We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength.

Acoustic wave propagation in bovine cancellous bone is experimentally and theoretically investigated in the frequency range of 0.5-1 MHz. The phase velocity, attenuation coefficient, and broadband ultrasonic attenuation (BUA) of bovine cancellous bone are measured as functions of frequency and porosity. For theoretical estimation, the Modified Biot-Attenborough (MBA) model is employed with three new phenomenological parameters: the boundary condition, phase velocity, and impedance parameters. The MBA model is based on the idealization of cancellous bone as a nonrigid porous medium with circular cylindrical pores oriented normal to the surface. It is experimentally observed that the phase velocity is approximately nondispersive and the attenuation coefficient linearly increases with frequency. The MBA model predicts a slightly negative dispersion of phase velocity linearly with frequency and the nonlinear relationships of attenuation and BUA with porosity. The experimental results are in good agreement with the theoretical results estimated with the MBA model. It is expected that the MBA model can be usefully employed in the field of clinical bone assessment for the diagnosis of osteoporosis.

Thermoacoustic theory is extended to stacks made of random bulk media. Characteristics of the porous stack such as the tortuosity and dynamic shape factors are introduced into the thermoacoustic wave equation in the low reduced frequency approximation. Basic thermoacoustic equations for a bulk porous medium are formulated analogously to the equations for a single pore. Use of different dynamic shape factors for the viscous and thermal effects is adopted and scaling using the dynamic shape factors and tortuosity is demonstrated. Comparisons of the calculated and experimentally derived thermoacoustic properties of reticulated vitreous carbon and aluminum foam show good agreement. A consistent mathematical model of sound propagation in a random porous medium with an imposed temperature is developed. This treatment leads to an expression for the coefficient of the temperature gradient in terms of scaled cylindrical thermoviscous functions.

An experimental and theoretical investigation of sound propagation in a porous sample composed of capillary tubes with rectangular cross sections is described in this paper. An experimental technique valid for low flow resistivity and high porosity porous samples was developed to measure the attenuation and phase velocity in the porous material. This technique uses transmission of a short pulse in a large tube through the porous sample and subsequent frequency domain analysis in the range 200-1300 Hz. Good agreement was obtained if an anomalous tortuosity factor of 1.1 is used in the theory. A scaling factor for relating cylindrical and square tube capillary theories, known as the dynamic shape factor, was investigated. Propagation constants computed from use of a near unity dynamic shape factor in the cylindrical pore theory agree favorably with calculations based on the square pore theory for the frequencies and pore radii used in the experiment.

The Maritime Security Laboratory (MSL) at Stevens Institute of Technology supports research in a range of areas relevant to harbor security, including passive acoustic detection of underwater threats. The difficulties in using passive detection in an urban estuarine environment include intensive and highly irregular ambient noise and the complexity of sound propagation in shallow water. MSL conducted a set of tests in the Hudson River near Manhattan in order to measure the main parameters defining the detection distance of a threat: source level of a scuba diver, transmission loss of acoustic signals, and ambient noise. The source level of the diver was measured by comparing the diver's sound with a reference signal from a calibrated emitter placed on his path. Transmission loss was measured by comparing noise levels of passing ships at various points along their routes, where their distance from the hydrophone was calculated with the help of cameras and custom software. The ambient noise in the Hudson River was recorded under varying environmental conditions and amounts of water traffic. The passive sonar equation was then applied to estimate the range of detection. Estimations were done for a subset of the recorded noise levels, and we demonstrated how variations in the noise level, attenuation, and the diver's source level influence the effective range of detection. Finally, we provided analytic estimates of how an array improves upon the detection distance calculated by a single hydrophone.

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Correlations between acoustic properties and bone density were investigated in the 12 defatted bovine cancellous bone specimens in vitro. Speed of sound (SOS) and broadband ultrasonic attenuation (BUA) were measured in three different frequency bandwidths from 0.5 to 2 MHz using three matched pairs of transducers with the center frequencies of 1, 2.25, and 3.5 MHz. The relative orientation between ultrasonic beam and bone specimen was the mediolateral (ML) direction of the bovine tibia. SOS shows significant linear positive correlation with apparent density for all three pairs of transducers. However, BUA shows relatively weak correlation with apparent density. SOS and BUA are only weakly correlated with each other. The linear combination of SOS and BUA in a multiple regression model leads to a significant improvement in predicting apparent density. The correlations among SOS, BUA, and bone density can be effectively and clearly represented in the three-dimensional space by the multiple regression model. These results suggest that the frequency range up to 1.5 MHz and the multiple regression model in the three-dimensional space can be useful in the osteoporosis diagnosis.

An electrochemical reaction as a branch of chemical reactions is one of the fundamental phenomena, but exact electrochemical reaction mechanisms have been unknown. We here propose a statistical thermodynamic theory for electrochemical reactions, which is vital to investigate electrochemical reactions for non-equilibrium, quasi-equilibrium, and equilibrium. The theory utilizes a postulate that electric potential, time, and space are independent and orthogonal variables in extended phase spaces. It is an internal Gibbs energy transport theory for electrochemical reactions leading to the unification of non-equilibrium and equilibrium reactions, a non-equilibrium generalization beyond quasi-equilibrium theories for migration and diffusion, and the integration of diffusion and convection mechanisms. It predicts that there are current density gaps and broken discrete symmetries at the activation potential, time, and displacement. It provides the Nernst equation, the rate equation, and the spatial cross section of electrochemical reactions. The electrochemical theory demonstrates relationships among electrochemical reactions, thermodynamics, and statistical physics.