Euclidean random matrices, the glass transition and the boson peak

In this paper I will describe some results that have been recently obtained in the study of random Euclidean matrices, i.e. matrices that are functions of random points in Euclidean space. In the case of translation invariant matrices one generically finds a phase transition between a phonon phase and a saddle phase. If we apply these considerations to the study of the Hessian of the Hamiltonian of the particles of a fluid, we find that this phonon-saddle transition corresponds to the dynamical phase transition in glasses, that has been studied in the framework of the mode coupling approximation. The boson peak observed in glasses at low temperature is a remanent of this transition. Received 4 May 2002     

Simulation of Voltage SET Operation in Phase-Change Random Access Memories with Heater Addition and Ring-Type Contactor for Low-Power Consumption by Finite Element Modeling

A three-dimensional finite element model for phase change random access memory is established to simulate electric, thermal and phase state distribution during （SET） operation. The model is applied to simulate the SET behaviors of the heater addition structure （HS） and the ring-type contact in the bottom electrode （RIB） structure. The simulation results indicate that the small bottom electrode contactor （BEC） is beneficial for heat efficiency and reliability in the HS cell, and the bottom electrode contactor with size Fx=80 nm is a good choice for the RIB cell. Also shown is that the appropriate SET pulse time is lOOns for the low power consumption and fast operation.     

Numerical studies of the vibrational isocoordinate rule in chalcogenide glasses

Many properties of alloyed chalcogenide glasses can be closely correlated with the average coordination of these compounds. This is the case, for example, of the ultrasonic constants, dilatometric softening temperature and the vibrational densities of states. What is striking, however, is that, at a given average coordination, these properties are nevertheless almost independent of the elemental composition. Here, we report on some numerical verification of this experimental rule as applied to the vibrational density of states. We find that this rule is not exact but holds qualitatively well over a wide range of compositions and local chemical correlations. Received 25 April 2000     

Boron distribution in the subsurface region of heavily doped IIb type diamond

For the first time investigations of the boron distribution in the subsurface region of HPHT boron-doped diamond that is promising for applications in electronics were carried out by X-ray photoelectron (XPS) and Raman spectroscopy. It was found from XPS data that the boron content decreased gradually more than one order of magnitude in depth of surface. The first-principle calculations have shown that the Raman polarizability in the crossed polarization configuration should increase considerably with boron doping. The Raman spectra from as-grown and polished surfaces of heavily boron-doped diamond are discussed in the context of theoretical results.     

Surface acoustic phonon modes of Ge nanocrystals embedded in SiO2

Ge nanocrystals (NCs) embedded in SiO₂ are synthesized by ion implantation, and the surface vibrational modes of the Ge NCs are investigated using the low-frequency Raman scattering (LFRS) technique. LFRS studies show distinct low-frequency Raman modes in the range 6.5-21.2 cm⁻¹ for the Ge NCs depending on the implant dose and annealing temperature. These low-frequency Raman modes are attributed to the confined surface acoustic phonon modes of Ge NCs with (0,0) spheroidal mode and (0,3) torsional modes. Our results are in excellent agreement with the recent theoretical predictions of surface vibrational modes in Ge NCs.     

The effects of experimental parameters in the thermal diffusivity measurements of oriented polymer films using mirage effect: Computer simulation

Computer simulations have been carried out to study the effects of the experimental parameters when the mirage method has been applied to thermal diffusivity measurements of oriented polymer films. The parameters under study are the thermal diffusivity of the fluid surrounding the sample, the modulation frequency and the radius of the heating beam, the height and the radius of the probe beam, and the sample thickness and thermal diffusivity. Proposals for the optimum parameter values to maximize the measurement sensitivity for the sample diffusivity are made and the difficulties arising from the low diffusivity of the samples are described. It is also concluded that because the thermal properties of the fluid surrounding the sample have a strong contribution to the mirage signals, the signals do not include any simple feature corresponding to the sample diffusivity. Therefore it should be determined from the entire measurement data using regression methods.     

On the dynamics of exotic matter: Towards creation of Perpetuum Mobile of third kind

The one-dimensional dynamics of a classical ideal ‘exotic’ fluid with equation of state p=p(?)<0$p=p(\mathrm{?})<0$ violating the weak energy condition is discussed. Under certain assumptions it is shown that the well-known Hwa–Bjorken exact solution of one-dimensional relativistic hydrodynamics is confined within the future/past light cone. It is also demonstrated that the total energy of such a solution is equal to zero and that there are regions within the light cone with negative (−)$(-)$ and positive (+)$(+)$ total energies. For certain equations of state there is a continuous energy transfer from the (−)$(-)$-regions to the (+)$(+)$-regions resulting in indefinite growth of energy in the (+)$(+)$-regions with time, which may be interpreted as action of a specific ‘Perpetuum Mobile’ (Perpetuum Motion). It is speculated that if it is possible to construct a three-dimensional non-stationary flow of an exotic fluid having a finite negative value of energy such a situation would also occur. Such a flow may continuously transfer positive energy to gravitational waves, resulting in a runaway. It is conjectured that theories plagued by such solutions should be discarded as inherently unstable.     

