Journal Description
Foundations
Foundations
is an international, peer-reviewed, open access journal on mathematics, physics and chemistry published quarterly online by MDPI.
- Open Access free for readers, with article processing charges (APC) paid by authors or their institutions.
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 32.4 days after submission; acceptance to publication is undertaken in 4.9 days (median values for papers published in this journal in the first half of 2024).
- Recognition of Reviewers: APC discount vouchers, optional signed peer review, and reviewer names published annually in the journal.
- Foundations is a companion journal of Molecules, Entropy and Mathematics.
Latest Articles
Finite Multiple Mixed Values
Foundations 2024, 4(3), 451-467; https://doi.org/10.3390/foundations4030029 - 6 Sep 2024
Abstract
In recent years, a variety of multiple zeta values (MZVs) variants have been defined and studied. One way to produce these variants is to restrict the indices in the definition of MZVs to some fixed parity pattern, which include Hoffman’s multiple t-values,
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In recent years, a variety of multiple zeta values (MZVs) variants have been defined and studied. One way to produce these variants is to restrict the indices in the definition of MZVs to some fixed parity pattern, which include Hoffman’s multiple t-values, Kaneko and Tsumura’s multiple T-values, and Xu and this paper’s author’s multiple S-values. Xu and this paper’s author have also considered the so-called multiple mixed values by allowing all possible parity patterns and have studied a few important relations among these values. In this paper, we turn to the finite analogs and the symmetric forms of the multiple mixed values, motivated by a deep conjecture of Kaneko and Zagier, which relates the finite MZVs and symmetric MZVs, and a generalized version of this conjecture by the author to the Euler sum (i.e., level two) setting. We present a few important relations among these values such as the stuffle, reversal, and linear shuffle relations. We also compute explicitly the (conjecturally smallest) generating set in weight one and two cases. In the appendix, we tabulate some dimension computations for various subspaces of the finite multiple mixed values and propose a conjecture.
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(This article belongs to the Collection Editorial Board Members’ Collection Series: Feature Papers in Mathematical Sciences)
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The Generalized Mehler–Fock Transform over Lebesgue Spaces
by
Jeetendrasingh Maan, Benito J. González and Emilio R. Negrín
Foundations 2024, 4(3), 442-450; https://doi.org/10.3390/foundations4030028 - 2 Sep 2024
Abstract
This paper focuses on establishing boundedness properties and Parseval–Goldstein-type relations for the generalized Mehler–Fock transform initially introduced by B. L. J. Braaksma and B. M. Meulenbeld (Compositio Math., 18(3):235–287, 1967). Also, we derive an inversion formula for this transform over Lebesgue spaces.
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(This article belongs to the Section Mathematical Sciences)
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A Double Legendre Polynomial Order N Benchmark Solution for the 1D Monoenergetic Neutron Transport Equation in Plane Geometry
by
Barry D. Ganapol
Foundations 2024, 4(3), 422-441; https://doi.org/10.3390/foundations4030027 - 21 Aug 2024
Abstract
As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of the numerical results becomes increasingly important. This presentation concerns the development of another benchmark for the linear neutron transport equation in a benchmark series, each
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As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of the numerical results becomes increasingly important. This presentation concerns the development of another benchmark for the linear neutron transport equation in a benchmark series, each employing a different method of solution. In 1D, there are numerous ways of analytically solving the monoenergetic transport equation, such as the Wiener–Hopf method, based on the analyticity of the solution, the method of singular eigenfunctions, inversion of the Laplace and Fourier transform solutions, and analytical discrete ordinates in the limit, which is arguably one of the most straightforward, to name a few. Another potential method is the PN (Legendre polynomial order N) method, where one expands the solution in terms of full-range orthogonal Legendre polynomials, and with orthogonality and series truncation, the moments form an open set of first-order ODEs. Because of the half-range boundary conditions for incoming particles, however, full-range Legendre expansions are inaccurate near material discontinuities. For this reason, a double PN (DPN) expansion in half-range Legendre polynomials is more appropriate, where one separately expands incoming and exiting flux distributions to preserve the discontinuity at material interfaces. Here, we propose and demonstrate a new method of solution for the DPN equations for an isotropically scattering medium. In comparison to a well-established fully analytical response matrix/discrete ordinate solution (RM/DOM) benchmark using an entirely different method of solution for a non-absorbing 1 mfp thick slab with both isotropic and beam sources, the DPN algorithm achieves nearly 8- and 7-place precision, respectively.
