A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems

In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {_n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {_n(a)}_{n N} is a -convergent sequence, for each nN, when { (a)} convergent to 0, {_n(a)} is -convergent, then when { (a)} convergent to 0, {_n(a)} are -convergent uniformly with respect to nN     

Microscopic theory of gas-surface interaction

A kinetic theory for inelastic scattering, trapping and desorption of gas molecules by surfaces is described. The theory is valid if the time scale _l = 1/r introduced by the relaxation ratesr in the kinetic equations (which is of the order of the life time of vibrational states of adsorbates) is sufficiently large compared to the vibrational period ₀. For sufficiently large activation energies of the adsorbates another time constant _res, the residence time of adsorbed particles, can be determined from the theory. One thus may distinguish four different partly overlapping regimes defined by the time scalest _{I l} , ₀t_II, _l t_III and _rest_IV. Regime I is governed by the Schrödinger equation regime II by the kinetic equations. In the region where both regimes overlap the kinetic coefficients can be expressed in terms of microscopic quantities which have been calculated previously. The relevant quantities in the other regimes are introduced and discussed from a unified point of view thus providing a link between the regimes I and IV which have been treated in detail before.     

The projection approach to the Fokker-Planck equation. I. Colored Gaussian noise

It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation ₁ and an unperturbed part ₀. The standard Fokker-Planck structure is recovered at the second order in ₁, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in ₁ the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in ₁, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in ₁ vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in ₁ vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation.     

How to measure the magnetic moment of the tau lepton

We present a method for obtaining bounds on the magnetic moment of the lepton. In order to do this, we study the radiative decayW as a function of the anomalous magnetic moment of the ,a . One can obtain bounds as good asa < 4.05×10^–2, 2.25×10^–2, 4.5×10^–3, and 2.5×10^–3 at the present Fermilab, future Fermilab, SSC, and LHC, respectively.     

Brownian dynamics of colloidal hard spheres. 3. Extended investigations at the phase transition regime

The phase behavior of hard-sphere colloidal systems in the volume fraction regime 0.46<<0.64 has been studied in detail using a new and efficient algorithm to treat the nonanalytic interaction pair potential. In particular the influence of various initial configurations such as purely random and facecentered cubic (FCC) has been investigated, and former simulations have been extended toward much longer time scales. Thus, in the case of randomly initiated systems, crystallization could be suppressed for a comparably long time (500 _R , where _R is the structural relaxation time) where the system remained in a metastable glassy state. The concentration dependence of the long-time self-diffusion coefficients of these systems has been analyzed according to free volume theory (Doolittle equation). Numerical data fit excellently to the theoretical predictions, and the volume fraction of zero particle mobility was found close to the expected value of random close packing. In case of the FCC initiated systems, samples remained crystalline within the simulated evolution time of 500 _R if their volume fraction was above the predicted freezing transition _F = 0.494, whereas at lower concentrations rapid melting into a fluidlike disordered state is observed. It should be noted that this algorithm, which neglects higher-order correlations, considering only direct pair interactions, nevertheless yields the correct hard-sphere crystallization phase behavior as predicted in the literature.     

Inertial effects on the escape rate of a particle driven by colored noise: An instanton approach

A recent calculation, in the weak-noise limit, of the rate of escape of a particle over a one-dimensional potential barrier is extended by including an inertial term in the Langevin equation. Specifically, we consider a system described by the Langevin equation , where is a Gaussian colored noise with mean zero and correlator (t)(t')=(D/)exp(–|t–t'|/). A pathintegral formulation is augmented by a steepest descent calculation valid in the weak-noise (D0) limit. This yields an escape rateexp(–S/D), where the actionS is the minimum, over paths characterizing escape over the barrier, of a generalized Onsager-Machlup functional, the extremal path being an instanton of the theory. The extremal actionS is calculated analytically for smallm and for general potentials, and numerical results forS are displayed for various ranges ofm and for the typical case of the quartic potentialV(x)=–x ₂/2+x ₄/4.     

Derivations commuting with abelian gauge actions on lattice systems

Let be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA is an AF-algebra. We show that if is a closed *-derivation onA commuting with , and the restriction of toA generates a one-parameter group of *-automorphisms, then itself is a generator. In particular, the result applies if is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation ₁ and ₂ are two derivations both satisfying the hypotheses on , and ₁ and ₂ have the same restriction toA , then there exists a one-parameter subgroup of the action with generator ₀ such thatD(₁)D(₂)D(₀) is a joint core for the three derivations, and ₂=₁+₀ on this core.     

Studies on the microstructure of phase transitions in two kinds of liquid crystals by PAT and DSC

The positron lifetime and DSC measerments for EBBA and DOBAMBC have been made with heating and cooling clycles. The experimental results show that a shorter lifetime (₁) is essentially independent of temperature while the longer lifetime (₂) and the intensity (I ₂) change abruptly double or triple with temperature. Consequently, the EBBA has only nematic phases while the DOBAMBC has two liquid-crystalline phases (smectic C* and smectic A) with transition temperatures as follows: for EBBA, solid nematic (304.5 K), nematic isotropic (356.5 K), isotropic nematic (356.5 K), nematic solid (301 K); and for DOBAMBC, solid smectic C* (346 K), smectic C* smectic A (357.5 K), smectic A isotropic (389 K). These critical temperatures are in accordance with the transition temperatures measured by DSC. In addition, the difference in the solid-nematic transition temperature in the heating and cooling cycles was also observed. A discussion about the correlation of the observed changes in lifetime (₂) with the changes in molecular orientational order (S) and dielectric anisotropy () is presented.     