Anisotropic fluid dynamics in the early stage of relativistic heavy-ion collisions

A formalism for anisotropic fluid dynamics is proposed. It is designed to describe boost-invariant systems with anisotropic pressure. Such systems are expected to be produced at the early stages of relativistic heavy-ion collisions, when the timescales are too short to achieve equal thermalization of transverse and longitudinal degrees of freedom. The approach is based on the energy–momentum and entropy conservation laws, and may be regarded as a minimal extension of the boost-invariant standard relativistic hydrodynamics of the perfect fluid. We show how the formalism may be used to describe the isotropization of the system (the transition from the initial state with no longitudinal pressure to the final state with equal longitudinal and transverse pressure).     

Unusual temperature dependence of the positron lifetime in a polymer of intrinsic microporosity

The performance of polymeric membranes for gas separation is mainly determined by the free volume. Polymers of intrinsic microporosity are interesting due to the high abundance of accessible free volume. We performed measurements of the temperature dependence of the positron lifetime, generally accepted for investigation of free volume, in two polymers of intrinsic microporosity (PIM‐1 and PIM‐7) in the range from 143 to 523 K. The mean value of the free volume calculated from the ortho‐positronium lifetime is in the range of typical values for high free volume polymers. However, the temperature dependence of the local free volume is non‐monotonous in contrast to the macroscopic thermal expansion. The explanation is linked to the spirocenters in the polymer. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimation of Kauzmann temperature and isenthalpic temperature of metallic glasses

We propose expressions for the estimation of the isenthalpic temperature T ₀ (T ₀ = αT _m , α is a semi-empirical parameter and 0 ⩽ α < 1, T _m is the solidus temperature) and the Kauzmann temperature T _k (T _k = T _m exp(α−1)) for glass forming alloys. It is found that T _k estimated by T _k = T _m exp(α−1) is in agreement with that directly calculated from the heat capacity data, indicating that T _k = T _m exp(α − 1) can be used to estimate T _k of glass forming alloys. T ₀ estimated by T ₀ = αT _m , on the other hand, widely deviates from that of directly calculated from the heat capacity data. This suggests that the enthalpy difference of the under-cooled liquid and the crystal might be a nonlinear function of the temperature below T _k . Moreover, the Gibbs free energy difference ΔG is not sensitive to the deviation of α.     

Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.     

<Emphasis Type="Italic">Comment on</Emphasis>¶Low temperature specific heat of blue bronze K <Emphasis Type="Bold">0.30</Emphasis>MoO <Emphasis Type="Bold">3</Emphasis>, by J. Odin,J.C. Lasjaunias,K. Biljaković, K. Hasselbach,and P. Monceau

Eur. Phys. J. B 24, 315 (2001) Here we comment on a recently published paper on the presence of a phason contribution in the low temperature heat capacity data of the charge-density-wave compounds K_0.3MoO₃ and (TaSe₄)₂I. We have shown that the anomaly in the C _P / T ³ data reported by Odin et al. is straightforwardly interpreted in terms of low energy phonon modes resulting from the peculiar topology of these compounds. Received 21 February 2002 Published online 19 July 2002     

A quantum field theory of the liquid-glass transition in multi-component liquids

An established unified theory of the liquid-glass transition in one-component liquids is extended to multi-component liquids. The universal features such as the Kauzmann paradox, the Vogel-Tamman-Fulcher (VTF) law on the relaxation times and the transport coefficients, the jump of the specific heat at the glass transition temperature and the Boson peaks are elucidated. The Kauzmann entropy in a form of a Curie law with a negative sign comes from the mixing between the sound and the intra-band fluctuation entropies, where the critical temperature corresponds to the sound instability temperature at a reciprocal particle distance. The VTF law is constructed from the Einstein relation on entropy and probability so that the Kauzmann entropy is included as a normal form in exponent of the VTF law. The Kauzmann entropy explains the Kauzmann paradox and the jump of the specific heat so that the universal features of the glass transition are elucidated consistently.     