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(This article belongs to the Collection Editorial Board Members’ Collection Series: Theory and Its Applications in Problems of Mathematical Physics and of Mathematical Chemistry)
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On the Speed of Light as a Key Element in the Structure of Quantum Mechanics
by
Tomer Shushi
Foundations 2024, 4(3), 411-421; https://doi.org/10.3390/foundations4030026 - 13 Aug 2024
Abstract
We follow the assumption that relativistic causality is a key element in the structure of quantum mechanics and integrate the speed of light, c, into quantum mechanics through the postulate that the (reduced) Planck constant is a function of c with a
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We follow the assumption that relativistic causality is a key element in the structure of quantum mechanics and integrate the speed of light, c, into quantum mechanics through the postulate that the (reduced) Planck constant is a function of c with a leading order of the form for a constant and We show how the limit implies classicality in quantum mechanics and explain why p has to be larger than . As the limit breaks down both relativity theory and quantum mechanics, as followed by the proposed model, it can then be understood through similar conceptual physical laws. We further show how the position-dependent speed of light gives rise to an effective curved space in quantum systems and show that a stronger gravitational field implies higher quantum uncertainties, followed by the varied We then discuss possible ways to find experimental evidence of the proposed model using set-ups to test the varying speed of light models and examine analogies of the model based on electrons in semiconductor heterostructures.
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(This article belongs to the Section Physical Sciences)
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Methods for Controlling Electrostatic Discharge and Electromagnetic Interference in Materials
by
Aris Alexopoulos and David Neudegg
Foundations 2024, 4(3), 376-410; https://doi.org/10.3390/foundations4030025 - 1 Aug 2024
Abstract
Methods for controlling electromagnetic fields in materials are presented that mitigate effects such as electrostatic discharge and electromagnetic/radio frequency interference. The first method determines the effective response of composite materials using a d-dimensional effective medium theory. The material consists of inhomogeneous two-layer
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Methods for controlling electromagnetic fields in materials are presented that mitigate effects such as electrostatic discharge and electromagnetic/radio frequency interference. The first method determines the effective response of composite materials using a d-dimensional effective medium theory. The material consists of inhomogeneous two-layer inclusions with hyperspherical geometry. Non-integer dimensions represent fractal limits. The material medium is composed of a low hypervolume fraction of inclusions that are randomly distributed inside it. The effective response of the dielectric function is obtained using a virial expansion of the Maxwell–Garnett theory. The other method uses the transformation medium theory and involves the transformation of the material’s permittivity and permeability tensors so that the material exhibits a predefined effective response. By selecting appropriate transformations, a homogeneous material medium is transformed into an inhomogeneous version, forcing the electromagnetic fields to propagate along geodesic paths. These geodesics determine the behaviour of the fields inside the material. As a result, the material can be made to exhibit similar physical characteristics as those of a material composed of hyperspherical inclusions. The theoretical analysis presented is further studied and validated via the use of full-wave numerical simulations of Maxwell’s equations.
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(This article belongs to the Section Physical Sciences)
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Experimental and Theoretical Investigation of the Coordination of 8-Hydroxquinoline Inhibitors to Biomimetic Zinc Complexes and Histone Deacetylase 8 (HDAC8)
by
Anthony M. Baudino, Harris F. Ciaccio, Michael J. Turski, Xavier A. Akins, Phoebus Sun Cao, Elisa Morales, Roger D. Sommer, Adam R. Johnson, Donald J. Wink, Kyle A. Grice and Kari L. Stone
Foundations 2024, 4(3), 362-375; https://doi.org/10.3390/foundations4030024 - 1 Aug 2024
Abstract
Zinc is integral to diverse biological functions, acting catalytically, structurally, and supportively in essential enzyme cycles, despite its limited amounts in the body. Targeting zinc enzymes with potent drugs, such as Vorinostat, demonstrates the therapeutic efficacy of zinc-binding ligands, notably in cutaneous T-cell
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Zinc is integral to diverse biological functions, acting catalytically, structurally, and supportively in essential enzyme cycles, despite its limited amounts in the body. Targeting zinc enzymes with potent drugs, such as Vorinostat, demonstrates the therapeutic efficacy of zinc-binding ligands, notably in cutaneous T-cell lymphoma treatments. Our study merges experimental and theoretical approaches to analyze the coordination of 8-hydroxylquinoline (8HQ) inhibitors with biomimetic zinc complexes and human histone deacetylase 8 (HDAC8), a monozinc hydrolase enzyme. Assessing 10 8HQ derivatives for structural and electronic characteristics against these models, we observe minimal inhibition efficacy, corroborated through protein–ligand docking analyses, highlighting the complexities of inhibitor–zinc enzyme interactions and suggesting intricate noncovalent interactions that are important for ligand binding to enzymes not accounted for in model zinc hydrolase mimics.
