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A Slinky is a loose helical coil spring and is a well-known educational toy. In this paper a model for a Slinky is presented. The Slinky is represented as a sequence of rigid half coils connected by torsional springs. A range of Slinky configurations in static equilibrium are calculated. Where possible the torsion spring model is compared with the much simpler point mass model of a Slinky, and a more sophisticated model that includes axial and shear deformation. The torsional spring model is shown for the most part to produce similar qualitative behaviour as the more complex model. The simplicity of the torsional spring model makes it a candidate for a discrete stair walking dynamic model of a Slinky, The point mass model is straightforward to derive and solve and makes it possible for an undergraduate engineering student in the early part of their degree course to understand. The torsional spring model is a useful tool for showing what can be done in a more advanced mechanics course to model a system that most students would have previous experience of. [ABSTRACT FROM AUTHOR]

Non-zonal methods of hybrid Reynolds Averaged Navier–Stokes (RANS) equations-Large Eddy Simulation (LES) with subfilter transport equations enable to simulate turbulent flows out of spectral equilibrium on relatively coarse grid resolution. They can operate from RANS to LES depending on a control parameter linked to the grid step size. Variational analysis gives a useful framework to specify the functional dependence of this parameter to the grid size. This is the case for the partially integrated transport modelling method originally established in spectral space for homogeneous turbulence. The partitioning control function then monitors the ratio of the subfilter part to the total turbulent energy and the same process is developed in the present work for the thermal or transported scalar variance as well. So, we demonstrate here that this control function mechanism can be derived by variational calculus from a mathematical physics formalism developed both for first-order and second-order moment closures. We show that the result is entirely consistent with the spectral model derivation made in previous papers and that this approach can be transposed to almost any subfilter transport model developed in hybrid RANS-LES methodology in full generality. As a result, it will be evidenced also that resolved turbulent diffusion terms play a significant role in the acting mechanisms of turbulence and cannot be therefore neglected, even if these terms do not explicitly appear in LES subfilter closure because they are computed by the simulation itself and not modelled by the subfilter model. In addition, numerical simulations have been performed for illustrating the theoretical results of the variational analysis. [ABSTRACT FROM AUTHOR]

The Nuclear Physics Institute (NPI) in the Czech Republic is a prominent research institution specializing in nuclear physics and related fields. With a staff of around 260, it is one of the largest institutions of its kind in the country. The NPI operates several accelerators, including the Isochronous Cyclotron U-120M, TR-24 Cyclotron, Tandetron, Microtron MT25, and Multi-Isotope Low-Energy Accelerator (MILEA), which are used for various purposes such as nuclear data measurement and accelerator mass spectrometry. The institute also conducts research in neutron physics and operates fast neutron generators. It collaborates internationally and offers research facilities like CANAM and LVR-15 vertical channels for bulk investigations and neutron activation analysis. The NPI is involved in large collaborations focused on nuclear matter and neutrino mass measurement, among other areas. Additionally, it conducts research in radiopharmaceuticals, radiation dosimetry, and theoretical physics. However, the institute may face challenges in the future due to funding limitations and the need to attract young scientists and technicians. [Extracted from the article]

We present the theoretical argument that the use of mathematics in physics can be productively conceptualized as using a language and that learning to make sense of physics equations and appropriating them into novel scientific inquiry can be understood as a process of learning to read fluently with a high level of reading comprehension and to express one's thoughts in writing. The data are drawn from a longitudinal ethnographic account of a high school student's year-long research apprenticeship, in which a significant part of the work required the derivation and interpretation of an advanced physics equation (the phase velocity of waves in liquids). The analysis examines in different timescales the extended learning process as a complex activity system. The findings illustrate empirically how this type of learning can be productively analyzed by researchers and instructionally implemented by teachers or mentors as engagement in practices, a perspective that complements more standard cognitivist accounts of mathematical sensemaking. We highlight productive pedagogical and discursive instructional moves that facilitated this process and explicitly connect them to the learning they induced in terms of change in the student's participation. While constrained by the scope of this case study, the concrete, microanalytic account of the learning process concretizes some of what physicists do with equations and suggests pathways to teaching students to meaningfully participate in this practice. [ABSTRACT FROM AUTHOR]

