International Journal of Modern Physics B

The study of mechanical resonances can provide a plethora of information concerning the physical behavior of a system, both at the macroscopic and microscopic level. Resonant ultrasound spectroscopy (RUS), through advances in electronics and computational power, has evolved into the premier method for the precise study of mechanical resonances of solids. The range of applications is diverse, and as the popularity of RUS continues to increase, so will its spectrum of applications. This article contains an overview of the method, a short discussion of elastic constants, elastic moduli, and a survey of some successful RUS applications.

Nanostructured powder of Ni–Zn ferrite was directly produced by high-energy ball milling of stoichiometric mixture of ZnO, NiO, and Fe₂O₃ powders. X-ray powder diffractometry, scanning electron microscopy, annealing, treatment, and vibrating sample magnetometer were used to investigate the structural, chemical, and magnetic aspects of Ni_0.5Zn_0.5Fe₂O₄ compound. The crystallite size of final product after 60 h of ball milling time was estimated to be 17 nm. Heat treatment of ball-milled Ni–Zn ferrite was performed to study the thermal behavior of ferrite. The effect of copper doping on structure and magnetic properties of Ni–Zn ferrite was also studied. The results showed that the Zn replacement with Cu led to a decrease of magnetization.

Normal squeezing, variance and entropy squeezing factors based on the Heisenberg uncertainty principle and Shannon information entropy theory, respectively, derived from the entangled states of two-mode coherent states in two-photon processes are numerically investigated through a previously developed generalized nonlinear Jaynes–Cummings two-level spin model. Numerical simulations are performed and discussed for two two-photon model Hamiltonians in both resonant and off-resonant states of the spin system with the bimodal cavity field.

A modified adaptive control scheme for synchronization of an uncertain Lorenz hyperchaotic system is proposed. Based on the Lyapunov stability theory, the sufficient condition for the synchronization is analyzed and proved theoretically. With the condition derived, parameter identification and synchronization of the Lorenz hyperchaotic system with all the unknown system parameters can be achieved simultaneously. Numerical simulations are presented to illustrate the effectiveness of the proposed synchronization scheme.

We calculate the inelastic scattering lifetime of an excited quasiparticle at low (or zero) temperature, due to electron-electron interaction for a clean two-dimensional (2D) electron gas within the random-phase approximation (RPA) and compare it with the lifetime measured from the tunnelling experiment. Our result obtained by direct numerical calculation increases the electron relaxation rate considerably, hence decreases the size of discrepancy (roughly by a factor of 4) between theory and experiment which exists in the literature. We also show that including local-field factors in the effective electron interaction yields small correction to the result calculated within the RPA for r_s ~ 1, corresponding to electron density of the sample in the tunnelling experiment. This result suggests that the RPA is reasonably accurate for a 2D electron gas in weak coupling limit.

The resultant electric field gradient (EFG) produced at the nucleus of an atom in a solid can be measured using the perturbed γ – γ angular correlation (PAC) method that employs radioactive probe atoms. Several EFGs, associated with different types of defects trapped by the probe, are reported from the crystal silicon and germanium semiconductors. However, the nature of the field gradients is not fully understood because of the many factors contributing for its properties. The proximity of an impurity atom to the probe in the host matrix particularly played a significant role in the determination of the magnitude of the EFG. We discuss here the temperature and stress dependence of the crystal EFGs caused by impurity trapping as well as by the actions of uniaxial stress on semiconductor substrates.

High quality GaN layers doped with Mg were grown on Si(111) substrates using high temperature AlN as buffer layer by radio-frequency molecular beam epitaxy. From the Hall measurements, fairly uniform high hole concentration as high as (4–5) × 10²⁰cm^-3 throughout the GaN was achieved. The fabrication of the device is very simple. Nickel ohmic contacts and Schottky contacts using indium were fabricated on Mg-doped p-GaN films. The light emission has been obtained from these thin film electroluminescent devices. Thin film electroluminescent devices were operated under direct current bias. Schottky and ohmic contacts used as cathode and anode were employed in these investigations. Alternatively, two Schottky contacts could be probed as cathode and anode. Thin film electroluminescent devices were able to emit light. However, electrical and optical differences could be observed from the two different probing methods. The red light color could be observed when the potential between the electrodes was increased gradually under forward bias of 8 V at room temperature. Electrical properties of these thin film electroluminescent devices were characterized by current–voltage (I–V) system, the heights of barriers determined from the I–V measurements were found to be related to the electroluminescence.

