Atomic force microscopy analysis of wool fibre surfaces in air and under water

Wool fibre surfaces have been treated by solvent cleaning which leaves the native covalently bound surface lipid layer intact, and by alcoholic alkali which removes the lipid layer. The resultant surfaces have been analysed by atomic force microscopy (AFM), with particular emphasis on force–distance (F–d) methods. Methodologies were developed for investigation in situ in water of both the surface topography and the characteristics of the lipid layer. Longitudinal surface texturing was resolved in images of wool fibre surfaces in air; the texturing remained prominent after exposure to water. High resolution F–d curves revealed features associated with the lipid layer. A simple formalism was used to show that the layer had a thickness of a few nm, and an effective stiffness of some 0.12±0.01 N/m. Strong adhesive interactions, equivalent to a pressure of 0.1 MPa, acted on the tip at the tip-to-substrate interface. The methodology and formalism are likely to be relevant in the broad field of thin-film analysis and for fibre technology.     

2D gravity+1D matter

We consider a formulation of nonperturbative two-dimensional quantum gravity coupled to a single bosonic field (d=1 matter). Starting from a matrix realization of the discretized model, we express the continuum theory as a double scaling limit in which the 2D cosmological constant g tends towards a critical value g_c, and the string coupling 1/N→0, with the scaling parameter ∝1n (g-g_c)/(g-g_c)N held fixed. We find that in this formulation logarithmic corrections already present at tree level persist to all higher genus, suggesting a behavior different from the previously considered cases of d<1 matter.     

Dimensional reduction of symmetries

It has been shown that ordinary (d−2)-dimensional quantum field theories are equivalent to corresponding quantum field theories defined on a (d+2)-dimensional superspace with two anticommuting variables. This dimensional reduction is a consequence of superrotation invariance in the superspace. In this letter we study general conformal transformations in the superspace and the properties of field theories which are invariant under such transformations. We show that the symmetries are dimensionally reduced.     

Direct transition from a stable equilibrium to quasiperiodicity in non-smooth systems

The purpose of this Letter is to show how a border-collision bifurcation in a piecewise-smooth dynamical system can produce a direct transition from a stable equilibrium point to a two-dimensional invariant torus. Considering a system of nonautonomous differential equations describing the behavior of a power electronic DC/DC converter, we first determine the chart of dynamical modes and show that there is a region of parameter space in which the system has a single stable equilibrium point. Under variation of the parameters, this equilibrium may collide with a discontinuity boundary between two smooth regions in phase space. When this happens, one can observe a number of different bifurcation scenarios. One scenario is the continuous transformation of the stable equilibrium into a stable period-1 cycle. Another is the transformation of the stable equilibrium into an unstable period-1 cycle with complex conjugate multipliers, and the associated formation of a two-dimensional (ergodic or resonant) torus.     

Interplay of topology and quantization: topological energy quantization in a cavity

The interplay between quantization and topology is investigated in the frame of a topological model of electromagnetism proposed by the author. In that model, the energy of electromagnetic radiation in a cubic cavity is where d is a topological integer index equal to the degree of a map between two orbifolds.     

Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences

We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).     

The d-dimensional sine-Gordon model in the presence of random fields

We study the properties of a d-dimensional sine-Gordon model in the presence of a random field that couples linearly to the sine-Gordon field using the Wilson renormalization group approach via the replica trick. No stable fixed point is found for dimensionalities d<4, corresponding to the absence of long-range order. Such a situation seems to occur in experiments on impurity-pinned charge-density-wave systems in which a “glassy behaviour” appears to be induced by arbitrarily weak symmetry-breaking randomness.     

Torus knots and polynomial invariants for a class of soliton equations

In this paper is shown how to interpret the nonlinear dynamics of a class of one-dimensional physical systems exhibiting soliton behavior in terms of Killing fields for the associated dynamical laws acting as generators of torus knots. Soliton equations are related to dynamical laws associated with the intrinsic kinematics of space curves and torus knots are obtained as traveling wave solutions to the soliton equations. For the sake of illustration a full calculation is carried out by considering the Killing field that is associated with the nonlinear Schrodinger equation. Torus knot solutions are obtained explicitly in cylindrical polar coordinates via perturbation techniques from the circular solution. Using the Hasimoto map, the soliton conserved quantities are interpreted in terms of global geometric quantities and it is shown how to express these quantities as polynomial invariants for torus knots. The techniques here employed are of general interest and lead us to make some conjectures on natural links between the nonlinear dynamics of one-dimensional extended objects and the topological classification of knots.     

