Theoretical Evaluation of Electrical Resistivity with Bloch-Gruneisen Function

This is the second of two volumes dealing with research problems concerned with the structural integrity of power plant condensers and related equipment. The development of a method for evaluating the effective bending properties of tubesheets accounting for the varied tube layouts found in large condenser structures is described. A simple analytical formula is developed which permits evaluation of the important effective bending stiffness parameter for arbitrary tube patterns. Results are presented of a research investigation undertaken to aid in the development of simple design codes for general heat exchanger tubesheets. A complete design method is developed for U-tube heat exchanger tubesheets which permits evaluation of significant stress values from a set of design curves and simple formulas. The results are applicable for arbitrary materials in tubesheet, shell, head, and tubes, and are also valid for arbitrary thicknesses and radii. The design method is compared with a very simple formula in the TEMA codes. A simple analytical formula for predicting the limit static loading on condenser hotwell floors is developed. The results are compared with an empirical design formula in the HEI Condenser Construction Standards. The evaluation of tubesheet stresses and maximum tube loads in a complex water box-tubesheet configuration is discussed. This is an initial attempt to develop a simplified method, based on beam theory, which will enable results to be obtained by a detailed analysis of representative tubesheet strips. The effect of the water box interaction is proposed to be reducible to the determination of an edge fixity factor which is included in the tubesheet beam strip analysis. The analytical model is developed, discussed, and evaluated for a representative unit. The edge fixity factor distribution evolves from a study using the finite element method.

An analytic formula is derived for the loss cone in toroidal helical systems. Particular emphasis is put on the loss region for the particles that are barely trapped in the helical ripples. Effects of the radial electric field and shifts of the magnetic axis are discussed. Comparison with the numerical calculation confirms that the simple analytic formula gives good approximations.

Application of the backward extrapolation method to pulsed neutron sources

Optimal design of a multimode interference (MMI) coupler for broadening the spectral response of an arrayed-waveguide grating (AWG) demultiplexer is considered. By using a Gaussian beam approximation, an analytical expression for the spectral response of an AWG demultiplexer (with an MMI section) is obtained. A simple analytical formula is derived to relate the optimal MMI length to the separation between the peaks of the twofold images in the MMI region. This peak separation is related to the width of the MMI section. In the proposed design method, a required 1-dB passband width determines the peak separation, which then determines the optimal value for the length of the MMI section according to the analytical formula. The designed flat-top AWG demultiplexer is verified by the beam propagation method.

Temperature-related effective properties and exact relations for thermo-magneto-electro-elastic fibrous composites

Compact high-resolution X-ray spectrometers with a one-dimensional temperature gradient at the analyzer crystal are considered. This gradient, combined with the use of a position-sensitive detector, makes it possible to relax the usual Rowland-circle condition, allowing increased space at the sample position for a given energy resolution or arm radius. Thus, for example, it is estimated that approximately meV resolution is possible with a 3 m analyzer arm and 200 mm clearance between the sample and detector. Simple analytic formulae are provided, supported by excellent agreement with ray-tracing simulations. One variation of this method also allows the detector position sensitivity to be used to determine momentum transfer, effectively improving momentum resolution without reducing (slitting down) the analyzer size. Application to medium-resolution ( approximately 10-100 meV) inelastic X-ray scattering spectrometers with large angular acceptance is discussed, where this method also allows increased space at the sample. In some cases the application of a temperature gradient can improve the energy resolution even with a single-element detector.

Dilute Bose gas with attractive interactions is considered at zero temperature, when practically all atoms are in Bose-Einstein condensate. The problem is addressed aiming at answering the question: What is the optimal trap shape allowing for the condensation of the maximal number of atoms with negative scattering lengths? Simple and accurate analytical formulas are derived allowing for an easy analysis of the optimal trap shapes. These analytical formulas are the main result of the paper.

We compute thermodynamical properties of a low-density hydrogen gas within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential. Our calculations are done using the exact scaled low-temperature (SLT) expansion, which provides a rigorous extension of the well-known virial expansion-valid in the fully ionized phase-into the Saha regime where the system is partially or fully recombined into hydrogen atoms. After recalling the SLT expansion of the pressure [A. Alastuey et al., J. Stat. Phys. 130, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to order exp(-|E_{H}|/kT) included (E_{H}≃-13.6 eV). Those truncated expansions describe the first five nonideal corrections to the ideal Saha law. They account exactly, up to the considered order, for all effects of interactions and thermal excitations, including the formation of bound states (atom H, ions H^{-} and H_{2}^{+}, molecule H_{2},⋯) and atom-charge and atom-atom interactions. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve well-defined internal partition functions for the molecule H_{2} and ions H^{-} and H_{2}^{+}, for which no closed-form analytical formula exist currently. We provide accurate low-temperature approximations for those partition functions by using known values of rotational and vibrational energies. We compare then the predictions of the SLT expansion, for the pressure and the internal energy, with, on the one hand, the equation-of-state tables obtained within the opacity program at Livermore (OPAL) and, on the other hand, data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulas reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities (ρ∼10^{-2} g/cm^{3}), some discrepancies among the SLT, OPAL, and PIMC results are observed.