A sensitive non-destructive method for measuring the Nd doping concentration in Nd : YAG with high spatial resolution

This paper reports on an experimental method for measuring in Nd:YAG the Nd doping concentration (C) with high sensitivity (0.01 at.%Nd) and high spatial resolution (50 m). The method is based on the measurement of the fluorescence lifetime _f of the upper Nd laser level. Additional parameters required to determine C are the intrinsic fluorescence lifetime ₀ and the quenching parameter Q. The measured values of _f, ₀ (256.47±0.14 s) and Q (4.45±0.40×10²⁰ cm^-3) allow us to calculate the Nd concentration C with an absolute accuracy of 0.1 at.%Nd. By using this method C is measured at the outer surfaces of standard laser rods and at the faces of boule slices (with diameters of up to 50 mm). The obtained results demonstrate a detection sensitivity of 0.01 at.%Nd. PACS 42.70.Hj; 81.70.Fy     

Steady-State Spectroscopic and Fluorescence Lifetime Measurements of New Two-Photon Absorbing Fluorene Derivatives

Steady-state excitation anisotropy, lifetimes, and time-resolved emission spectra of new 2-photon absorbing fluorene derivatives were measured in aprotic solvents at room temperature. Excitation anisotropy spectra in viscous silicon oil allowed the determination of the spectral position of three electronic transitions S₀ S₁, S₀ S₂, S₀ S₃ (S_i, i = 1, 2, 3 are the singlet electronic states) and the angles ( 30°) between absorption S₀ S₁ and emission S₁ S₀ dipole moments for the first electronic transition. Solvate relaxation processes in the first excited state of the investigated fluorene molecules affect the lifetimes of these states, ₁, so that experimental values of ₁ do not correspond to those calculated by Strickler and Berg theory. The influence of the molecular concentration on the fluorescence quantum yields and ₁ have been investigated.     

Kinetic equation in the kinetic region of the dilute and nonuniform electron plasma

Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t _c) satisfies _Dbl _f , _D t _{c f} , with _D the Debye length, _D ^–1= _p the plasma frequency, andl _f and _f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl _f and _D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies _Dbr ₀, _Dt _{c 0}, withr ₀ the Landau length and ₀ the corresponding time scale.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Dispersion of the permittivity of high-resistance semiconductors

We consider the mechanism of macroscopic polarization of semiconducting plates owing to the interaction of free carriers with an impurity level, in which role the level of the residual impurity of compensated semiconductors may appear. This mechanism, in combination with the diffusion-drift mechanism of polarization, results in additional dispersion of the real () and imaginary () parts of the dielectric permittivity, this being particularly significant for semiconductors of thickness smaller than the screening length L_s of free carriers. The character of the behavior of and depends on the relation between the Maxwell relation time _M and the times of carrier capture: _c and ejection _e by an impurity center. For _cetm and (/L_s) _e/_c1 the dispersion of and is the same as for thick plates (/L_s1). For _{c m e} and (/L_s)_e/_c1 the () curve has a characteristic kink in the region 1/_e, indicating additional absorption associated with the ejection of carriers into the surface region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 11–13, October, 1981.     

Certain features of radiation transport in spatially bounded media with anisotropic scattering

The problem of radiation transport (RT) in media with a nonsymmetric scattering index is examined under multiple scattering conditions. The governing influence on the nature of the RT is exerted by the integral index parameters that take account of the forward-backward radiation. Nonsymmetry of the index /, equal to three produces a relative energy redistribution through the side faces of the medium within 20% limits, where the maximum redistribution is observed for small transverse dimensions _y=_z=5. For large transverse dimensions the effect of index nonsymmetry does not appear. It is shown that the degree of anisotropy is less in spatially bounded media as compared with an unbounded layer of equal optical thickness.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 69–72, December, 1989. Original article submitted January 11, 1988.     

Spannungsverläufe Nach Wechseln der Verformungsgeschwindigkeit an Metalleinkristallen

The theoretical relations between _v and measured stress changes are discussed and compared with experimental results. For instantaneous change in the strain rate, the first deviation of the stress increase from the linearity ( _C ) can be used as a measure of _v for small deformation only. The comparison of _C with the extrapolated value _A enables to reveal the presence of recovery. The comparison of stress changes measured after a given rate change at the same strain on unrecovering (low temperatures) and recovering (higher temperatures) samples enables to differentiate between various types of recovery.     

Symmetry vector fields and similarity solutions of a nonlinear field equation describing the relaxation to a maxwell distribution

In the study of the formulation of Maxwellian tails the nonlinear partial differential equation ² u/x +u/x+u ²=0 arises. We determine the Lie point symmetry vector fields and calculate the similarity ansätze. Then we discuss the resulting ordinary differential equations. Finally, the existence of Lie Bäcklund vector fields is studied and a Painlevé analysis is performed.     

Dynamic critical behavior of a Swendsen-Wang-Type algorithm for the Ashkin-Teller model

We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model. We find that the Li-Sokal bound on the autocorrelation time (_int. const xC _H ) holds along the self-dual curve of the symmetric Ashkin-Teller model, and is almost, but not quite sharp. The ratio _int./C _H appears to tend to infinity either as a logarithm or as a small power (0.05p0.12). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.