Nonlocal properties of dynamical three-body Casimir-Polder forces

We consider the three-body Casimir-Polder interaction between three atoms during their dynamical self-dressing. We show that the time-dependent three-body Casimir-Polder interaction energy displays nonlocal features related to quantum properties of the electromagnetic field and to the nonlocality of spatial field correlations. We discuss the measurability of this intriguing phenomenon and its relation with the usual concept of stationary three-body forces.     

Effects of electromagnetic field on the dynamical instability of expansionfree gravitational collapse

In this paper, we discuss the effects of electromagnetic field on the dynamical instability of a spherically symmetric expansionfree gravitational collapse. Darmois junction conditions are formulated by matching interior spherically symmetric spacetime to exterior Reissner–Nordström spacetime. We investigate the role of different terms in the dynamical equation at Newtonian and post Newtonian regimes by using perturbation scheme. It is concluded that instability range depends upon pressure anisotropy, radial profile of energy density and electromagnetic field, but not on the adiabatic index Γ. In particular, the electromagnetic field reduces the unstable region.     

4p-4d fano-like resonance in rhodium

Photoemission measurements of Rh films in the photon energy range 40–120 eV show that the 4p-4d intrashell interaction has a Fano-like resonance. The 4d photoemission intensity goes through a sharp dip in the vicinity of the 4p⁶4dⁿ+hv → 4p⁵4dⁿ⁺¹ threshold followed by a resonant enhancement before decreasing again. All parts of the 4d band show the same resonant behavior in contrast to previous resonant photoemission results. The resonant behavior of Rh is compared with Co which is the 3d analog of Rh.     

Choice of targets for inertial confinement fusion

We propose a simple target in the form of a miniature torus, in which the heavy shell is used to confine the plasma spread, for a solution of the laser-fusion problem. We achieve a significant decrease of heat losses using an external magnetic field and/or as a result of a self-sustaining magnetic field that is generated in the plasma. We formulate the conditions and determine the energy of the laser pulse (or of a beam of fast charged particles) required to ignite a thermonuclear DD reaction and obtain a positive energy yield. We show that the stopping range of α-particles does not exceed the small radius of the torus within a broad range of the plasma and magnetic-field parameters.     

Binding energy of an exciton bound to ionized donors in quantum dots

Binding energies for an exciton (X) trapped in the two-dimensional quantum dot by a positive ion located on the z axis at a distance d from the dot plane are calculated by using the method of few-body physics. This configuration is called a barrier (D⁺,X) center. The dependence of the binding energy of the ground state of the barrier (D⁺,X) center on the dot radius for a few values of the distance d between the fixed positive ion on the z axis and the dot plane is obtained. We find that when d<0.2nm the barrier (D⁺,X) center does not form a bound state.     

Pseudorapidity distributions of charged particles as a function of centrality in Pb–Pb collisions at 158 and 40 GeV per nucleon incident energy

The charged particle distributions dN_ch/dη have been measured by the NA50 experiment in Pb–Pb collisions at the CERN SPS. Measurements have been done at incident energies of 158 and 40 GeV per nucleon over a broad impact parameter range. Results obtained with two independent centrality estimators, namely the neutral transverse energy E_T and the forward energy E_ZDC, are reported.     

Yang–Lee zeros of the Ising model on random graphs of non planar topology

We obtain in a closed form the 1/N² contribution to the free energy of the two Hermitian N×N random matrix model with nonsymmetric quartic potential. From this result, we calculate numerically the Yang–Lee zeros of the 2D Ising model on dynamical random graphs with the topology of a torus up to n=16 vertices. They are found to be located on the unit circle on the complex fugacity plane. In order to include contributions of even higher topologies we calculated analytically the nonperturbative (sum over all genus) partition function of the model for the special cases of N=1,2 and graphs with n≤20 vertices. Once again the Yang–Lee zeros are shown numerically to lie on the unit circle on the complex fugacity plane. Our results thus generalize previous numerical results on random graphs by going beyond the planar approximation and strongly indicate that there might be a generalization of the Lee–Yang circle theorem for dynamical random graphs.     