A numerical investigation into the ultrasound-induced collapse of air bubbles near soft materials, utilizing a novel multi-material diffuse interface method (DIM) model with block-structured adaptive mesh refinement is presented. The present work expands from a previous five-equation DIM by incorporating Eulerian hyperelasticity. The model is applicable to any arbitrary number of interacting fluid and solid material. A single conservation law for the elastic stretch tensor enables tracking the deformations for all the solid materials. A series of benchmark cases are conducted, and the solution is found to be in excellent agreement against theoretical data. Subsequently, the ultrasound-induced bubble-tissue flow interactions are examined. The bubble radius was found to play a crucial role in dictating the stresses experienced by the tissue, underscoring its significance in medical applications. The results reveal that soft tissues primarily experience tensile forces during these interactions, suggesting potential tensile-driven injuries that may occur in relevant treatments. Moreover, regions of maximal tensile forces align with tissue elongation areas. It is documented that while early bubble dynamics remain relatively unaffected by changes in shear modulus, at later stages of the penetration processes and the deformation shapes, exhibit notable variations. Lastly, it is demonstrated that decreasing standoff distances enhances the interaction between bubbles and tissue, thereby increasing the stress levels in the tissue, although the behavior of the bubble dynamics remains largely unchanged.

Dynamics of domain walls governed by the convective Cahn–Hilliard equation

Cold-formed lipped channel columns (CFLCCs) have been widely used in light gauge steel constructions. The distortional buckling is one of the important buckling modes for CFLCCs and the distortional buckling critical load depends significantly on the rotational restrain stiffness generated by the web to the lipped flange. First, a simplified explicit expression for the rotational restraint stiffness of the lipped flange has been derived. Using the expression, the characteristics of the rotational restraint stiffness of the lipped flange have been investigated. The results show that there is a linear coupling relationship between the applied forces and the rotational restraint stiffness of the lipped flange. Based on the explicit expression of the rotational restraint stiffness of the lipped flange, a simplified analytical formula has been derived which can determine the elastic distortional buckling critical stress of the CFLCCs subjected to axial compression. The simplified analytical formula developed in this study has been shown to be accurate through the comparisons with results from the distortional buckling analyses using the ANSYS finite element software. The developed analytical formula is easy to apply, and can be used directly in practical design and incorporated into future design codes and guidelines.

A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature β. For 2×2 matrices with Gaussian distribution we analytically compute the nearest-neighbor spacing distribution of complex eigenvalues in radial distance. Because it does not provide such a good approximation as the Wigner surmise in 1D, we introduce an effective β_{eff}(β) in our analytic formula that describes the spacing obtained numerically from the 2D Coulomb gas well for small values of β. It reproduces the 2D Poisson distribution at β=0 exactly, that is valid for a large particle number. The surmise is used to fit data in two examples, from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles of non-Hermitian random matrices, that are only known numerically, are very well fitted by noninteger values β=1.4 and β=2.6 from a 2D Coulomb gas, respectively. These two ensembles have been suggested as the only two symmetry classes, where the 2D bulk statistics is different from the Ginibre ensemble.

Electromagnetic (EM) fields at radio frequencies (RF) cannot penetrate deep into media with high conductivity such as sea water, wet soil, etc. However, moving to the ultralow frequency (ULF) range (300 Hz-3 kHz) allows a considerable range of communication due to the decreased medium loss at low frequencies and a possibility to use the penetrating near field. Magnetically coupled coils are commonly used for near-field magneto-inductive (MI) communication. Alternatively, it is possible to create ULF magnetic fields of sufficient amplitude by rotating permanent magnets. In this work, a ULF magnetic field generator has been created using a rotating permanent magnet. It has been shown that the proposed field generator outperforms a conventional coil source (23 dB of field strength for the same volume and dissipated power that is 0.35 W), which can be a considerable advantage for low size, weight, and power applications. A method to produce amplitude shift keying (ASK) modulation signals using a modulation coil was proposed and analyzed. It was demonstrated that the inductance of the modulation coil is not critical for achieving acceptable modulation ratios, which opens a possibility for a compact ASK generator design. A simple circuit model and analytical formula for modulation efficiency of the generator were proposed and validated by measurement.

We have derived simplified analytic expressions for various magneto-optical Kerr effects of an optically thick medium having an arbitrary magnetization direction. We have found that the simplified formulae for the Kerr effects of p and s waves consisted of a product of two factors: the prefactor dependent pure optical parameters of the system and the main factor of the polar Kerr effect for a normal incidence case. The measured magneto-optic polar Kerr rotation angles of Co/Pd multilayers and the longitudinal Kerr rotation angles of Cu/Co multilayers with varying incident angles could be well fitted using the simplified analytical formulae.

Plume rise in different atmospheres: a practical scheme and some comparisons with lidar measurements