Casimir Force on a Dielectric Cylinder

The Casimir surface force density on a compact material cylinder of radius a is calculated, at zero temperature. A Green function approach is followed. The general theory is formulated so as to hold for arbitrary permittivities ε(ω) and permeabilities μ(ω), whereas when it comes to explicit calculations the condition ε(ω) μ(ω) = 1 is assumed to hold. A simple dispersion relation is chosen, implying a high frequency cutoff ω₀. The theory yet diverges, at high angular momenta. Divergences of this sort usually appear whenever there are curved boundaries present. On physical grounds an angular momentum cutoff m₀ can be introduced, being of order ω₀a. A semi-quantitative calculation of the force thereby becomes possible. The calculated force is attractive.     

Dynamical mechanism for varying light velocity as a solution to cosmological problems

A dynamical model for varying light velocity in cosmology is developed, based on the idea that there are two metrics in spacetime. One metric g_μν describes the standard gravitational vacuum, and the other describes the geometry through which matter fields propagate. Matter propagating causally with respect to can provide acausal contributions to the matter stress-energy tensor in the field equations for g_μν, which, as we explicitly demonstrate with perfect fluid and scalar field matter models, provides a mechanism for the solution of the horizon, flatness and magnetic monopole problems in an FRW universe. The field equations also provide a ‘graceful exit' to the inflationary epoch since below an energy scale (related to the mass of ψ_μ) we recover exactly the standard FRW field equations.     

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.     

An analysis of DC conductivity in terms of degradation mechanisms induced by thermal aging in polypyrrole/polyaniline blends

Measurements of the d.c. electrical conductivity on thermally treated polypyrrole/polyaniline (PPy/PANI) samples, in which the PPy content increased by 10% w.w. starting from pure PANI to pure PPy, followed a σ(t, T) = σ₀(t)exp[−(T₀/T)^1/2] law. This is consistent with a heterogeneous structure of the granular metal type, in which aging is accompanied by the shrinking of the conductive grains causing the decrease of the sample conductivity, a process which is described by the increase of the parameter T₀. The preexponential factor σ₀(t) depends on the intrinsic conductivity of the grains and geometrical factors affecting the carrier paths through the energy barriers, as are the grain size distribution and the mean volume occupied by the conducting grains in the material. It was found that for the samples as a whole the thermal aging law, which predicts ln σ(t, T)∝t^1/2 is followed for a given temperature T, where t is the time of the thermal treatment, in accordance with a granular metal type structure. On the other hand, the preexponential factor σ₀(t) decreases with the aging, following a different law [σ(t = 0, T)−σ(t, T)]/σ(t = 0, T)∝t^1/2, where σ(t = 0, T) is the initial value of σ₀(t), that of the fresh sample. This law reveals an aging caused by a degradation proceeding into the interior of the grains in a diffusion-like manner. So, the two different laws of aging, one from T₀ and the other from σ₀, reveal that the aging does not simply reduce the size of the grains, but affects their interior, this degradation decreases with depth.     

Brownian Motion with Dry Friction

A small object (Solid or droplet) is placed on a horizontally vibrating plate, imposing an acceleration γ(t) in the form of a white noise. The object experiences dry friction (due to soild/solid interaction, or to contact angle hysteresis in the case of a droplet). The object is driven by a force γ(t) – Δσ(t) where σ(t), =±1, depending on the sign of the velocity. We discuss the motion at two levels: (i) in terms of simple scaling laws, (ii) by a propagator technique. (a) When Δ is below a certain crossover value Δ*, we expect an unperturbed (Langevin) Brownian motion. (b) When Δ > Δ*, we expect a reduced diffusion coefficient proportional to Δ⁻⁴ for small Δ.     