The study discussed in this article is driven by the realization that many physical processes may be understood by using applications of fractional operators and special functions. In this study, we present and examine a fractional integral operator with an I-function in its kernel. This operator is used to solve several fractional differential equations (FDEs). FDE has a set of particular cases whose solutions represent different physical phenomena. Many mathematical physics, biology, engineering, and chemistry problems are identified and solved using FDE. Specifically, a few exciting relations involving the new fractional operator with incomplete I-function (IIF) in its kernel and classical Riemann Liouville fractional integral and derivative operators, the Hilfer fractional derivative operator, and the generalized composite fractional derivate (GCFD) operator are established. The discovery and investigation of several important exceptional cases follow this. [ABSTRACT FROM AUTHOR]

Retention of quality attributes during drying of fruit and vegetables is a prime concern since the product's acceptability depends on the overall quality; particularly on the nutritional, color, and physical attributes. However, these quality parameters deteriorate during drying. Food quality changes are strongly related to the drying conditions and researchers have attempted to develop mathematical models to understand these relationships. A better insight toward the degradation of quality attributes is crucial for making real predictions and minimizing the quality deterioration. The previous empirical quality models employed kinetic modeling approaches to describe the quality changes and therefore, lack the realistic understanding of fundamental transport mechanisms. In order to develop a physics based mathematical model for the prediction of quality changes during drying, an in-depth understanding of research progress made toward this direction is indispensable. Therefore, the main goal of this paper is to present a critical review of the mathematical models developed and applied to describe the degradation kinetics of nutritional, color, and texture attributes during drying of fruit and vegetables and microbial growth model during storage. This review also presents the advantages and drawbacks of the existing models along with their industrial relevance. Finally, future research propositions toward developing physics-based mathematical model are presented. [ABSTRACT FROM AUTHOR]

A double Poisson bracket, in the sense of M. Van den Bergh, is an operation on an associative algebra A which induces a Poisson bracket on each representation space Rep (A , n) in an explicit way. In this note, we study the impact of changing the Leibniz rules underlying a double bracket. This change amounts to make a suitable choice of A-bimodule structure on A ⊗ A . In the most important cases, we describe how the choice of A-bimodule structure fixes an analogue to Jacobi identity, and we obtain induced Poisson brackets on representation spaces. The present theory also encodes a formalization of the widespread tensor notation used to write Poisson brackets of matrices in mathematical physics. Communicated by P. Kolesnikov [ABSTRACT FROM AUTHOR]

Gottfried Münzenberg, a prominent scientist in the field of nuclear physics, passed away in January 2024. He played a significant role in shaping the scientific and instrumental portfolio of the Society for Heavy Ion Research (GSI) in Germany. Münzenberg made important contributions to various areas of nuclear physics, including the discovery of new chemical elements and the development of in-beam positron emission tomography. He was also involved in international collaborations and received numerous awards and honors for his work. Münzenberg is remembered not only for his scientific achievements but also for his wit and friendship. [Extracted from the article]

3 J. G. Bednorz, and K. A. Müller, Possible high T c superconductivity in the Ba - La - Cu - O system, Z Physik B - Condens. In late 1983, Müller, alongside his colleague J. Georg Bednorz, initiated a new project to search for superconductivity in oxides. Alex Müller (1984), from I Ferroelectrics i B 89 b , iv (1989) [[1]] With great sadness, the international ferroelectrics community mourns the loss of Professor Karl Alexander Müller, who passed away in Zurich, Switzerland, on January 9, 2023, at the age of 95. [Extracted from the article]

In mathematical physics and beyond, one encounters many beautiful inequalities that relate geometric or physical quantities describing the shape or size of a set. Such isoperimetric inequalities often have a long history and many important applications. For instance, the eponymous and most classical of all isoperimetric inequalities was known already in antiquity. It asserts that among all closed planar curves of a given length, the circles with perimeter equal to that length, and only they, enclose the largest area. Though not nearly as well-known, an isoperimetric inequality conjectured by Saint-Venant in the 1850s and first proved by Pólya almost a century later, is also very beautiful and important. By presenting a short proof as well as two simple physical interpretations, this article illustrates why the result deserves to be cherished by every student of applied analysis. [ABSTRACT FROM AUTHOR]

