 meV, J₁⁺ = 0·424 meV, J₂¹ = 0·446 meV and a phenomenological parameter for anisotropy D₁ = 0·059 meV. The effect of the actual dipole-dipole Hamiltonian is shown to give a priori a very good account of the lifting of the degeneracy of spin waves near the Brillouin zone center. The Bloch model for interacting spin waves and theories based on Green function approximations have been adapted to the MnO case, in order to compute the main properties (mean magnetization of a sublattice, anisotropic deformation, extra isotropic contraction and magnon spectrum) at many temperatures. Comparison of these with experimental results tends to favour a generalized Callen renormalization model, which gives an overall fit from 4 °K, to temperalures close to T_N.     

A Brinkman penalization method for compressible flows in complex geometries

To simulate flows around solid obstacles of complex geometries, various immersed boundary methods had been developed. Their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non-body conformal Cartesian grids. The Brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations. Its main idea is to model solid obstacles as porous media with porosity, ϕ, and viscous permeability approaching zero. It has the pronounced advantages of mathematical proof of error bound, strong convergence, and ease of numerical implementation with the volume penalization technique. In this paper, it is extended to compressible flows. The straightforward extension of penalizing momentum and energy equations using Brinkman penalization with respective normalized viscous, η, and thermal, η_T, permeabilities produces unsatisfactory results, mostly due to nonphysical wave transmissions into obstacles, resulting in considerable energy and mass losses in reflected waves. The objective of this paper is to extend the Brinkman penalization technique to compressible flows based on a physically sound mathematical model for compressible flows through porous media. In addition to penalizing momentum and energy equations, the continuity equation for porous media is considered inside obstacles. In this model, the penalized porous region acts as a high impedance medium, resulting in negligible wave transmissions. The asymptotic analysis reveals that the proposed Brinkman penalization technique results in the amplitude and phase errors of order O((ηϕ)^1/2) and O((η/η_T)^1/4ϕ^3/4), when the boundary layer within the porous media is respectively resolved or unresolved. The proposed method is tested using 1- and 2-D benchmark problems. The results of direct numerical simulation are in excellent agreement with the analytical solutions. The numerical simulations verify the accuracy and convergence rates.     

High-temperature absorption coefficient of methane at 3.392μ

The spectral absorption coefficient of methane at 3.392μ has been measured in the temperature range 965 ?T, °K≤2710 behind incident and reflected shock waves. It is given by the relation P'=P'₀(T₀/T)ⁿ where P'₀=(1.34±0.58)x10²cm^-1atm^-1 at T₀=300°K and n=2.88±0.21. The empirically determined temperature exponent n may be approximately accounted for by a simplified theoretical analysis.     

Free Molecular Flow with Boundary Effect

We study the dissipative effect of the boundary condition in the kinetic theory. We focus our study on the simplest situation of the free molecular flow with diffuse reflection boundary condition and constant boundary temperature, T _*. The geometry is also chosen to be the simplest ones, a bounded symmetric domain in ${\mathbb{R}^d}$ : an interval for d = 1, a disk for d = 2, and a ball for d = 3. It is shown that the solution converges to the global Maxwellian with the given boundary temperature T _*. We obtain the optimal convergence rates of (t + 1)^?d . The stochastic formulation of Shih-Hsien Yu is refined and generalized for our analysis.     

TRANSIENT RESPONSE ANALYSIS OF LARGE-SCALE ROTOR-BEARING SYSTEM WITH STRONG NON-LINEAR ELEMENTS BY A TRANSFER MATRIX-NEWMARK FORMULATION ITEGRATION METHOD

This paper extends the transfer matrix technique (TMT) to the transient response analysis of a large complex non-linear rotor-bearing system by a transfer matrix-Newmark formulation itegration method. Firstly, the transfer matrix is obtained via the Newmark formulation. Secondly, the deflections and velocities at the stations, containing non-linear element, are determined by iteration. Finally, the deflections, velocities and accelerations of all stations are computed by TMT and the Newmark formulation consistent with the boundary conditions. In order to eliminate the numerical instability of TMT, the transfer vector {f^T ? ë^T}^T is used, instead of the traditional one {f^T ? ë^T}^T. Owing to the advantages of TMT and the Newmark formulation, this method can be applied to calculate the transient response of a large-scale rotor-bearing system with strong non-linear elements, and to analyze its stability. Two illustration examples are given, and the results agree well with those by Runge-Kutta method, and by modal synthetic method.     

Ultrasonic determination of the temperature dependence of the electron mean free path in cesium single crystal

The ultrasonic attenuation of high frequency longitudinal waves has been measured in transverse and oblique magnetic fields to determine the temperature dependence of the phonon-limited mean free path in cesium single crystals. Below 2.5°K, the mean free path varies as T^4.8. The results are compared with electrical resistivity measurements in cesium.     

