Hasil untuk "Analytic mechanics"

José Carlos Goulart de Siqueira, B. Bonatto

D. Maugis

J. Onuchic, Z. Luthey-Schulten, P. Wolynes

G. Taylor

Richard J.A.M. Stevens, C. Meneveau

Eneko Lazpita, Jesús Garicano-Mena, Soledad Le Clainche

Accurate and efficient modelling of cardiac blood flow is crucial for advancing data-driven tools in cardiovascular research and clinical applications. Recently, the accuracy and availability of computational fluid dynamics methodologies for simulating intraventricular flow have increased. However, these methods remain complex and computationally costly. This study presents a reduced-order model (ROM) based on higher-order dynamic mode decomposition (HODMD). The proposed approach enables accurate reconstruction and long-term prediction of left ventricle flow fields. The method is tested on two idealized ventricular geometries exhibiting distinct flow regimes to assess its robustness under different hemodynamic conditions. By leveraging a small number of training snapshots and focusing on the dominant periodic components representing the physics of the system, the HODMD-based model accurately reconstructs the flow field over entire cardiac cycles and provides reliable long-term predictions beyond the training window. The reconstruction and prediction errors remain below 5 % for the first geometry and below 10 % for the second, even when using as few as the first three cycles of simulated data, representing the transitory regime. Additionally, the approach reduces computational costs with a speed-up factor of at least $10^{5}$ compared with full-order simulations, enabling fast surrogate modelling of complex cardiac flows. These results highlight the potential of spectrally constrained HODMD as a robust and interpretable ROM for simulating intraventricular hemodynamics. This approach shows promise for integration in real-time analysis and patient specific models.

Motohiko Ezawa

Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the spin degrees of freedom. It is related to electromagnetic cross-responses. Quantum geometry is generalized to non-Hermitian systems and density matrices. In particular, the latter is quantum information geometry, where the quantum Fisher information naturally arises as a quantum metric. We apply these results to the X -wave magnets, which include d -wave, g -wave and i -wave altermagnets as well as p -wave and f -wave magnets. They have universal physics for anomalous Hall conductivity, tunneling magneto-resistance and planar Hall effects. We also study magneto-optical conductivity, magnetic circular dichroism and Friedel oscillations in the X -wave magnets. Various analytic formulas are derived in the case of two-band Hamiltonians. This paper presents a review of the recent progress together with some original results.

Xunan Wang, Xu Chen, Mengke Xu et al.

Quantum mechanics enables the generation of genuine randomness through its intrinsic indeterminacy. In device-independent (DI) and semi-device-independent (SDI) frameworks, randomness generation protocols can further ensure that the output remains secure and unaffected by internal device imperfections, with certification grounded in violations of generalized Bell inequalities. In this work, we propose an SDI randomness expansion protocol using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mspace width="-0.166667em"></mspace><mspace width="-0.166667em"></mspace><mo>→</mo><mspace width="-0.166667em"></mspace><mspace width="-0.166667em"></mspace><mn>1</mn></mrow></semantics></math></inline-formula> parity-oblivious quantum random access code (PO-QRAC), where the presence of true quantum randomness is certified through the violation of a two-dimensional quantum witness. For various values of <i>n</i>, we derive the corresponding maximal expected success probabilities. Notably, for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula>, the expected success probability obtained under our protocol exceeds the upper bound reported in prior work. Furthermore, we establish an analytic relationship between the certifiable min-entropy and the quantum witness value, and demonstrate that, for a fixed witness value, PO-QRAC–based protocols certify more randomness than those based on standard QRACs. Among all configurations satisfying the parity-obliviousness constraint, the protocol based on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mspace width="-0.166667em"></mspace><mspace width="-0.166667em"></mspace><mo>→</mo><mspace width="-0.166667em"></mspace><mspace width="-0.166667em"></mspace><mn>1</mn></mrow></semantics></math></inline-formula> PO-QRAC achieves optimal randomness expansion performance.

Kanhu Kishore Nanda, K. Narayan, Somnath Porey et al.

