Diffusion on a random comb: Distribution function of the survival probability

We investigate the distribution functionQ(P) describing the survival probability on a comb consisting of a backbone with lateral, randomly disconnected infinite branches. Two different regimes are analyzed in some detail: (i) at short times,Q(P) is shown to have a self-similar structure (devil's staircase); (ii) at large times, this function becomes smooth and tends toward a rather well-defined unit step function. The disorder-averaged survival probability <p ₀(t)> is expected to decrease ast ^–3/4 at large times, whereas the relative fluctuations of the sample-dependentp ₀(t) display a very slow decay in time, going to zero liket ^–1/8.     

Convergence to Equilibrium of Random Ising Models in the Griffiths Phase

We consider Glauber-type dynamics for disordered Ising spin systems with nearest neighbor pair interactions in the Griffiths phase. We prove that in a nontrivial portion of the Griffiths phase the system has exponentially decaying correlations of distant functions with probability exponentially close to 1. This condition has, in turn, been shown elsewhere to imply that the convergence to equilibrium is faster than any stretched exponential, and that the average over the disorder of the time-autocorrelation function goes to equilibrium faster than exp[–k(log t) ^d/(d–1)]. We then show that for the diluted Ising model these upper bounds are optimal.     

Methyl and t-butyl reorientation in an organic molecular solid

We have determined the molecular and crystal structure of 4,5-dibromo-2,7-di-t-butyl-9,9-dimethylxanthene and measured the ¹H spin–lattice relaxation rate from 87 to 270 K at NMR frequencies of ω/2π=8.50, 22.5, and 53.0 MHz. All molecules in the crystal see the same intra and intermolecular environment and the repeating unit is half a molecule. We have extended models developed for ¹H spin–lattice relaxation resulting from the reorientation of a t-butyl group and its constituent methyl groups to include these rotors and the 9-methyl groups. The relaxation rate data is well-fitted assuming that the t-butyl groups and all three of their constituent methyl groups, as well as the 9-methyl groups all reorient with an NMR activation energy of 15.8±1.6 kJ mol⁻¹ corresponding to a barrier of 17.4±3.2 kJ mol⁻¹. Only intramethyl and intra-t-butyl intermethyl spin–spin interactions need be considered. A unique random-motion Debye (or BPP) spectral density will not fit the data for any reasonable choice of parameters. A distribution of activation energies is required.     

Separation of the ortho and para NMR signals in solid deuterium via DQ filtering

Double quantum (DQ) filtering is shown to lead to an effective separation of the NMR signals from the para (I = 1) and ortho (I = 2) molecules in solid deuterium. The separation is achieved by the pulse sequence 90_φ^°–t_pr–90_φ^°–t_ev–90_x^°–t, where the phase-cycled first two pulses create the DQ coherence. Two components are observed after the third pulse; the para signal shows the maximum at a short time t while the ortho signal reaches the maximum at a longer t. The observed signal can be expressed as ∑_I [F_I(t_pr − t) − F_I(t_pr + t)], where F_I(t) is a proper fitting function for the free induction signal of the para and ortho molecules (with I = 1 or 2, respectively). Numerical fits to experimental data at 4.2 and 2 K show that this method can be used to determine the ratio F₁(0)/F₂(0) and thus, because the initial value F_I(0) is proportional to the respective magnetization before the pulse sequence, the ortho and para concentrations in solid deuterium.     