Anomalous electric-field dependence of the temperature-independent electron mobilities in organic molecular crystals

The model proposed by the present author (this journal $\text{28}$, 309 (1978)), which explained successfully the temperature (T)-independent mobilities above about the Debye temperature θ, predicts that the drift velocity becomes saturated in the high-electric-field region when T?θ, and that it makes a peak in the low-field one with an intermediate minimum when $\text{T « θ}$. The boundary between the two regions is on the order of 10⁵ V/cm.     

Phase diagrams and elementary excitations

On the phase boundary separating two crystalline phases, it is shown that d(Tⁿ)/dp/_T=0=constant. The index n depends on the dominant elementary excitations, being 4,$\text{5}\text{2}$ and 2 for phonons, magnons and electronic single-particle excitations respectively.     

Three-nucleon calculations without the explicit use of two-body potentials

Using as two-nucleon interaction input the ³S₁-³D₁ and ¹S₀ partial waves, the Faddeev equations are solved for the three-nucleon bound state. The ³S₁³D₁T-matrix is calculated from the Reid potential. Avoiding the usual potential fit, the ¹S₀T-matrix is directly continued off-shell and is constructed consistent with the ¹S₀ phase shift of elastic two-nucleon scattering. The off-shell part of the ¹S₀T-matrix is parametrized and with this parametrization the dependence of the three-nucleon bound-state properties is studied. As a result it is found that the binding energy varies only between 6.2 MeV and 6.8 MeV, while the minimum in the charge form factor for electron scattering from ³He lies between 12.9 fm^?2 and 18.7 fm^?2. The larger (smaller) ³He binding energy is accompanied by a ³He charge form factor whose minimum is at larger (smaller) momentum transfers.     

Quantum effects in the Gowdy T3 cosmology

The Gowdy T³ Cosmology is an exact solution to the vacuum Einstein equations interpreted to be a single polarization of gravitational waves propagating in an anisotropic, spatially inhomogeneous background. The classical behavior is reviewed and related to standard cosmological parameters. Canonical quantization of the dynamical degrees of freedom is reviewed. An adiabatic vacuum state is constructed. Adiabatic regularization is used to obtain non-divergent stress-energy tensor vacuum expectation values. Casimir energy terms due to T³ imposed discrete modes are evaluated. The vacuum expectation values are analyzed in early and late time limits and evaluated numerically. The regularized expectation value is used as a source for the classical background spacetime in the spirit of semi-classical gravity. An entirely vacuum expectation value source term produces essentially the time reverse of the classical evolution. Classical stress-energy added to the source restores the classical behavior at late times only. The combined system collapses from infinite to small but non-zero volume and reexpands. The classical singularity is replaced by a symmetric bounce.     

Ultrasonic determination of electron-phonon scattering rates in copper

Electron-phonon scattering rates in ultrapure single crystals of copper have been determined from the temperature dependence of the magnetoacoustic oscillation amplitudes for various orbits on the Fermi surface using both longitudinal and transverse waves. The central belly orbit seattering rate is found to be (6.0±0.3)×10⁶ T ³ sec^?1. Additionally, a rate of (2.9±0.2)×10⁶ T ³ sec^?1 is found which is attributed to belly orbits displaced from the zone center by about 1.25/a ₀, wherea ₀ is the lattice constant. Geometric oscillations associated with the [111]—directed open orbit are observed at low fields forq‖ [113] and the rate for this orbit is found to be (4.8±0.3)×10⁶ T ³ sec^?1. Geometric oscillations for the dog's bone and neck orbits are observable but rates for these orbits are believed to be unreliable. Our measured rates are compared with those of other workers.     

Properties of the Ising magnet confined in a corner geometry

The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ±h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field −h acts. For temperatures T less than the critical temperature T_c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T_f(h) runs from the upper left corner to the lower right corner, while for T<T_f(h) this interface is localized either close to the lower left corner or close to the upper right corner. It is shown that for T=T_f(h) the magnetization profile m(z) in the z-direction normal to the interface simply is linear and the interfacial width scales as w∝L, while for T>T_f(h) it scales as . The distribution P(?) of the interface position ? (measured along the z-direction from the corners) decays exponentially for T<T_f(h) from either corner, is essentially flat for T=T_f(h), and is a Gaussian centered at the middle of the diagonal for T>T_f(h). Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.     

SH Acoustic Waves in a Lithium Niobate Plate and the Effect of Electrical Boundary Conditions on Their Properties

It is theoretically and experimentally confirmed that the electromechanical coupling coefficient of SH waves propagating in a Y-cut lithium niobate plate along the X direction can exceed 30% when the plate thickness satisfies the condition h/λ= 0.02–0.15. This value of the coupling coefficient is approximately six to seven times greater than the maximal value obtained for SAW in the same material. Such a high value of K ² offers a possibility to control the wave velocity by varying the electrical boundary conditions, e.g., by moving a conducting screen toward the plate surface. The effect of such a screen on the properties of the SH waves is studied both theoretically and experimentally. On the whole, the results of the study show that the use of SH waves offers considerable improvements in the parameters of the known SAW devices and also opens up the possibilities for the development of new devices and sensors that have to operate in contact with a liquid medium.