Beyond the relativistic point particle: A reciprocally invariant system and its generalisation

We investigate a reciprocally invariant system proposed by Low and Govaerts et al., whose action contains both the orthogonal and the symplectic forms and is invariant under global O(2,4)∩Sp(2,4) transformations. We find that the general solution to the classical equations of motion has no linear term in the evolution parameter, τ, but only the oscillatory terms, and therefore cannot represent a particle propagating in spacetime. As a remedy, we consider a generalisation of the action by adopting a procedure similar to that of Bars et al., who introduced the concept of a τ derivative that is covariant under local Sp(2) transformations between the phase space variables x^μ(τ) and p^μ(τ). This system, in particular, is similar to a rigid particle whose action contains the extrinsic curvature of the world line, which turns out to be helical in spacetime. Another possible generalisation is the introduction of a symplectic potential proposed by Montesinos. We show how the latter approach is related to Kaluza–Klein theories and to the concept of Clifford space, a manifold whose tangent space at any point is Clifford algebra Cl(8), a promising framework for the unification of particles and forces.     

Condition for adiabatic passage in the earth’s-field NMR technique

The equation of motion dM/dt=γ M×B(t) is solved for the case B(t)=jB_p(t)+kB_e. The field B_e is a small static field, typically the earth’s field. The field B_p(t) decays exponentially toward zero with time constant T. This decay is produced by an overdamped switching transient that occurs near the end of the rapid cutoff of the coil current used to polarize the sample. It is assumed that B_p is initially large compared to B_e, and that magnetization M is initially along the resultant field B. Exact solutions are obtained numerically for several decay time constants of B_p, and the motion of M is depicted graphically. It is found that for adiabatic passage, the final cone angle β of the precession in field B_e is related to the decay time constant of B_p by β=2e^{−(π/2)ω_eT}. This is confirmed by measurements of the amplitudes of the ensuing free-precession signals for various decay rates of B_p. Near-perfect adiabatic passage (magnetization aligned within 2° of the earth’s field) can be achieved for time constants T2.6/ω_e. For the case of sudden passage, an approximate analytic solution is developed by linearizing the equation of motion in the laboratory frame of reference. For the adiabatic case, an approximate analytic solution is obtained by linearizing the equation of motion in a rotating frame of reference that follows the resultant field B=B_p+B_e.     

Extracting (α/π) Σa,μνGμνGμν from gauge theories on a lattice

The quantity G = (α/π) Σ_a,μνG_μν^aG_μν^a is extracted from Monte Carlo data for SU(2) lattice gauge theory We find G = 0.015 ± 0.002 GeV⁴.     

Resonances in at rest

Data on at rest show two resonant processes: (a) f₀(1370)η,f₀(1370)→σσ and ρρ, (b) η(1440)σ, η(1440)→ηπ⁺π⁻. The branching ratio BR[f₀(1370)→ρρ]/BR[f₀(1370)→σσ]=0.98±0.25 in the mass range available here. Using data on , the ratio Γ_4π/Γ_2π5 for f₀(1370). The effects of the strongly s-dependent width of f₀(1370) are discussed in some detail.The η(1440) is observed decaying to ησ and a₀(980)π, with strong destructive interference between them. In its decay to a₀(980)π, a narrow peak appears in the ηπ mass spectrum, but 30–50 MeV above that usually attributed to a₀(980) and significantly above the KK threshold. This effect is explained naturally by a two-step process: η(1440)→K^*(890)K followed by rescattering of the two kaons through a₀(980) to ηπ above the KK threshold.     

The Modified Korteweg-de Vries Equation on the Half-Line with a Sine-Wave as Dirichlet Datum

Boundary value problems for integrable nonlinear evolution PDEs, like the modified KdV equation, formulated on the half-line can be analyzed by the so-called unified transform method. For the modified KdV equation, this method yields the solution in terms of the solution of a matrix Riemann-Hilbert problem uniquely determined in terms of the initial datum q(x,0), as well as of the boundary values {q(0, t),qx(0, t),qxx(0, t)}. For the Dirichlet problem, it is necessary to characterize the unknown boundary values qx(0, t) and qxx(0, t) in terms of the given data q(x, 0) and q(0, t). It is shown here that in the particular case of a vanishing initial datum and of a sine wave as Dirichlet datum, qx(0, t) and qxx(0, t) can be computed explicitly at least up to third order in a perturbative expansion and that at least up to this order, these functions are asymptotically periodic for large t.     