On the presence of spatial pattern formation in a bistable dynamical system

The aim is to investigate whether in a structural bistable reaction-diffusion system pattern formation may emerge simultaneously from both steady states. Therefore, a dynamical system is modelled by three coupled nonlinear differential equations from which synergetic ordering may arise. In addition, the nonlinear terms are chosen such that the homogeneous system is governed by the canonical form of a cusp bifurcation in a two-dimensional control space. Thus, structural bistability is established. Based on a linear stability analysis the region of bistability is decomposed into four different domains in the control plane. It is shown that in one of these domains self-organization can lead to pattern formation from both steady states simultaneously. In two other domains self-organization can arise from only one steady state and finally in one domain patterning is impossible. An expression for the wavelength of a spatial structure is derived and discussed in terms of parameters of the system. As a possible application of the present results a crystal under irradiation with particles of high energy is considered. It is demonstrated for the case of steel that the parameters of the system can be chosen such that a two-fold spatial instability for irradiation induced cavities may emerge.     

A realistic model of superfluidity in the neutron star inner crust

A semi-microscopic self-consistent quantum approach developed recently to describe the inner-crust structure of neutron stars within the Wigner-Seitz (WS) method with the explicit inclusion of neutron and proton pairing correlations is further developed. In this approach, the generalized energy functional is used which contains the anomalous term describing the pairing. It is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the WS cell with the one calculated microscopically for neutron matter. Previously, the anomalous part of the latter was calculated within the BCS approximation. In this work corrections to the BCS theory which are known from the many-body theory of pairing in neutron matter are included into the energy functional in an approximate way. These modifications have a sizable influence on the equilibrium configuration of the inner crust, i.e. on the proton charge Z and the radius R _c of the WS cell. The effects are quite significant in the region where the neutron pairing gap is larger.     

On the possibility of a phonon mediated transport anomaly in MgB2 under compression

Results of electrical resistance measurements on MgB₂ at ambient temperature up to 25 GPa are presented. An abrupt reduction of nearly 30% in resistance around 18 GPa is observed. Band structure calculations in the presence of a frozen-in distortion of the E_2g phonon mode reveal that one of the closed Fermi sheets corresponding to the σ-band opens along the Γ-A direction at this pressure. It is suggested that the anomaly observed in the resistance is due to this phonon mediated electronic topological transition (ETT).     

On the range of interaction from finite size scaling in magnetic Ni nanowires

A recent experiment reporting a thickness dependence of magnetic properties of Ni nanowires has been re-interpreted in terms of spin–spin interactions eventually ranging beyond nearest neighbors. An analysis following the Ginzburg argument indicated that the system is in the crossover regime from 3D Ising to classical critical behavior as a function of the normalized range of interactions R$R$. The range of the interactions covering three to four coordination spheres of an Ni atom has been found by the fit to literature experimental data on Ni nanowires. Consistency with recent first-principles calculations are discussed.     

Effect of graded interlayer on the mode I edge delamination by residual stresses in multilayer coating-based systems

The mode I edge delamination could be initiated due to the presence of the interfacial peeling stresses near the edges of the multilayered systems due to the material mismatches between the adjacent layers. However, the exact peeling stress distributions could not be obtained by using the existing analytical and numerical models. It was proposed recently that the peeling moment resulting from the localized peeling stresses could be used to characterize mode I edge delamination. In this paper, the effect of the graded interlayer on the mode I edge delamination by thermal residual stresses in multilayer coating-based systems was investigated. Following the previous analysis approaches, the exact closed-form solutions for the peeling moments at individual interfaces and the curvatures for bilayer system, typical thermal barrier coating (TBC) system and TBC-based system with a graded interlayer inserted between the metallic layer and the ceramic layer were, respectively, derived. Case studies showed that the edge delamination by thermal stress could be impeded by properly selecting the coating materials and individual layer thicknesses. These studies may provide some important insights for developing fail-safe designing methodologies for multilayered systems.     

Interaction of the single-particle and collective degrees of freedom in non-magic nuclei: The role of phonon tadpole terms

A method of consistent treatment of phonon contributions to the self-energy and gap terms in non-magic nuclei is developed in so-called g ² approximation, where g is the creation amplitude of a low-lying phonon. The method simultaneously takes into account both usual non-local and local phonon tadpole terms. Relations that allow the tadpoles to be calculated without introduction of new parameters are derived. As an application of the method, the effect of the phonon tadpoles on the single-particle strength distribution, single-particle energies and gap values is considered. Hypothesis of the surface nature of pairing correlations is discussed in the light of the tadpole effect.