Alternative Derivation Research Articles

A nonequilibrium statistical mechanics derivation of the hydrodynamic equations of simple fluids using a noncanonical form of the Poisson bracket

The continuum level hydrodynamic equations of a simple fluid were derived by Irving and Kirkwood directly from discrete particle dynamics using statistical mechanics almost 75 years ago. Their elegant derivation demonstrated the fundamental molecular basis of macroscopic fluid flow and culminated in molecular expressions for the stress tensor and heat current density that have since been employed in countless molecular simulations to date. In this article, an alternative derivation is presented, which leads to more general expressions for the fundamental transport relationships and which arrives at them in a more straightforward chain of consistency that ensues directly from the Principle of Least Action. The main point of departure from the Irving–Kirkwood derivation is the application of a transformation mapping of the total momentum of each individual particle onto the sum of its peculiar momentum and its momentum relative to the local velocity field. This mapping provides a phase-space distribution function applicable in the space of particle positions and peculiar momentum, from which a noncanonical Poisson bracket can be derived in terms of the same set of microscopic variables. For a given dynamic variable, expressed in terms of particle positions and peculiar momenta, the expectation value of the noncanonical Poisson bracket of the dynamic variable is shown to correspond to the evolution equation of the expectation value of the dynamic variable. This allows for a direct derivation of all macroscopic density evolution equations (mass, momentum, and energy density fields) using a systematic procedure free of assumptions concerning the macroscopic state of the system. Furthermore, an explicit expression of the time evolution of the entropy density at the hydrodynamic level is derived following the same procedure. Finally, in the limit of short-range interparticle interactions, a molecular-based expression for the local stress tensor as properly defined from continuum mechanics is developed at the hydrodynamic level that elucidates the continuum mechanics connection of the general stress expression of Irving and Kirkwood.

Efficient fidelity estimation: alternative derivation and related applications

In [Phys. Rev. A 107 012427 (2023)], Baldwin and Jones prove that Uhlmann–Jozsa’s fidelity between two quantum states ρ and σ, i.e., F(ρ,σ)≔Trρσρ2 , can be written in a simplified form as F(ρ,σ)=Trρσ2 . In this article, we give an alternative proof of this result, using a function power series expansion and the properties of the trace function. Our approach not only reinforces the validity of the simplified expression but also facilitates the exploration of novel dissimilarity functions for quantum states and more complex trace functions of density operators.

Relational bulk reconstruction from modular flow

The entanglement wedge reconstruction paradigm in AdS/CFT states that for a bulk qudit within the entanglement wedge of a boundary subregion A¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{A} $$\\end{document}, operators acting on the bulk qudit can be reconstructed as CFT operators on A¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{A} $$\\end{document}. This naturally fits within the framework of quantum error correction, with the CFT states containing the bulk qudit forming a code protected against the erasure of the boundary subregion A. In this paper, we set up and study a framework for relational bulk reconstruction in holography: given two code subspaces both protected against erasure of the boundary region A, the goal is to relate the operator reconstructions between the two spaces. To accomplish this, we assume that the two code subspaces are smoothly connected by a one-parameter family of codes all protected against the erasure of A, and that the maximally-entangled states on these codes are all full-rank. We argue that such code subspaces can naturally be constructed in holography in a “measurement-based” setting. In this setting, we derive a flow equation for the operator reconstruction of a fixed code subspace operator using modular theory which can, in principle, be integrated to relate the reconstructed operators all along the flow. We observe a striking resemblance between our formulas for relational bulk reconstruction and the infinite-time limit of Connes cocycle flow, and take some steps towards making this connection more rigorous. We also provide alternative derivations of our reconstruction formulas in terms of a canonical reconstruction map we call the modular reflection operator.

A new 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 duality from the superconformal index

In this paper we propose a physical derivation of a 4d conjectural duality for USp(2N) with an anti-symmetric rank-two tensor and fundamental flavors, in presence of a non-trivial superpotential. This duality has been conjectured as a consequence of an exact identity between the superconformal indices of the two phases, proved in the mathematical literature. Here we show that the duality can be derived by a combined sequence of known dualities, deconfinement of tensor matter, RG flow and Higgsing. Furthermore, by following these steps on the superconformal index, we provide an alternative derivation of the integral identity as well.