Long-Time Asymptotics for Strong Solutions¶of the Thin Film Equation

In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation u _t =−(u u _xxx ) _x , modeling the evolution of the interface of a spreading droplet. For nonnegative initial values u ₀(x)∈H ¹(ℝ), both compactly supported or of finite second moment, we prove explicit and universal algebraic decay in the L ¹-norm of the strong solution u(x,t) towards the unique (among source type solutions) strong source type solution of the equation with the same mass. The method we use is based on the study of the time decay of the entropy introduced in [13] for the porous medium equation, and uses analogies between the thin film equation and the porous medium equation. Received: 2 February 2001 / Accepted: 7 October 2001     

Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems

We develop a level set method for the computation of multi-valued physical observables (density, velocity, energy, etc.) for the high frequency limit of symmetric hyperbolic systems in any number of space dimensions. We take two approaches to derive the method.The first one starts with a weakly coupled system of an eikonal equation for phase S and a transport equation for density ρ:

The main idea is to evolve the density near the n-dimensional bi-characteristic manifold of the eikonal (Hamiltonian–Jacobi) equation, which is identified as the common zeros of n level set functions in phase space . These level set functions are generated from solving the Liouville equation with initial data chosen to embed the phase gradient. Simultaneously, we track a new quantity f = ρ(t,x,k)|det(_k)| by solving again the Liouville equation near the obtained zero level set = 0 but with initial density as initial data. The multi-valued density and higher moments are thus resolved by integrating f along the bi-characteristic manifold in the phase directions.The second one uses the high frequency limit of symmetric hyperbolic systems derived by the Wigner transform. This gives rise to Liouville equations in the phase space with measure-valued solution in its initial data. Due to the linearity of the Liouville equation we can decompose the density distribution into products of function, each of which solves the Liouville equation with L^∞ initial data on any bounded domain. It yields higher order moments such as energy and energy flux.The main advantages of these new approaches, in contrast to the standard kinetic equation approach using the Liouville equation with a Dirac measure initial data, include: (1) the Liouville equations are solved with L^∞ initial data, and a singular integral involving the Dirac-δ function is evaluated only in the post-processing step, thus avoiding oscillations and excessive numerical smearing; (2) a local level set method can be utilized to significantly reduce the computation in the phase space. These methods can be used to compute all physical observables for multi-dimensional problems.Our method applies to the wave fields corresponding to simple eigenvalues of the dispersion matrix. One such example is the wave equation, which will be studied numerically in this paper.     

Boolean delay equations. II. Periodic and aperiodic solutions

Boolean delay equations (BDEs) areevolution equations for a vector of discrete variables x(t). The value of each componentX _i (t), 0 or 1. depends on previous values of all componentsx _j (t– t _ij ), x _i (t)=f _i (x₁(t–t _i1),...,x _n (t –t _in )). BDEs model the evolution of biological and physical systems with threshold behavior and nonlinear feedbacks. The delays model distinct interaction times between pairs of variables. In this paper, BDEs are studied by algebraic, analytic, and numerical methods. It is shown that solutions depend continuously on the initial data and on the delays. BDEs are classified intoconservative anddissipative. All BDEs with rational delays only haveperiodic solutions only. But conservative BDEs with rationally unrelated delays haveaperiodic solutions of increasing complexity. These solutions can be approximated arbitrarily well by periodic solutions of increasing period.Self-similarity andintermittency of aperiodic solutions is studied as a function of delay values, and certain number-theoretic questions related toresonances and diophantine approximation are raised. Period length is shown to be a lower semicontinuous function of the delays for a given BDE, and can be evaluated explicitly for linear equations. We prove that a BDE isstructurable stable if and only if it has eventually periodic solutions of bounded period, and if the length of initial transients is bounded. It is shown that, for dissipative BDEs, asymptotic solution behavior is typically governed by areduced BDE. Applications toclimate dynamics and other problems are outlined.     