Cosmology with time-varyingG

It is shown that a Universe with a time-varying gravitational constantG necessarily implies creation if the rest mass of matter particlesm _p is constant. In this case, from Einstein's field equations, the conditions for energy-momentum propagation are ·(GT ^v ) from which matter and photon propagation equations are derived. Free matter particle propagation is not affected by creation that is given byGN _pm_p=const, whereN _p is the number of matter particles within a proper volume. This relation introduces explicitly the rest mass of the Universe into the field equations. Free photon propagation is affected by creation that is given byGT v R=const, whereN is the number of photons within a proper volume, which is the cosmic red shift law. Conservation of the cosmic background photon distribution determines photon creation asG ³ N ⁴ . The results are applied to the caseG t ^–1 equivalent toN _p ÷ t.It is found that at an aget=1, 0^–40 t _o, of the order light takes to travel a proton size, Planck's units become of the order of the proton's massm _p, sizer _p, and timer _p/c. Hence, matter particles at this age are quantum black holes. Evaporation of these quantum black holes at this age gives a background blackbody radiation that, red shifted to present timet ₀, gives the present cosmic microwave background.A cosmological model of the Friedmann type is constructed. The red shift versus distance relation is derived taking into account creation. Using a Hubble's constantH _obs=50 km sec^–1 Mpc^–1 and a deceleration parameterq _obs=1.0 the model is of the typek=1 and gives a present aget ₀=6.81×10⁹ yr, consistent with Uranium model ages. Thus, the three results for the age of the Universe, i.e., radioactive decay, Hubble's constant, and stellar evolution are brought together in this creation model. The matter-dominated era occurs fort>7.6×10^–3 t ₀, while the radiation-dominated era occurs for 7.6×10^–3 t _o>t>10^–40 t _o. The origin of the Universe is placed at this last limit, which is Planck's time at the corresponding G, consisting of quantum black holes at a temperature T_i=3×10¹¹K.     

Dynamic recrystallization of austenite during hot plastic deformation

The kinetics of dynamic recrystallization is dependent on the thermomechanical conditions in which plastic deformation is taking place. To determine the timet _p needed for the onset of dynamic recrystallization, experimental work was performed on low-carbon austenite to check the validity of the equationW= 2·1 × 10^–1 Z ^–0.94, whereW= t_pexp(–Q/RT),Z represents the Zener-Hollomon parameter, and Q=276 kJ mol^–1.     

Study of the pion trajectory in the photoproduction of leading neutrons at HERA

Energetic neutrons produced in ep collisions at HERA have been studied with the ZEUS detector in the photoproduction regime at a mean photon–proton center-of-mass energy of 220 GeV. The neutrons carry a large fraction 0.64<x_L<0.925 of the incoming proton energy, and the four-momentum transfer squared at the proton–neutron vertex is small, |t|<0.425 GeV². The x_L distribution of the neutrons is measured in bins of t. The (1−x_L) distributions in the t bins studied satisfy a power law dN/dx_L∝(1−x_L)^a(t), with the powers a(t) following a linear function of t: . This result is consistent with the expectations of pion-exchange models, in which the incoming proton fluctuates to a neutron–pion state, and the electron interacts with the pion.     

Phase transition of directed polymer in random potentials on 4+1 dimensions

Finite-temperature-directed polymer in random potentials is described by a transfer matrix method. On 4+1 dimensions, the evidence for a finite-temperature phase transition is found at T_c≈0.18, where the free energy fluctuation grows logarithmically as a function of time t. When TT_c, the fluctuation of the free energy grows as t^ω with ω≈0.156. The phase transition of the restricted solid-on-solid model, which is closely related to the directed polymer problem through the Kardar–Parisi–Zhang equation, is also discussed.     

Interfacial Adsorption in Two-Dimensional Potts Models

The interfacial adsorption W at the first-order transition in two-dimensional q-state Potts models is studied. In particular, findings of Monte Carlo simulations and of density-matrix renormalization group calculations at q=16 are consistent with the analytic result, obtained in the Hamiltonian limit at large values of q, that Wt ^–1/3 on approach to the bulk critical temperature T _c, t=|T _c–T|/T _c. In addition, the numerical findings allow to estimate corrections to scaling. Our study supports and quantifies a previous conclusion by Bricmont and Lebowitz based on low temperature expansions.     

Low temperature transport properties of thin SOI MOSFETs

Fabrication and 4.2 K mobility measurements of silicon-on-insulator (SOI) metal–oxide-field-effect-transistors are reported. The three sets of samples fabricated in this work include devices for which the SOI film thicknesses (t_SOI) are in the ranges of 10–15, 16–19 and 56–61 nm. The peak mobility of the devices that have the SOI film thickness above 16.5 nm is 1.9 m²/V s. The set of devices with thinnest channel (t_SOI=10–15 nm) suggest that the peak mobility decreases with decreasing t_SOI.     