The Scale-Invariant Vacuum Paradigm: Main Results and Current Progress Review (Part II)

This is a summary of the main results within the Scale-Invariant Vacuum (SIV) paradigm based on Weyl integrable geometry. We also review the mathematical framework and utilize alternative derivations of the key equations based on the reparametrization invariance as well. The main results discussed are related to the early universe; that is, applications to inflation, Big Bang Nucleosynthesis, and the growth of the density fluctuations within the SIV. Some of the key SIV results for the early universe are a natural exit from inflation within the SIV in a later time texit with value related to the parameters of the inflationary potential along with the possibility for the density fluctuations to grow sufficiently fast within the SIV without the need for dark matter to seed the growth of structure in the universe. In the late-time universe, the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and dwarf spheroidals, where one can find MOND to be a peculiar case of the SIV theory. Finally, within the recent time epoch, we highlight that some of the change in the length-of-the-day (LOD), about 0.92 cm/yr, can be accounted for by SIV effects in the Earth–Moon system.

Systematic review and meta-analysis of Murray's law in the coronary arterial circulation.

Murray's law has been viewed as a fundamental law of physiology. Relating blood flow ([Formula: see text]) to vessel diameter (D) ([Formula: see text]·∝·D3), it dictates minimum lumen area (MLA) targets for coronary bifurcation percutaneous coronary intervention (PCI). The cubic exponent (3.0), however, has long been disputed, with alternative theoretical derivations, arguing this should be closer to 2.33 (7/3). The aim of this meta-analysis was to quantify the optimum flow-diameter exponent in human and mammalian coronary arteries. We conducted a systematic review and meta-analysis of all articles quantifying an optimum flow-diameter exponent for mammalian coronary arteries within the Cochrane library, PubMed Medline, Scopus, and Embase databases on 20 March 2023. A random-effects meta-analysis was used to determine a pooled flow-diameter exponent. Risk of bias was assessed with the National Institutes of Health (NIH) quality assessment tool, funnel plots, and Egger regression. From a total of 4,772 articles, 18 were suitable for meta-analysis. Studies included data from 1,070 unique coronary trees, taken from 372 humans and 112 animals. The pooled flow diameter exponent across both epicardial and transmural arteries was 2.39 (95% confidence interval: 2.24-2.54; I2 = 99%). The pooled exponent of 2.39 showed very close agreement with the theoretical exponent of 2.33 (7/3) reported by Kassab and colleagues. This exponent may provide a more accurate description of coronary morphometric scaling in human and mammalian coronary arteries, as compared with Murray's original law. This has important implications for the assessment, diagnosis, and interventional treatment of coronary artery disease.

Gauge field fluctuation corrected QED3 effective action by fermionic particle-vortex duality

We present a non-perturbative framework for incorporating gauge field fluctuations into effective actions of QED3 in the infrared using fermionic particle-vortex duality. This approach is demonstrated through the applications to models containing N species of 2-component Dirac fermions in solvable and interpretable electromagnetic backgrounds, focusing on N = 1 or 2. For the N = 1 model, we establish a correspondence between fermion Casimir energy at finite density and the magnetic Euler-Heisenberg Lagrangian, and further evaluate the corrections to their amplitudes. This predicts amplification of charge susceptibility and reduction of magnetic permeability. We additionally provide physical interpretations for each component of our calculation and offer alternative derivations based on energy density measurements in different characteristic lengths. For N = 2, we show that magnetic catalysis is erased in a U(1) × U(1) QED3, indicating no breakdown of chiral symmetry. Reasoning is offered based on the properties of the lowest Landau level wave functions.

Ralph Kenna's Scaling Relations in Critical Phenomena.

In this note, we revisit the scaling relations among "hatted critical exponents", which were first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the correlation function, we will propose an alternative form since we believe that the expression is erroneous in the work of Ralph and his collaborators.

Matrix factorizations for the generalized Charlier and Meixner orthogonal polynomials

The Cholesky factorization of the moment matrix is considered for the generalized Charlier and generalized Meixner discrete orthogonal polynomials. For the generalized Charlier, we present an alternative derivation of the Laguerre–Freud relations found by Smet and Van Assche. Third-order and second-order nonlinear ordinary differential equations are found for the recursion coefficient γn, that happen to be forms of the Painlevé deg-PV in disguise. New Laguerre–Freud relations are also found for the generalized Meixner case, which are compared with those of Smet and Van Assche.

