A Student's Guide to Laplace Transforms

The Laplace transform is a useful mathematical tool encountered by students of physics, engineering, and applied mathematics, within a wide variety of important applications in mechanics, electronics, thermodynamics and more. However, students often struggle with the rationale behind these transforms, and the physical meaning of the transform results. Using the same approach that has proven highly popular in his other Student's Guides, Professor Fleisch addresses the topics that his students have found most troublesome; providing a detailed and accessible description of Laplace transforms and how they relate to Fourier and Z-transforms. Written in plain language and including numerous, fully worked examples. The book is accompanied by a website containing a rich set of freely available supporting materials, including interactive solutions for every problem in the text, and a series of podcasts in which the author explains the important concepts, equations, and graphs of every section of the book.

Discussion and Analysis of Dumbbell Defect-Ground-Structure (DB-DGS) Resonators for Sensing Applications from a Circuit Theory Perspective

Microstrip transmission lines loaded with dumbbell defect-ground-structure (DB-DGS) resonators transversally oriented have been exhaustively used in microwave circuits and sensors. Typically, these structures have been modelled by means of a parallel LC resonant tank series connected to the host line. However, the inductance and capacitance of such model do not have a physical meaning, since this model is inferred by transformation of a more realistic model, where the DB-DGS resonator, described by means of a resonant tank with inductance and capacitance related to the geometry of the DB-DGS, is magnetically coupled to the host line. From parameter extraction, the circuit parameters of both models are obtained by considering the DB-DGS covered with semi-infinite materials with different dielectric constant. The extracted parameters are coherent and reveal that the general assumption of considering the simple LC resonant tank series-connected to the line to describe the DB-DGS-loaded line is reasonable with some caution. The implications on the sensitivity, when the structure is devoted to operating as a permittivity sensor, are discussed.

1S0 Pairing Gaps, Chemical Potentials and Entrainment Matrix in Superfluid Neutron-Star Cores for the Brussels–Montreal Functionals

Temperature and velocity-dependent 1S0 pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron–proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree–Fock–Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for npeμ in beta-equilibrium using the Brussels–Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores.

The principle of materiality of space and the theory of fundamental fields

The work formulates the principle of materiality of space and on its basis a brief critical analysis of the general ideology of the Special and General Theories of Relativity is carried out. The connection of the new principle with the previously developed Topological Theory of Fundamental Fields (TTFF) is considered. A method of constructive implementation of the principle of materiality in the framework of the physical theory of fundamental fields is considered. General equations of the dynamics of markers of material points of physical space are derived and their physical meaning is established.

Method for critical current angular dependencies analysis of superconducting tapes

Various applications of superconducting materials require accounting of the critical current anisotropy relative to magnetic field direction - I c7(θ). However, today there is no sufficiently comprehensive model that takes into account the anisotropy, therefore the angular dependences are usually not analysed, but only described using various mathematical formulas. As a result, the fitting parameters have no physical meaning and it is difficult to correlate the picture with the features of the microstructure. In this paper, we propose a method for analysing the critical current angular dependences based on the anisotropic pinning model. The applicability of this model for conventional superconducting Nb-Ti tapes with one peak in the I c7(θ) dependence is shown. The possibility of extending this model to analyse the angular dependences of HTS materials is discussed.

Novel Modeling of Parameters Related to Intra-Firm Diffusion Innovation

In this paper, we present a novel intra-firm diffusion model to predict the variation of Penetration Level (PL) with the Intensity of Use (IU) and Speed of Adoption (SA) with respect to information and communication technologies (I.C.T) within Tunisian Small Medium Enterprises (SMEs). The study was motivated by the work of Youssef et al., (2014), and its inspired data scope/range. The method of modeling focuses on optimization and non-linear regression. The first model has the capacity to compute the variation of PL with IU. However, this first model was modified to a second model through transformation in order to derive physical meaning to the parameters. The modified second model shows a quasi-vertical curvature which approximates the reciprocal of hyperbolic tangent. The Variation of PL with the SA was computed using the second model which estimated the parameters with the variables explaining about 62% variation in PL with SA χ2=0.0655, R2=0.61651 . We further formulated a third model to predict correlation of SA with PL, while imposing boundary assumptions to avoid problems of divergence; with the final model having a PL as the only adjustable parameter. The model exhibited a plateau effect at points (0.9933,0.4373) and (0,0) between two steeply vertical asymptotes at -0.06105 and 1.0013, respectively. The developed model can be useful for eliciting information when data from different countries (or surveys) are compared for same or different span time through examining the behavior of the parameters, especially after Covid-19 era.

Study on Strategic Equilibria of Tobacco Industry Power Energy Markets in Post-epidemic Era

This paper aims to solve the strategic balance issues in tobacco industry energy markets in the post-epidemic era, based on the game theory, a strategic equilibrium model for power networks is proposed after evaluating users, power grid company in tobacco industry, and new power entities. By analyzing the claims and interests of relevant transaction subjects, an optimization computation model for tobacco industry power energy markets is constructed, meanwhile the flowchart of finding the Nash optimized solutions is also presented on basis of the genetic algorithm (GA), and the physical meaning of the Nash solutions are explained. The research results can provide some fundamental support and practical suggestions for the related aspects of the power energy markets, along with the economists who study the market design and prediction.