Foundations

11 pages, 387 KiB

Open AccessArticle

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

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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 [...] Read more.

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

ℏ (c) \sim Λ / c^{p}

for a constant

Λ > 0,

and

p > 1 .

We show how the limit

c \to \infty

implies classicality in quantum mechanics and explain why p has to be larger than

1

. As the limit

c \to \infty

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

c .

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. Full article

(This article belongs to the Section Physical Sciences)

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35 pages, 2314 KiB

Open AccessArticle

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

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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 [...] Read more.

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. Full article

(This article belongs to the Section Physical Sciences)

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14 pages, 5026 KiB

Open AccessArticle

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

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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 [...] Read more.

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. Full article

(This article belongs to the Section Chemical Sciences)

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17 pages, 378 KiB

Open AccessArticle

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

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Abstract

Computation of the solution of the nonlinear Caputo fractional differential equation is essential for using

q,

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 [...] Read more.

Computation of the solution of the nonlinear Caputo fractional differential equation is essential for using

q,

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

[0, \infty) .

Full article

(This article belongs to the Section Mathematical Sciences)

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9 pages, 578 KiB

Open AccessArticle

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

Viewed by 401

Abstract

We explicitly calculate the value of the cosmological constant,

Λ

, 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 [...] Read more.

We explicitly calculate the value of the cosmological constant,

Λ

, 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

Λ ~ R_{U}^{- 2}

. Full article

(This article belongs to the Section Physical Sciences)

12 pages, 2318 KiB

Open AccessArticle

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

Viewed by 552

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 [...] Read more.

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. Full article

(This article belongs to the Section Chemical Sciences)

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18 pages, 363 KiB

Open AccessArticle

On the Algebraic Geometry of Multiview

by Edoardo Ballico

Foundations 2024, 4(3), 306-323; https://doi.org/10.3390/foundations4030020 - 4 Jul 2024

Viewed by 315

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, [...] Read more.

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. Full article

(This article belongs to the Section Mathematical Sciences)

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Foundations, Volume 4, Issue 3 (September 2024) – 7 articles

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