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(This article belongs to the Section Chemical Sciences)
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Generalized Quasilinearization Method for Caputo Fractional Differential Equations with Initial Conditions with Applications
by
Aghalaya S. Vatsala and Govinda Pageni
Foundations 2024, 4(3), 345-361; https://doi.org/10.3390/foundations4030023 - 25 Jul 2024
Abstract
Computation of the solution of the nonlinear Caputo fractional differential equation is essential for using which is the order of the derivative, as a parameter. The value of q can be determined to enhance the mathematical model in question using the
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Computation of the solution of the nonlinear Caputo fractional differential equation is essential for using which is the order of the derivative, as a parameter. The value of q can be determined to enhance the mathematical model in question using the data. The numerical methods available in the literature provide only the local existence of the solution. However, the interval of existence is known and guaranteed by the natural upper and lower solutions of the nonlinear differential equations. In this work, we develop monotone iterates, together with lower and upper solutions that converge uniformly, monotonically, and quadratically to the unique solution of the Caputo nonlinear fractional differential equation over its entire interval of existence. The nonlinear function is assumed to be the sum of convex and concave functions. The method is referred to as the generalized quasilinearization method. We provide a Caputo fractional logistic equation as an example whose interval of existence is
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(This article belongs to the Section Mathematical Sciences)
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On the Value of the Cosmological Constant in Entropic Gravity
by
Andreas Schlatter
Foundations 2024, 4(3), 336-344; https://doi.org/10.3390/foundations4030022 - 18 Jul 2024
Abstract
We explicitly calculate the value of the cosmological constant, , based on the recently developed theory connecting entropic gravity with quantum events induced by transactions, called transactional gravity. We suggest a novel interpretation of the cosmological constant and rigorously show its inverse
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We explicitly calculate the value of the cosmological constant, , based on the recently developed theory connecting entropic gravity with quantum events induced by transactions, called transactional gravity. We suggest a novel interpretation of the cosmological constant and rigorously show its inverse proportionality to the squared radius of the causal universe .
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(This article belongs to the Section Physical Sciences)
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Effects of Colored Noise in the Dynamic Motions and Conformational Exploration of Enzymes
by
Pedro Ojeda-May and Alexander Vergara
Foundations 2024, 4(3), 324-335; https://doi.org/10.3390/foundations4030021 - 8 Jul 2024
Abstract
The intracellular environment displays complex dynamics influenced by factors such as molecular crowding and the low Reynolds number of the cytoplasm. Enzymes exhibiting active matter properties further heighten this complexity which can lead to memory effects. Molecular simulations often neglect these factors, treating
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The intracellular environment displays complex dynamics influenced by factors such as molecular crowding and the low Reynolds number of the cytoplasm. Enzymes exhibiting active matter properties further heighten this complexity which can lead to memory effects. Molecular simulations often neglect these factors, treating the environment as a “thermal bath” using the Langevin equation (LE) with white noise. One way to consider these factors is by using colored noise instead within the generalized Langevin equation (GLE) framework, which allows for the incorporation of memory effects that have been observed in experimental data. We investigated the structural and dynamic differences in Shikimate kinase (SK) using LE and GLE simulations. Our results suggest that GLE simulations, which reveal significant changes, could be utilized for assessing conformational motions’ impact on catalytic reactions.