The Riddle of the Thread: On Arabic ghazal

Ghazal is the Arabic word for “amatory verse”, and in other languages of the Islamic world it designates a sonnet-like poetic form. The notion that the word stems from Arabic ghazl “spinning thread” is widely held, despite the absence of support for this in classical lexicography and poetry criticism. Comparison to Semitic cognates points to an alternative derivation of ghazal from a verb of speaking – specifically, speech that is ambiguous and suggestive – by way of attraction to the gazelle (Arabic ghazāl), an ancient Near Eastern idiom for the beloved. While ghazal poetry emerged in Western Arabia during the first century of Islam, the genesis of ghazal as a term of art predates the literary record, as may be appreciated in a poem by ʿAmr ibn Qamīʾa (6th century CE) that has been called the earliest complete qaṣīda in Arabic manuscript tradition.

RG flows on two-dimensional spherical defects

We study two-dimensional spherical defects in d-dimensional Conformal Field Theories. We argue that the Renormalization Group (RG) flows on such defects admit the existence of a decreasing entropy function. At the fixed points of the flow, the entropy function equals the anomaly coefficient which multiplies the Euler density in the defect’s Weyl anomaly. Our construction demonstrates an alternative derivation of the irreversibility of RG flows on two-dimensional defects. Moreover, in the case of perturbative RG flows induced by weakly relevant deformations, the entropy function decreases monotonically and plays the role of a C-function. We provide a simple example to explicitly work out the RG flow details in the proposed construction.

Information Theory and the Pricing of Contingent Claims: An Alternative Derivation of the Black–Scholes–Merton Formula

This paper seeks to determine the best subjective probability to use to carry out expectation values of uncertain future cash flows with the smallest number of assumptions. This results in the unique distribution that guarantees no more information is present other than the stated assumptions. The result is a novel derivation of the well-known Black–Scholes equation without the need to introduce high-level mathematical machinery. This formalism fits nicely into introductory courses of finance, where the value of any financial instrument is given by the present value of uncertain future cash flows.

Alternative Derivations in (1,1) Rings

Objectives: To show the associativity in one of the subclass of non-associative (γ,δ) rings. Method: Derivation alternator rings are limiting case of associative rings. The ring (1,1) is one of the sub class of (γ,δ) rings. Consider a (1,1) derivation alternator ring R, with characteristic ≠ 2, and it is well known that this ring is neither alternative nor flexible. In this paper it will be proved that right alternative property (R,x,x) holds in R and flexibility follows, finally associativity arrives in R. Findings: If this ring R does not contain nilpotent elements even though it will be associative. Novelty: Further investigators may extend the applications of these rings in science and engineering fields. Mathematics Subject Classification: 2010 MSC 17D

An alternative derivation of propagator for a linear potential

An alternative derivation of propagator for a linear potential

REGULARIZED EQUATIONS FOR DYNAMICS OF THE HETEROGENEOUS BINARY MIXTURES OF THE NOBLE-ABEL STIFFENED-GASES AND THEIR APPLICATION

We consider the so-called four-equation model for dynamics of the heterogeneous compressible binary mixtures with the Noble-Abel stiffened-gas equations of state. We exploit its quasi-homogeneous form arising after excluding the volume concentrations from the sought functions and based on a quadratic equation for the common pressure of the components. We present new properties of this equation and a simple formula for the squared speed of sound, suggest an alternative derivation for a formula relating it to the squared Wood speed of sound and state the pressure balance equation. For the first time, we give quasi-gasdynamic-type regularization of the heterogeneous model (in the quasi-homogeneous form), construct explicit two-level in time and symmetric three point in space finite-difference scheme without limiters to implement it in the 1D case and present numerical results.

An alternative derivation of weak convergence concerning quasi-likelihood estimation with a small-sample correction for simultaneous testing

Often arises in counting data analysis that both violation of distributional assumption and large-scale over-dispersion substantially impair the validity of the methods for multiple comparisons. For over-dispersed data fitting to the generalized linear models, we describe the simultaneous inference method in assessing a sequence of estimable functions based on the root using the quasi-likelihood estimation of the regression coefficients. A new method for deriving the limiting distributions of the score function and the root under a list of mild regularity conditions is presented. This approach has a close connection to the asymptotic normality of the root in general linear models that it provides a heuristic analogy for classroom presentation. Hence, researchers can routinely estimate quantiles based on the limiting distribution of the root for simultaneous inference. We apply the percentile bootstrap method to estimate the quantiles as a resampling-based alternative. As will be shown, the simultaneous test based on both the approximation methods above is anti-conservative in designs with small sample sizes. We propose the simultaneous testing method using Efron's bias-corrected percentile bootstrapping procedure as an improvement. In small-sample designs, we demonstrate through the simulation study that the proposed method provides a viable alternative to the large-sample and the percentile bootstrap approximation methods. Moreover, the proposed method persists in controlling the familywise error rate in simultaneous testing for highly over-dispersed data from substantially small-sample designs, where the percentile-t bootstrap method provides a liberal test.