Scaling behavior in a Fibonacci-sequenced system

The rudiments of dynamical systems theory are employed to analyze the transmission of light through a two-element medium in which the elements are arranged in a Fibonacci sequence. A dynamical map, introduced by previous authors, is extended so that the enlarged map generates direct predictions about the behavior of the transmission coefficient for phases in the neighborhood of certain critical values. These values correspond to unique periodic orbits of the map. Lowest-order calculations are performed analytically to study the properties of scaling near the critical phases. A scale factor is defined to describe this behavior. The study examines three cases in which the map has a fixed point, a 3-cycle, and a 6-cycle. The first two cases have the property that their scale factors are given by exactly the same Fibonacci number. In contrast, the third case has the property that its scale factor depends explicitly on a parameter of the physical system. Speculative remarks are added in conclusion to argue for the occurrence of a type of scaling whose features originate in the abstract structure of the Fibonacci sequence and are independent of the particular choice of physical system.     

Kaluza–Klein reductions and AdS/Ricci-flat correspondence

The AdS/Ricci-flat (AdS/RF) correspondence is a map between families of asymptotically locally AdS solutions on a torus and families of asymptotically flat spacetimes on a sphere. The aim of this work is to perturbatively extend this map to general AdS and asymptotically flat solutions. A prime application for such map would be the development of holography for Minkowski spacetime. In this paper we perform a Kaluza–Klein (KK) reduction of AdS on a torus and of Minkowski on a sphere, keeping all massive KK modes. Such computation is interesting on its own, as there are relatively few examples of such explicit KK reductions in the literature. We perform both KK reductions in parallel to illustrate their similarity. In particular, we show how to construct gauge invariant variables, find the field equations they satisfy, and construct a corresponding effective action. We further diagonalize all equations and find their general solution in closed form. Surprisingly, in the limit of large dimension of the compact manifolds (torus and sphere), the AdS/RF correspondence maps individual KK modes from one side to the other. In a sequel of this paper we will discuss how the AdS/RF maps acts on general linear perturbations.     

The dynamical entropy of the quantum Arnold cat map

We present a rigorous computation of the dynamical entropyh of the quantum Arnold cat map. This map, which describes a flow on the noncommutative two-dimensional torus, is a simple example of a quantum dynamical system with optimal mixing properties, characterized by Lyapunov exponents ± 1n ⁺, ⁺ > 1. We show that, for all values of the quantum deformation parameter,h coincides with the positive Lyapunov exponent of the dynamics.     

Resonant enhancement of field-induced annihilation rate for (π–π) atom: a possibility to measure np–ns energy splitting

Some possibilities are discussed for measuring the np–ns energy splitting in (π⁺–π⁻) atoms in experiments with relativistic particle beams, using the electromagnetic field control of annihilation process. Significant resonant enhancement of annihilation probability may be observed in an oscillating field. The resonance provides much more spectacular changes in the decay rate than corresponding decay rate changes in a steady field. The position of resonance on the frequency axis gives an additional and more accurate information on the np–ns transition energy, than the data on the ratio between the field-free and dc-field-induced annihilation rates. Numerical results are presented for the states n=2 and n=3.     

Study of the chemical bonding of titanium with silicon and oxygen by AES and SEELS

Auger electron Spectroscopy (AES) and slow electron energy loss Spectroscopy (SEELS) have been employed to study the electronic structure of Ti, TiSi₂ and TiO₂. The changes in the Auger and loss spectra when Ti chemically binds with silicon to form TiSi₂ and with oxygen to form TiO₂ have been understood as manifestations of changes in electronic participation. AES spectra show distinct changes in line shapes of transitions involving the Ti valence electrons. The SEELS spectra provide information regarding shallow core levels, valence band and the collective excitation energies of the volume and surface plasmons. By monitoring the changes in the Auger peak at 387 eV and the 3p→ 3d quasiatomic transition (at about 45 eV), the role of d-orbital occupancies are studied in Ti and its compounds. The SEELS studies in the 0-80 eV range have enabled the authors to observe the behaviour of the 3p → 3d quasiatomic transition in Ti, which persists after oxidation but almost disappears during TiSi₂ formation. The values of the plasmon losses are related to the collective behaviour of conduction electrons.