Abstract We develop further previous work on de Sitter extremal surfaces and time entanglement structures in quantum mechanics. In the first part, we first discuss explicit quotient geometries. Then we construct smooth bulk geometries with replica boundary conditions at the future boundary and evaluate boundary Renyi entropies in dS/CFT. The bulk calculation pertains to the semiclassical de Sitter Wavefunction and thus evaluates pseudo-Renyi entropies. In 3-dimensions, the geometry in quotient variables is Schwarzschild de Sitter. The 4-dim dS geometry involves hyperbolic foliations and is a complex geometry satisfying a regularity criterion that amounts to requiring a smooth Euclidean continuation. Overall this puts on a firmer footing previous Lewkowycz-Maldacena replica arguments based on analytic continuation for the extremal surface areas via appropriate cosmic branes. In the second part (independent of de Sitter), we study various aspects of time entanglement in quantum mechanics, in particular the reduced time evolution operator, weak values of operators localized to subregions, a transition matrix operator with two copies of the time evolution operator, autocorrelation functions for operators localized to subregions, and finally future-past entangled states and factorization. Based on these, we then give some comments on a cosmological transition matrix using the de Sitter Wavefunction.

Yihao Yang, Jijie Fu, Kai Mu et al.

Rotary flow focusing (RFF) is distinguished from conventional microfluidic platforms through its capacity to accommodate wide viscosity ranges in both continuous and dispersed phases during droplet formation. The dynamic mechanisms during droplet formation and the parametric dependencies within RFF systems are examined systematically. Four distinct flow modes, including squeezing, dripping, jetting and tip-streaming, are achieved by varying the rotational velocity and the dispersed-phase flow rate, and the corresponding transition boundaries are identified. In the squeezing and dripping modes, scaling laws are derived to predict droplet size based on interfacial dynamics during the breakup of the dispersed phase. In the jetting mode, functional relationships describing how jet diameter, droplet size and jet length depend on flow parameters are established through external flow field analysis. The tip-streaming mode facilitates the production of droplets at very small scale, with the effects of flow control parameters on droplet size quantitatively evaluated. Additionally, the effects of geometric parameters and fluid physical properties on RFF performance are investigated, enabling the successful production of high-viscosity fluid droplets ranging from micrometre to millimetre scales.

T. Azero˘glu, B.N. Örnek, T. Düzenli

In this paper, we investigate the geometric properties of a specific subclass of analytic functions satisfying  the condition f' (z) ≺ cosh(√ z) meaning that the function f '(z) is subordinate to the function cosh(√ z). Also, we focus on deriving sharp inequalities for Taylor coefficients, particularly for b2 and the modulus of the second derivative f''(z). Utilizing the Schwarz lemma, both on the unit disc and on its boundary, we provide essential insights into the distortion and growth behaviors of these functions. The paper demonstrates the sharpness of these inequalities through extremal functions and applies the Julia–Wolff lemma to establish boundary behavior results. These findings contribute significantly to the understanding of the analytic functions associated with the hyperbolic cosine function, with potential applications in geometric function theory. It is considered that the extremal functions obtained in this study could be potential hyperbolic activation functions in neural network architectures. This perspective builds a conceptual bridge between geometric function theory and artificial intelligence, indicating that insights from complex analysis can inspire the development of more effective and theoretically grounded activation mechanisms in deep learning. Empirical evaluation of architectures built with novel activation functions may be considered as potential future work.

Murat Yaylacı, Erdal Öner, G. Adıyaman et al.

Abstract Contact mechanics analysis is crucial because such problems often arise in engineering practice. When examining contact mechanics, the material property of the contacting components is a crucially significant aspect. It is more complex to solve the contact mechanics of systems that are composed of materials that do not have a homogenous structure compared to materials that have homogeneous qualities throughout. While many studies on contact problems with homogeneous materials exist, those involving non-homogeneous materials are scarce in the literature. As material technology improves fast, there will be a greater need to solve such problems. In this respect, analytical and finite element method (FEM) solutions of the continuous and discontinuous contact problems of a functionally graded (FG) layer are carried out in this article. The FG layer in the problem rests on a rigid foundation and is pressed with a rigid punch. From the solutions, the contact length, contact stress, initial separation distance, and beginning and ending points of separation were determined, and the results were compared. It has been concluded that the FEM findings are consistent with the analytical results to a satisfactory degree. This study analyzes contact problem using different approaches and accounts for the influence of body force in a contact geometry that has yet to be reported.