Alternative Derivation of the Non-Abelian Stokes Theorem in Two Dimensions

The relation between the holonomy along a loop with the curvature form is a well-known fact, where the small square loop approximation of aholonomy Hγ,O is proportional to Rσ. In an attempt to generalize the relation for arbitrary loops, we encounter the following ambiguity. For a given loop γ embedded in a manifold M, Hγ,O is an element of a Lie group G; the curvature Rσ∈g is an element of the Lie algebra of G. However, it turns out that the curvature form Rσ obtained from the small loop approximation is ambiguous, as the information of γ and Hγ,O are insufficient for determining a specific plane σ responsible for Rσ. To resolve this ambiguity, it is necessary to specify the surface S enclosed by the loop γ; hence, σ is defined as the limit of S when γ shrinks to a point. In this article, we try to understand this problem more clearly. As a result, we obtain an exact relation between the holonomy along a loop with the integral of the curvature form over a surface that it encloses. The derivation of this result can be viewed as an alternative proof of the non-Abelian Stokes theorem in two dimensions with some generalizations.

Understanding Structure-Activity Relationship in Pt-loaded g-C3 N4 for Efficient Solar- Photoreforming of Polyethylene Terephthalate Plastic and Hydrogen Production.

Coupling the hydrogen evolution reaction with plastic waste photoreforming provides a synergistic path for simultaneous production of green hydrogen and recycling of post-consumer products, two major enablers for establishment of a circular economy. Graphitic carbon nitride (g-C3 N4 ) is a promising photocatalyst due to its suitable optoelectronic and physicochemical properties, and inexpensive fabrication. Herein, a mechanistic investigation of the structure-activity relationship of g-C3 N4 for poly(ethylene terephthalate) (PET) photoreforming is reported by carefully controlling its fabrication from a subset of earth-abundant precursors, such as dicyandiamide, melamine, urea, and thiourea. These findings reveal that melamine-derived g-C3 N4 with 3wt.% Pt has significantly higher performance than alternative derivations, achieving a maximum hydrogen evolution rate of 7.33mmolH2 gcat -1 h-1 , and simultaneously photoconverting PET into valuable organic products including formate, glyoxal, and acetate, with excellent stability for over 30h of continuous production. This is attributed to the higher crystallinity and associated chemical resistance of melamine-derived g-C3 N4 , playing a major role in stabilization of its morphology and surface properties. These new insights on the role of precursors and structural properties in dictating the photoactivity of g-C3 N4 set the foundation for the further development of photocatalytic processes for combined green hydrogen production and plastic waste reforming.

Go with the Flow: Estimating Wind Using Uncrewed Aircraft

This paper presents a fundamentally different approach to wind estimation using Uncrewed Aircraft (UA) than the vast majority of existing methods. This method uses no on-board flow sensor and does not attempt to estimate thrust or drag forces. Using only GPS and orientation sensors, the strategy estimates wind vectors in an Earth-fixed frame during turning maneuvers. The method presented here is called the Wind-Arc method. The philosophy behind this method has been seen in practice, but this paper presents an alternative derivation with resulting performance evaluations in simulations and flight tests. The simulations verify the method provides perfect performance under ideal conditions using simulated GPS, heading angle, and satisfied assumptions. When applied to experimental flight test data, the method works and follows both the airspeed and wind speed trends, but improvements can still be made. Wind triangles are displayed at each instant in time along the flight path that illustrate the graphical nature of the approach and solution. Future work will include wind gust estimation and a Quality of Estimate (QoE) metric to determine what conditions provide good wind speed estimates while preserving the method’s generality and simplicity.

Krylov complexity in Calabi–Yau quantum mechanics

Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric Calabi–Yau geometries, as well as some nonrelativistic models. We find that for the Calabi–Yau models, the Lanczos coefficients grow slower than linearly for small [Formula: see text]’s, consistent with the behavior of integrable models. On the other hand, for the nonrelativistic models, the Lanczos coefficients initially grow linearly for small [Formula: see text]’s, then reach a plateau. Although this looks like the behavior of a chaotic system, it is mostly likely due to saddle-dominated scrambling effects instead, as argued in the literature. In our cases, the slopes of linearly growing Lanczos coefficients almost saturate a bound by the temperature. During our study, we also provide an alternative general derivation of the bound for the slope.