Amorphous/nanocrystalline 50Ni–50Ti powders were synthesized from elemental Ti and Ni powders by solid state synthesis utilizing low energy mechanical alloying with times up to 100 h. The produced powders were investigated by X-ray diffraction and differential scanning calorimetry to study phase transformations that occurred during heating in the calorimeter. It was found that at the first stage of the heating process, a disordered NiTi phase was formed at temperature of about 400°C. Further investigations indicated that this phase transformed into the Ni₃Ti and Ti₂Ni intermetallic compounds after heating at a temperature of about 800°C.

The present paper is a review of the phenomena related to nonequilibrium electron relaxation in bulk and nano-scale metallic samples. The workable Two-Temperature Model (TTM) based on Boltzmann–Bloch–Peierls kinetic equation has been applied to study the ultra-fast (femto-second) electronic relaxation in various metallic systems. The advent of new ultra-fast (femto-second) laser technology and pump-probe spectroscopy has produced wealth of new results for micro- and nano-scale electronic technology. The aim of this paper is to clarify the TTM, conditions of its validity and nonvalidity, its modifications for nano-systems, to sum-up the progress, and to point out open problems in this field. We also give a phenomenological integro-differential equation for the kinetics of nondegenerate electrons that goes beyond the TTM.

Employing the Bethe–Salpeter equation (BSE) and the Matsubara recipe, and invoking both the electron–electron and the hole–hole scattering channels, we establish that the binding energy (W) of a Cooper pair (CP) is real, and equals the BCS energy gap (Δ) for all T ≤ T_c for a one-component superconductor. Given that the BCS theory is a generalization of the Hartree–Fock theory (generalized to allow for particle number fluctuations), the cognescenti would expect this result as a direct consequence of Koopman's theorem, proved for and well-known in the latter theory. However, this theorem is seldom mentioned in the literature on superconductivity; on the contrary, there is the statement in well-known texts that the binding energy of a CP becomes imaginary when the above-stated scattering channels are invoked for their formation. The importance of |W| = |Δ| for high-T_c superconductors is brought out by replacing the one-particle propagator in the BSE by a superpropagator — a field-theoretic construct apt for dealing with composite superconductors (CSs). A set of generalized BCS equations is thus obtained which, with the input of the multiple gaps of a CS, enables one to calculate its T_c uniquely. Applications of these equations will be taken up in a subsequent paper.

Several integrable properties of the Sine-Laplace equation arising from an inviscid incompressible fluid are symbolically presented, including the Lax pair, auto-Bäcklund transformation, nonlinear superposition formula, bilinear form, and static N-soliton solution. Furthermore, with symbolic computation, two similarity reductions for the Sine-Laplace equation are derived by virtue of the classical Lie group method of infinitesimal transformations. One reduces to the third Painlevé equation and the other to a known ordinary differential equation. Sample static solutions are discussed and pictured.

We have used some of the most reliable high pressure equations of state (EOS) to determine the thermoelastic Grüneisen parameter and its higher order volume derivatives for the lower mantle, outer core and inner core of the Earth. The cross derivatives of bulk modulus with respect to pressure and temperature have also been obtained for the deep interior of the Earth using the results based on the modified free volume theory for the Grüneisen parameter. We have used five EOS viz. (a) modified Rydberg EOS, (b) modified Poirier–Tarantola EOS, (c) Hama–Suito EOS, (d) Stacey EOS, and (e) Kushwah EOS to determine pressure derivatives of bulk modulus. The results for thermoelastic parameters obtained in the present study show systematic variations with the increase in pressure.

We study the phenomenon of spatial coherence resonance (SCR) on Hodgkin–Huxley (HH) neuronal networks that are characterized with information transmission delay. In particular, we examine the ability of additive Gaussian noise to optimally extract a particular spatial frequency of excitatory waves in diffusive and small-world networks on which information transmission amongst directly connected neurons is not instantaneous. On diffusively coupled HH networks, we find that for short delay lengths, there always exists an intermediate noise level by which the noise-induced spatial dynamics is maximally ordered, hence implying the possibility of SCR in the system. Importantly thereby, the noise level warranting optimally ordered excitatory waves increases linearly with the increasing delay time, suggesting that extremely long delays might nevertheless preclude the observation of SCR on diffusive networks. Moreover, we find that the small-world topology introduces another obstacle for the emergence of ordered spatial dynamics out of noise because the magnitude of SCR fades progressively as the fraction of rewired links increases, hence evidencing decoherence of noise-induced spatial dynamics on delayed small-world HH networks. Presented results thus provide insights that could facilitate the understanding of the joint impact of noise and information transmission delay on realistic neuronal networks.