An energy-momentum tensor in gauge theories

We consider the renormalization of the twist two, dimension four gauge invariant operator O_μν⁽¹⁾ = − F_μσF_νσ − g_{μν 0}. By using the general theory of renormalization of gauge invariant operators, we find the gauge noninvariant operator O⁽²⁾ with which it mixes. We construct a finite combination of O⁽¹⁾ and O⁽²⁾ and show that it is an acceptable energy momentum tensor for gauge theories. We compare our energy momentum tensor with that constructed by Freedman, Muzinich, and Weinberg.     

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.     

On integrability of generalized Veronese curves of distributions

Given a 1-parameter family of 1-forms γ(t) = γ₀+tγ₁+ ···+tⁿψ_n, consider the condition dγ(t)γ(t) = 0 (of integrability for the annihilated by γ(t) distribution w(t)). We prove that in order that this condition is satisfied for any t it is sufficient that it is satisfied for N = n + 3 different values of t (the corresponding implication for N = 2n + 1 is obvious). In fact we give a stronger result dealing with distributions of higher codimension. This result is related to the so-called Veronese webs and can be applied in the theory of bihamiltonian structures.     

Effect of aerosil dispersions on the nematic-to-isotropic interface

The effect of silica aerosils on the kinetics of the first-order nematic-isotropic (NI) phase transition is phenomenologically described in the framework of the time-dependent Landau-Ginzburg equation. A steady-state solution to the equation is presented such that the NI interface may propagate with a solitary-like wave profile under constant quenching. The results provide a plausible basis for the interpretation of the dynamical effects of quenched disorder in the liquid-crystal systems, caused by randomly interconnected porous media, such as aerosils. In the low silica aerosil ρ_s ( ≤0.1 g/cm^3) regime, the calculated values of the interface velocity v(T,ρ_s), the interface thickness κ(T,ρ_s), and the critical radius of a spherical nucleus of new nematic phase in a bulk isotropic environment, composed of polar molecules, such as 4-n-octyl- 4^′- cyanobiphenyl and 4-n-heptyl- 4^′- cyanobiphenyl shows that the effect of silica aerosils on the kinetics is reflected in a shifting of the set of temperature-dependent curves to lower temperature values.-1     

Three-dimensional array structures associated with Richtmyer-Meshkov and Rayleigh-Taylor instability

A boundary separating adjacent gas or liquid media is frequently unstable. Richtmyer-Meshkov and Rayleigh-Taylor instability cause the growth of intricate structures on such boundaries. All the lattice symmetries [rectangular (pmm2), square (p4mm), hexagonal (p6mm), and triangular (p3m1) lattices] which are of interest in connection with the instability of the surface of a fluid are studied for the first time. They are obtained from initial disturbances consisting of one (planar case, two-dimensional flow), two (rectangular cells), or three (hexagons and triangles) harmonic waves. It is shown that the dynamic system undergoes a transition during development from an initial, weakly disturbed state to a limiting or asymptotic stationary state (stationary point). The stability of these points (stationary states) is investigated. It is shown that the stationary states are stable toward large-scale disturbances both in the case of Richtmyer-Meshkov instability and in the case of Rayleigh-Taylor instability. It is discovered that the symmetry increases as the system evolves in certain cases. In one example the initial Richtmyer-Meshkov or Rayleigh-Taylor disturbance is a sum of two waves perpendicular to one another with equal wave numbers, but unequal amplitudes: a ₁(t=0)≠a ₂(t=0). Then, during evolution, the flow has p2 symmetry (rotation relative to the vertical axis by 180°), which goes over to p4 symmetry (rotation by 90°) at t→∞, since the amplitudes equalize in the stationary state: a ₁(t=∞)=a ₂(t=∞). It is shown that the hexagonal and triangular arrays are complementary. Upon time inversion (t→−t), “rephasing” occurs, and the bubbles of a hexagonal array transform into jets of a triangular array and vice versa. Zh. éksp. Teor. Fiz. 116, 908–939 (September 1999)     

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.