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(This article belongs to the Section Chemical Sciences)
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On the Algebraic Geometry of Multiview
by
Edoardo Ballico
Foundations 2024, 4(3), 306-323; https://doi.org/10.3390/foundations4030020 - 4 Jul 2024
Abstract
We study the multiviews of algebraic space curves X from n pin-hole cameras of a real or complex projective space. We assume the pin-hole centers to be known, i.e., we do not reconstruct them. Our tools are algebro-geometric. We give some general theorems,
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We study the multiviews of algebraic space curves X from n pin-hole cameras of a real or complex projective space. We assume the pin-hole centers to be known, i.e., we do not reconstruct them. Our tools are algebro-geometric. We give some general theorems, e.g., we prove that a projective curve (over complex or real numbers) may be reconstructed using four general cameras. Several examples show that no number of badly placed cameras can make a reconstruction possible. The tools are powerful, but we warn the reader (with examples) that over real numbers, just using them correctly, but in a bad way, may give ghosts: real curves which are images of the emptyset. We prove that ghosts do not occur if the cameras are general. Most of this paper is devoted to three important cases of space curves: unions of a prescribed number of lines (using the Grassmannian of all lines in a 3-dimensional projective space), plane curves, and curves of low degree. In these cases, we also see when two cameras may reconstruct the curve, but different curves need different pairs of cameras.
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(This article belongs to the Section Mathematical Sciences)
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Quantum Brain Dynamics: Optical and Acoustic Super-Radiance via a Microtubule
by
Akihiro Nishiyama, Shigenori Tanaka and Jack A. Tuszynski
Foundations 2024, 4(2), 288-305; https://doi.org/10.3390/foundations4020019 - 18 Jun 2024
Abstract
We aim to derive a super-radiance solution of coherent light and sound waves involving water degrees of freedom in the environment of a microtubule. We introduce a Lagrangian density functional of quantum electrodynamics with non-relativistic charged bosons as a model of quantum brain
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We aim to derive a super-radiance solution of coherent light and sound waves involving water degrees of freedom in the environment of a microtubule. We introduce a Lagrangian density functional of quantum electrodynamics with non-relativistic charged bosons as a model of quantum brain dynamics (QBD) involving water molecular conformational states and photon fields. We also introduce the model of charged boson fields (water degrees of freedom) coupled with phonons. Both optical and acoustic super-radiance solutions are derived in our approach. An acoustic super-radiance mechanism involving information transfer is proposed as an additional candidate to solve the binding problem and to achieve acoustic holography. Our results can be applied to achieve holographic memory storage and information processing in QBD.
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(This article belongs to the Section Physical Sciences)
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Characterization of the Solution Properties of Sodium Dodecylsulphate Containing Alkaline–Surfactant–Polymer Flooding Media
by
Csaba Bús, Bence Kutus, Áron Ágoston, László Janovák and Pál Sipos
Foundations 2024, 4(2), 273-287; https://doi.org/10.3390/foundations4020018 - 11 Jun 2024
Abstract
Alkaline–surfactant–polymer (ASP) flooding by means of which alkali additives, surfactant and polymer are inserted as the same slug is one of the most favourable worldwide focuses of Chemical Enhanced Oil Recovery (cEOR) research and field trials, due to the individual synergy of the
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Alkaline–surfactant–polymer (ASP) flooding by means of which alkali additives, surfactant and polymer are inserted as the same slug is one of the most favourable worldwide focuses of Chemical Enhanced Oil Recovery (cEOR) research and field trials, due to the individual synergy of the three chemical components. To develop efficient oil recovery chemicals, it is essential to fully understand the mechanism behind ASP flooding. Nonetheless, there are hardly any studies reporting a systematic characterization of the ASP process. Thus, the present paper focuses on modelling this process in a laboratory by the use of an anionic surfactant—sodium dodecyl sulphate (SDS) in alkaline–polymer media—which is composed of a commercial water-soluble polymer (Flopaam AN125SH®, SNF Floerger, Andrézieux-Bouthéon, France) and alkali compounds (NaOH and Na2CO3). The samples were characterized using rheometry, dynamic light scattering (DLS), infrared spectroscopy (IR) and measurement of inferfacial tension (IFT) between the samples and rapeseed oil. In accordance with the experimental results, surprisingly lower IFT values were recorded between the alkaline–polymer solutions and rapeseed oil than the samples which contained SDS. Increasing polymer and sodium chloride concentration caused a decrease (from 0.591 mN/m to 0.0486 mN/m) in IFT between the surfactant containing samples and rapeseed oil. The IR measurements confirmed that the surfactant was not detected in the oil phase in the absence of NaOH and Na2CO3. The effects of SDS on the viscosity of the mixtures were also investigated, as viscosity is a considerably important parameter in processes using polymers.