An alternative method for obtaining analytical solutions of the time-independent Schrödinger equation (TISE) is developed and applied to 1-dimensional model quantum systems of interest in atomic and molecular physics. The method is based on proposing a wave function that is a product of two functions, one of them an integrating factor. The differential equation resulting from operating the TISE on the product wave function is compared with a differential equation with a known solution. This comparison produces a system of differential equations for the integrating factor. This system of equations is easily solved for model quantum systems such as the harmonic oscillator, the hydrogen atom and the Morse oscillator. The method presented simplifies some approaches shown in textbooks, based on asymptotic analyses of the TISE, and power series methods with recurrence relations. In addition, the method presented here facilitates the understanding of the relationship between the ordinary differential equations of the mathematical physics and the TISE of physical models as the harmonic oscillator, the Hydrogen atom, and the Morse oscillator. [ABSTRACT FROM AUTHOR]

In 1811, Legendre published an identity between integrals involving the constant k : = sin ⁡ π 12 that inspired Abel to create his brilliant theory of complex multiplication. Then k reappeared as the eccentricity of an ellipse whose arclength Ramanujan computed explicitly in terms of gamma functions with rational arguments. Finally, the constant appeared as a consequence of the three-body choreography along Bernoulli's lemniscate. We develop these results in detail as well as mentioning random walks on a cubic lattice and the renormalization of the period of the simple pendulum. All this shows the wonderful unity underlying seemingly different branches of mathematics and physics. [ABSTRACT FROM AUTHOR]

In this paper we present the analytical calculations to derive the magnetic field of a solenoid by solving exactly a fractional integral with the use of a novel method. Starting from the Biot-Savart law, we consider a coil of negligible thickness with a stationary electric current. We derive the expressions of the on- and off-axes magnetic field components. The results have been compared to some simplified and known analytical formulae as well as to a commercial numerical code showing a good agreement. [ABSTRACT FROM AUTHOR]

The solitary wave naturally arises in many areas of mathematical physics, including in nonlinear optics, plasma physics, quantum field theory, and fluid mechanics. In the past few years, for an advanced nuclear energy system, a particular class of traveling wave reactor called the Constant Axial shape of Neutron flux, nuclide number densities and power shape During Life of Energy production (CANDLE) reactor has been proposed, and an analytical solution has been desired since it could reveal the global characters of the solution. In this study, from the perspective of the solitary wave, the analytical solution of this advanced nuclear energy system is demonstrated through coupling the one-group neutron diffusion equation with the burnup equation. The tanh-function method is applied to solve that nonlinear partial differential equation. The relationship between the velocity of the solitary wave, wave amplitude, or neutron flux and the evolution of the nuclide is revealed by the analytical method. The results demonstrate that the neutron flux is proportional to the wave velocity. The results also imply that the amplitude of the neutron flux is proportional to the square root of the diffusion coefficient but is inversely proportional to the initial 238U density. [ABSTRACT FROM AUTHOR]

The International Mathematical Congress of 1924 will be held in Toronto, Canada, marking the first time the Congress is held on the American continent. The Congress will focus on the practical applications of mathematics, particularly in engineering, and contributions have been invited from mathematical physicists and engineers. The proceedings of the Congress will be printed to provide a comprehensive account of the pure and applied mathematical sciences. Seventy scientific institutions in the Americas and ninety in Europe and elsewhere will send delegates to the Congress, which will be divided into sections covering various mathematical disciplines. [Extracted from the article]

The contact zone between algorithms and creative writing has become an increasingly fertile ground for literary experimentation in the last decades, with more accessible digital technologies broadening the scope of potential artistic productions and allowing the exploration of new forms of creativity. Inspired by the playful collaboration between arts and sciences embodied by the experimental creations of the French literary group OuLiPo, we borrow from physics and mathematics the concept of self-avoiding random walk to create original poems. This model is adapted here to generate random poems through potentially infinite combinations of a finite set of verses distributed on a virtual two-dimensional grid. The highly versatile algorithm we designed allows to randomly generate unexpected poems and provide, for each, a unique path with the graphical representation of a random walk. [ABSTRACT FROM AUTHOR]