A nontrivial Renormalization Group fixed point for the Dyson-Baker hierarchical model

We prove the existence of a nontrivial Renormalization Group (RG) fixed point for the Dyson-Baker hierarchical model ind=3 dimensions. The single spin distribution of the fixed point is shown to be entire analytic, and bounded by exp(–const×t ⁶) for large real values of the spint. Our proof is based on estimates for the zeros of a RG fixed point for Gallavotti's hierarchical model. We also present some general results for the heat flow on a space of entire functions, including an order preserving property for zeros, which is used in the RG analysis.Supported in Part by the National Science Foundation under Grant No. DMS-9103590.Supported in Part by the Swiss National Science Foundation.     

Random-matrix approach to RPA equations. I

We study the RPA equations in their most general form by taking the matrix elements appearing in the RPA equations as random. This yields either a unitary or an orthogonally invariant random-matrix model that does not appear in the Altland–Zirnbauer classification. The average spectrum of the model is studied with the help of a generalized Pastur equation. Two independent parameters govern the behaviour of the system: the strength α² of the coupling between positive- and negative-energy states and the distance between the origin and the centers of the two semicircles that describe the average spectrum for α² = 0, the latter measured in units of the equal radii of the two semicircles. With increasing α², positive- and negative-energy states become mixed and ever more of the spectral strength of the positive-energy states is transferred to those at negative energy, and vice versa. The two semicircles are deformed and pulled toward each other. As they begin to overlap, the RPA equations yield non-real eigenvalues: The system becomes unstable. We determine analytically the critical value of the strength for the instability to occur. Several features of the model are illustrated numerically.     

Kinetics of the Late Stage of Disintegration of Supersaturated Solid Solutions with Pronounced Crystalline Structure

The kinetics of disintegration of a supersaturated solid solution is studied in the context of the Lifshits–Slezov–Wagner (LSW) theory for a quasi-coherent interface between the new phase precipitates and the matrix. It is shown that the particle size distribution lies within a very narrow range of relative particle size (r _m/r _c = 6/5) and that the critical or average particle size varies with time as t^1/6 (r _c t ^1/6).     

Influencing the satellite transitions of half-integer quadrupolar nuclei for the enhancement of magic angle spinning spectra

Double frequency sweeps can induce spin transitions in a set of satellites of a half-integer quadrupolar nucleus by simultaneously passing through resonance for a satellite pair. It is shown that by transferring population from the outer spin levels to the inner |1/2 and |−1/2 levels an increased intensity for central transition spectra is obtained. Although Magic Angle Spinning in principle interferes with this process, and the adiabaticity of the passages is different for every crystallite in a powder, enhanced spectra with undistorted line shapes are obtained for I=3/2 (²³Na) and 5/2 (²⁷Al) spins experiencing quadrupolar interactions with ω_Q in the range 0.1–3 MHz. Even at spinning speeds up to 30 kHz significant enhancements are obtained. An analysis of the combined effects of double frequency sweeps (DFS) and MAS indeed shows strongly different effects for different crystallites in powder ranging from no gain at all to the theoretical maximum gain of 2I. As the effects are randomly distributed over all orientations on a sphere this is averaged over the whole line shape. Therefore, undistorted powder patterns are obtained enhanced by the average gain over the individual crystallites. Saturation of the satellite transitions, which can only be achieved if spin–spin relaxation is sufficiently strong, leads to identical results. Optimization of the sweeps should be toward an optimal effect on the population transfer to the central levels and chosen short with respect to spin–lattice relaxation times.     

Asymptotic time behavior of correlation functions. III. Local equilibrium and mode-coupling theory

The decay to equilibrium is discussed from a general point of view based on the assumed rapid approach to local equilibrium for well-chosen initial states. The assumption is applied to the problem of time correlation functions and it is shown that the mode-coupling formula describes the asymptotics of the so-called projected wavenumber-dependent correlation functions. The local equilibrium assumption thus provides a general basis for thet ^–3/2 behavior of correlation functions derived in previous papers in this series, as well as for the infinite series of correction termst ^–(2–Pn (n 2), withPn=2^–n, and for the corresponding series of corrections of orderk ^3–Pn (n1) to Navier-Stokes hydrodynamics.     