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(This article belongs to the Section Chemical Sciences)
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Classifying Sets of Type (4,n) in PG(3,q)
by
Stefano Innamorati
Foundations 2024, 4(2), 263-272; https://doi.org/10.3390/foundations4020017 - 4 Jun 2024
Abstract
In the present work, we classify sets of type (4,n) in PG(3,q). We prove that PG(3,q), apart from the planes of PG(3,3), contains only sets of type (4,n) with standard parameters. Thus, somewhat surprisingly, we
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In the present work, we classify sets of type (4,n) in PG(3,q). We prove that PG(3,q), apart from the planes of PG(3,3), contains only sets of type (4,n) with standard parameters. Thus, somewhat surprisingly, we conclude that there are no sets of type (4,n) in PG(3,q), q ≠ 3, with non-standard parameters.
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(This article belongs to the Section Mathematical Sciences)
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The Covariety of Saturated Numerical Semigroups with Fixed Frobenius Number
by
José Carlos Rosales and María Ángeles Moreno-Frías
Foundations 2024, 4(2), 249-262; https://doi.org/10.3390/foundations4020016 - 3 Jun 2024
Abstract
In this work, we show that if F is a positive integer, then is a saturated numerical semigroup with Frobenius number F} is a covariety. As a consequence, we present two algorithms: one
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In this work, we show that if F is a positive integer, then is a saturated numerical semigroup with Frobenius number F} is a covariety. As a consequence, we present two algorithms: one that computes and another which computes all the elements of with a fixed genus. If for some then we see that there exists the least element of containing X. This element is denoted by If , then we define the -rank of S as the minimum of In this paper, we present an algorithm to compute all the elements of with a given -rank.
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(This article belongs to the Section Mathematical Sciences)
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Do Pores Exist?—Foundational Issues in Pore Structural Characterisation
by
Sean P. Rigby
Foundations 2024, 4(2), 225-248; https://doi.org/10.3390/foundations4020015 - 20 May 2024
Cited by 1
Abstract
This work reviews a range of fundamental theoretical considerations in pore structural characterisation. The pore concept is essential for providing a better understanding of physical processes arising within porous media than purely phenomenological approaches. The notion of a pore structure is found to
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This work reviews a range of fundamental theoretical considerations in pore structural characterisation. The pore concept is essential for providing a better understanding of physical processes arising within porous media than purely phenomenological approaches. The notion of a pore structure is found to be independently valid and invariant during theory change concerning said physical processes, even for structural models obtained via indirect methods. While imaging methods provide a more direct characterisation of porous solids, there is often a surfeit of information beyond that which can be wielded with current computing power to predict processes sufficiently accurately. Unfortunately, the pore network model extraction methods cannot decide in advance the level of simplification necessary to obtain the optimum minimal idealisation for a given physical process. Pore network models can be obtained with differing geometrical and topological properties, but similar mass transfer rates, for reasons that are often not clear. In contrast, the ‘pore-sifting’ strategy aims to explicitly identify the key feature of the void space that controls a mass transport process of interest.
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(This article belongs to the Section Chemical Sciences)
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Minimal Conditioned Stiffness Matrices with Frequency-Dependent Path Following for Arbitrary Elastic Layers over Half-Spaces
by
Andrew T. Peplow and Bilong Liu
Foundations 2024, 4(2), 205-224; https://doi.org/10.3390/foundations4020014 - 14 May 2024
Abstract
This paper introduces an efficient computational procedure for analyzing the propagation of harmonic waves in layered elastic media. This offers several advantages, including the ability to handle arbitrary frequencies, depths, and the number of layers above an elastic half-space, and efforts to follow
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This paper introduces an efficient computational procedure for analyzing the propagation of harmonic waves in layered elastic media. This offers several advantages, including the ability to handle arbitrary frequencies, depths, and the number of layers above an elastic half-space, and efforts to follow dispersion curves and flag up possible singularities are investigated. While there are inherent limitations in terms of computational accuracy and capacity, this methodology is straightforward to implement for studying free or forced vibrations and obtaining relevant response data. We present computations of wavenumber dispersion diagrams, phase velocity plots, and response data in both the frequency and time domains. These computational results are provided for two example cases: plane strain and axisymmetry. Our methodology is grounded in a well-conditioned dynamic stiffness approach specifically tailored for deep-layered strata analysis. We introduce an innovative method for efficiently computing wavenumber dispersion curves. By tracking the slope of these curves, users can effectively manage continuation parameters. We illustrate this technique through numerical evidence of a layer resonance in a real-life case study characterized by a fold in the dispersion curves. Furthermore, this framework is particularly advantageous for engineers addressing problems related to ground-borne vibrations. It enables the analysis of phenomena such as zero group velocity (ZGV), where a singularity occurs, both in the frequency and time domains, shedding light on the unique characteristics of such cases. Given the reduced dimension of the problem, this formulation can considerably aid geophysicists and engineers in areas such as MASW or SASW techniques.