This paper concerns the reflection of harmonic functions, w (x , y) , defined in a neighborhood of a real-analytic curve in the plane subject to the Robin condition, a w + b ∂ n w = φ w , on that curve. Here a and b are constants, and φ w is the restriction of a holomorphic function onto the curve. For the case, when φ w = 0 , while a and b are real-analytic functions, a reflection formula was derived in Belinskiy and Savina [The Schwarz reflection principle for harmonic functions in R 2 subject to the Robin condition. J Math Anal Appl. 2008;348:685–691], using the reflected fundamental solution method. Here, we construct a Robin-to-Neumann mapping and use it for obtaining the reflection operator. Since the two formulae look different, we show their equivalence when a and b are constants and φ w = 0. As examples, we show reflection formulae for non-homogeneous Neumann and Robin conditions on the common within mathematical physics curves, such as circles and lines. [ABSTRACT FROM AUTHOR]

In a reference letter for Feyerabend's application to UC Berkeley, Carl Hempel writes that 'Mr. Feyerabend combines a forceful and penetrating analytic mind with a remarkably thorough training and high competence in theoretical physics and mathematics' (Collodel and Oberheim, [2], 80). The hope is to better understand Feyerabend's philosophy of physics, its historical impact and reception, and discern what fruits Feyerabend's philosophy of physics may still bear. Del Santo shows how Feyerabend's growing "resentment" toward his authoritarian father-figure and Popper's growing frustration with Feyerabend centred on disagreements concerning quantum mechanics: how to interpret it, how to criticize it, and how to teach it. [Extracted from the article]

The ALTO research platform gathers two accelerators that are unique in France: a 15 MV Tandem-type electrostatic accelerator for stable beams from proton to aggregates, and an electron linear accelerator for the production of radioactive beams by photofission. IJCLab should host an Energy Recovery Linac accelerator demonstrator as part of the European particle physics roadmap, providing an intense 250 MeV (upgradable to 500 MeV) electron beam. The Laboratoire de Physique des 2 Infinis Irène Joliot-Curie [Laboratory of the Physics of the Two Infinities Irène Joliot-Curie; IJCLab) was created on 1 January 2020. Accelerator Physics IJCLab is currently playing a major role in the field of particle accelerators, as it involves teams from two former laboratories (LAL and IPN) that have been developing a unique expertise on accelerators for about 30 years. [Extracted from the article]

In this article we shall derive functional limit theorems for the multi-dimensional elephant random walk (MERW) and thus extend the results provided for the one-dimensional marginal by Bercu and Laulin. The MERW is a non-Markovian discrete-time random walk on Z d which has a complete memory of its whole past, in allusion to the traditional saying that an elephant never forgets. As the name suggests, the MERW is a d-dimensional generalization of the elephant random walk (ERW), the latter was first introduced by Schütz and Trimper in 2004. We measure the influence of the elephant's memory by a so-called memory parameter p between zero and one. A striking feature that has been observed in Schütz and Trimper is that the long-time behavior of the ERW exhibits a phase transition at some critical memory parameter pc. We investigate the asymptotic behavior of the MERW in all memory regimes by exploiting a connection between the MERW and Pólya urns, following similar ideas as in the work by Baur and Bertoin for the ERW. [ABSTRACT FROM AUTHOR]

Who's Who in Mineral Names: Marie Sklodowska-Curie (1867-1934) Most references list curite as a namesake mineral for both Pierre and Marie Curie; however, it appears to have been named only after Pierre Curie (Schoep [10]). Nominally three minerals were named after French-Polish physicist Marie Sklodowska-Curie: curite, sklodowskite, and cuprosklodowskite. [Extracted from the article]

In this paper, the conformable sub-equation method is proposed to construct exact solutions of the space-time resonant nonlinear Schrödinger equation (R-NLSE). Conformable derivatives are described by Atangana's-conformable derivative. Some soliton solutions are constructed under some constraint conditions. The solutions obtained confirm that the conformable sub-equation method is a powerful an efficient technique for analytic treatment of a wide variety of nonlinear conformable partial differential equations in mathematical physics. [ABSTRACT FROM AUTHOR]