Broad band antireflection coating on zinc sulphide simultaneously effective in SWIR, MWIR and LWIR regions

In recent years multi-spectral imagery is steadily growing popularity. Multi-channel imaging which includes short-wave infrared (SWIR), mid-wave infrared (MWIR) and long-wave infrared (LWIR) systems are useful for threat detection, tracking, thermal signature detection and terrain analysis. In this paper, a broad band antireflection coating on ZnS substrate, simultaneously effective in SWIR, MWIR and LWIR is reported. The coating design approach was evolved using gradient index concept, where refractive index varies gradually from incident media to the ZnS (n = 2.2) substrate. The gradient index profile depicted by 4th degree polynomial n(t) = −0.45t⁴ + 1.9t³ − 2.7t² + 1.9t + 1,where n(t) is the refractive index at the distance t from ambient, and t is the thickness in micron. The profile is best approximated by eight discrete step index layers, whose first layer is thorium fluoride (n = 1.42; lowest index stable material available). Other seven layers are replaced by two equivalent layer system of real materials thorium fluoride and zinc sulphide. Final 15 layers design is deposited by e-beam evaporation. The maximum layer thickness was restricted around 0.7 μm to overcome the stress problem in the film. This 15 layers coating has shown average transmission 95% in 0.9–10.5 μm spectral band having peak 99% at 9 μm.     

Effect of disorder on relaxation in the one-dimensional Glauber model

We study the long-time relaxation of magnetization in a disordered linear chain of Ising spins from an initially aligned state. The coupling constants are ferromagnetic and nearest-neighbor only, taking valuesJ ₀ andJ ₁ with probabilitiesp and 1–p, respectively. The time evolution of the system is governed by the Glauber master equation. It is shown that for large timest, the magnetizationM(t) varies as [exp(–₀ t](t), where ₀ is a function of the stronger bond strengthJ ₀ only, and (t) decreases slower than an exponential. For very long times, we find that ln (t) varies as –t ^1/3. For low enough temperatures, there is an intermediate time regime when ln (t) varies as –t ^1/2. The results can be extended to more general probability distributions of ferromagnetic coupling constants, assuming thatM(t) can only increase if any bond in the chain is strengthened. If the coupling constants have a continuous distribution in which the probability density varies as a power law near some maximum valueJ ₀, we find that ln (t) varies as –t ^1/3(lnt)^2/3 for large times.     

A diffusion model of metal surface modification during plasma nitriding

A diffusion model of metal surface modification by plasma nitriding has been developed. This model takes into account the erosion effects at the plasma/solid interface occurring due to the ion bombardment of the surface. For constant sputtering rate, which is the usual situation during plasma nitriding, the growth of the sub-layers is well described by the analytical expressiong(t) =g ₀,f ^–1 (t/t ₀), whereg(t) is the sub-layer thickness at timet,g ₀ andt ₀ are parameters which depend on the treated material and plasma characteristics,f ^–1 is the inverse of the function — In(1 - x) + x), 0 x 1. Under negligible erosion effects, the expression forg(t) reduces to the parabolic law. The diffusion zone (substratum) growth does not follow the parabolic law as well. However, the deviation occurs after long plasma nitriding time. The model can be used for experimentally determining the effective diffusion coefficients and the erosion rate during plasma nitriding of metal surfaces.     

Electroweak corrections to the fermionic decay width of the standard Higgs boson

The partial decay width of the standard model Higgs particle into a general species of fermions is given at the electroweak 1-loop level. The analytic formulae are applicable to light and heavy fermions. Numerical results are presented for Higgs decays intob andt quarks and into charged leptons. For not too heavy Higgs bosons the radiative corrections are of the order of a few per cent. In particular for Higgs bosons below theW ⁺ W ^– threshold the correction to the partial width intob quarks is very small and insensitive to the top mass. For every heavy Higgs bosons the 1-loop corrections increase the fermionic decay widths for all channels up to 15%.