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(This article belongs to the Section Physical Sciences)
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A Fundamental Duality in the Exact Sciences: The Application to Quantum Mechanics
by
David Ellerman
Foundations 2024, 4(2), 175-204; https://doi.org/10.3390/foundations4020013 - 11 May 2024
Abstract
There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that
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There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are shown to start with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences.
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(This article belongs to the Section Physical Sciences)
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Exchangeable Quantities and Power Laws: Τhe Case of Pores in Solids
by
Antigoni G. Margellou and Philippos J. Pomonis
Foundations 2024, 4(2), 156-174; https://doi.org/10.3390/foundations4020012 - 23 Apr 2024
Abstract
In this work we suggest that the common cause for the development of various power laws is the existence of a suitable exchangeable quantity between the agents of a set. Examples of such exchangeable quantities, leading to eponymous power laws, include money (Pareto’s
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In this work we suggest that the common cause for the development of various power laws is the existence of a suitable exchangeable quantity between the agents of a set. Examples of such exchangeable quantities, leading to eponymous power laws, include money (Pareto’s Law), scientific knowledge (Lotka’s Law), people (Auerbach’s Law), and written or verbal information (Zipf’s Law), as well as less common cases like bullets during deadly conflicts, recognition in social networks, heat between the atmosphere and sea-ice floes, and, finally, mass of water vapors between pores in solids. This last case is examined closely in the present article based on extensive experimental data. It is shown that the transferred mass between pores, which eventually grow towards a power law distribution, may be expressed using different parameters, either transferred surface area, or transferred volume, or transferred pore length or transferred pore anisotropy. These distinctions lead to different power laws of variable strength as reflected by the corresponding exponent. The exponents depend quantitatively on the spread of frequency distribution of the examined parameter and tend to zero as the spread of distribution tends to a single order of magnitude. A comparison between the energy and the entropy of different kinds of pore distributions reveals that these two statistical parameters are linearly related, implying that the system poise at a critical state and the exchangeable quantities are the most convenient operations helping to keep this balance.
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(This article belongs to the Section Chemical Sciences)
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On Mach’s Principle in Entropic Gravity
by
A. Schlatter and R. E. Kastner
Foundations 2024, 4(2), 146-155; https://doi.org/10.3390/foundations4020011 - 3 Apr 2024
Abstract
The question of where the inertial properties of matter come from has been open for a long time. Isaac Newton considered inertia an intrinsic property of matter. Ernst Mach held a different view whereby the inertia of a body comes from its interaction
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The question of where the inertial properties of matter come from has been open for a long time. Isaac Newton considered inertia an intrinsic property of matter. Ernst Mach held a different view whereby the inertia of a body comes from its interaction with the rest of the universe. This idea is known today as Mach’s principle. We discuss Mach’s principle based on transactional gravity, the recently developed connection of entropic gravity to the physics of quantum events, induced by transactions. It is shown that Mach’s principle holds and that there is a fundamental relation between the gravitational constant and the total mass in the causal universe. This relationship, derived by means of entropic principles, is rigorously proven.
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(This article belongs to the Section Physical Sciences)
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Dirac Field, van der Waals Gas, Weyssenhoff Fluid, and Newton Particle
by
Luca Fabbri
Foundations 2024, 4(2), 134-145; https://doi.org/10.3390/foundations4020010 - 28 Mar 2024
Abstract
This article considers the Dirac field in polar formulation and shows that when torsion is taken in effective approximation the theory has the thermodynamic properties of a van der Waals gas. It is then shown that in the limit of zero chiral angle
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This article considers the Dirac field in polar formulation and shows that when torsion is taken in effective approximation the theory has the thermodynamic properties of a van der Waals gas. It is then shown that in the limit of zero chiral angle the van der Waals gas reduces to a Weyssenhoff fluid, and in spinlessness regime the Weyssenhoff fluid further reduces to a Newton particle. This nesting of approximations allows us to interpret the various spinor quantities. We will see that torsion will provide a form of negative pressure, while the chiral angle will be related to a type of temperature.
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(This article belongs to the Section Physical Sciences)
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