Investigation is conducted on a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics and plasma physics. By virtue of the homoclinic-test, ansatz and polynomial-expansion methods, we construct the breather and lump solutions, shock wave solutions and travelling-wave solutions, respectively. We observe that the breather propagates steadily along a straight line with certain angles with the x, y and z axes. We observe that the amplitude and shape of the bright-dark lump wave keep unchanged during the propagation. We observe that the amplitude and the shape of the shock wave keep unchanged during the propagation. We graphically analyse the effects of the coefficients in the equation on the breather, lump and shock waves. We find that the lump is the most stable while the shock wave is the least stable under the same perturbation among the breather, lump and shock waves. [ABSTRACT FROM AUTHOR]

To integrate traditional classical mechanics topics into a broader view, that some authors associate to drawing from I the theory of complex systems i [[13]], would be a great contribution to new generations of physics students. The new book constitutes a new modern approach to teaching mechanics, in particular under the context of facing classical mechanics versus quantum mechanics, and showing connections to quantum mechanics, classical field theory, gravitation and current ideas on astrophysics. And finally, how classical mechanics is related to modern physics, especially quantum mechanics and general relativity. A modern approach to teaching classical mechanics: A review of Modern classical mechanics by T. M. Helliwell and V. V. Sahakian, Cambridge, Cambridge University Press, 2020, 704 pp., £56.00, (hardback), ISBN 978-1-10-883497-1. [Extracted from the article]

In this paper, the inverse scattering transform of a two-component modified Korteweg–de Vries equation is under investigation, which is one of the important nonlinear models in mathematics and physics. The spectral analysis with a 4 × 4 Lax pair is performed for the two-component modified Korteweg–de Vries equation, from which a Riemann Hilbert problem is strictly formulated. Moreover, multi-soliton solutions to the two-component modified Korteweg–de Vries equation are obtained through a particular Riemann–Hilbert formulation. Finally, some figures are presented to reveal the soliton features of the two-component modified Korteweg–de Vries equation. [ABSTRACT FROM AUTHOR]

The Laguerre calculus is widely used for the inversion of differential operators on the Heisenberg group. Applying the Laguerre calculus established on nilpotent Lie groups of step two in Chang et al. [The Laguerre calculus on the nilpotent Lie group of step two. Preprint; 2019. Available from: ], we find the explicit formulas for the heat kernel of sub-Laplace operator and the fundamental solution of power of sub-Laplace operator on nilpotent Lie groups of step two. Calin, Chang and Markina [Generalized Hamilton–Jacobi equation and heat kernel on step two nilpotent Lie groups. In: Gustafsson B, Vasil'ev A, editors. Analysis and mathematical physics. Basel: Birkhüser; 2009 (Trends in mathematics)] also get the formulas for the heat kernel of sub-Laplace operator on nilpotent Lie groups of step two by using the Hamiltonian and Lagrangian formalisms that are related to geometric mechanics. In this paper, we use a totally different method to prove our main results by using the Laguerre calculus, which is more direct from the point of view of Fourier analysis. [ABSTRACT FROM AUTHOR]

The problem of 'applicability' of mathematics to modern physical sciences has been labeled as an 'unreasonably effective' and unexplainable 'miracle' by prominent physicists such as Eugene Wigner and Paul Dirac. Philosophers of science from contending traditions have also contributed to the debates at large. While some have tried to trivialize the problem, others, in particular those with a phenomenological orientation, have attempted to eliminate this riddle, claiming that the two domains are 'identical'. This paper, while challenging some of these interpretations, proposes a solution from a dialectical materialist position. Drawing on Evald Ilyenkov's concept of the 'ideal' as the objectivized form of human activity in social nature, it is suggested that the two realms are necessarily interconnected as schemata of human activity which aim for a highly quantified conceptualization of reality. [ABSTRACT FROM AUTHOR]

This experimental fact leads to the natural question: I What happens for «> i Graph HT ht I ? This study highlights the special role played by the value «> Graph HT ht , which is needed for Stirling's estimate. To be precise, Hammett proves that «> Graph HT