A. Ashyralyev, I.M. Ibrahim

Local and nonlocal boundary value problems (LNBVPs) related to fourth-order differential equations (FODEs) were explored. To tackle these problems numerically, we introduce novel compact four-step difference schemes (DSs) that achieve eighth-order of approximation. These DSs are derived from a novel Taylor series expansion involving five points. The theoretical foundations of these DSs are validated through extensive numerical experiments, demonstrating their effectiveness and precision.

G.Sh. Iskakova, M.S. Aitenova, A.K. Sexenbayeva

Parameters such as various integral and differential characteristics of functions, smoothness properties of regions and their boundaries, as well as many classes of weight functions cause complex relationships and embedding conditions for multi-weighted anisotropic Sobolev type spaces. The desire not to restrict these parameters leads to the development of new approaches based on the introduction of alternative definitions of spaces and norms in them or on special localization methods. This article examines the embeddings of multi-weighted anisotropic Sobolev type spaces with anisotropy in all the defining characteristics of the norm of space, including differential indices, summability indices, as well as weight coefficients. The applied localization method made it possible to obtain an embedding for the case of an arbitrary domain and weights of a general type, which is important in applications in differential operators’ theory, numerical analysis.

B.Sh. Kulpeshov, S.V. Sudoplatov

This article concerns the notion of weak circular minimality being a variant of o-minimality for circularly ordered structures. Algebras of binary isolating formulas are studied for countably categorical weakly circularly minimal theories of convexity rank greater than 1 having both a 1-transitive non-primitive automorphism group and a non-trivial strictly monotonic function acting on the universe of a structure. On the basis of the study, the authors present a description of these algebras. It is shown that there exist both commutative and non-commutative algebras among these ones. A strict m-deterministicity of such algebras for some natural number m is also established.

M.I. Akylbayev, I.E. Kaspirovich

The numerical solution of a system of differential equations with constraints can be unstable due to the accumulation of rounding errors during the implementation of the difference scheme of numerical integration. To limit the amount of accumulation, the Baumgarte constraint stabilization method is used. In order to estimate the deviation of real solution from the numerical one the method of constraint stabilization can be used to derive required formulas. The well-known technique of expansion the deviation function to Taylor series is being used. The paper considers the estimation of the error of the numerical solution obtained by the first-order Euler method.

O. Zienkiewicz, R. Taylor

M.O. Mamchuev

A boundary value problem in a rectangular domain for a system of partial differential equations with the Dzhrbashyan-Nersesyan fractional differentiation operators with constant coefficients is studied in the case when the matrix coefficients of the system have complex eigenvalues. Existence and uniqueness theorems for the solution to the boundary value problem under study are proved. The solution is constructed explicitly in terms of the Wright function of the matrix argument.

A.K. Attaev, M.I. Ramazanov, M.T. Omarov

The paper studies the problems of the correctness of setting boundary value problems for a loaded parabolic equation. The a feature of the problems is that the order of the derivative in the loaded term is less than or equal to the order of the differential part of the equation, and the load point moves according to a nonlinear law. At the same time, the distinctive characteristic is that the line, on which the loaded term is set, is at the zero point. On the basis of the study the authors proved the theorems about correctness of the studied boundary value problems.

K.Zh. Nazarova, K.I. Usmanov

In this paper we consider a boundary value problem for systems of Fredholm type integral-differential equations with involutive transformation, containing derivative of the required function on the right-hand side under the integral sign. Applying properties of an involutive transformation, original boundary value problem is reduced to a boundary value problem for systems of integral-differential equations, containing derivative of the required function on the right side under the integral sign. Assuming existence of resolvent of the integral equation with respect to the kernel K ˜2( t,s ) (this is the kernel of the integral equation that contains the derivative of the desired function) and using properties of the resolvent, integral-differential equation with a derivative on the right-hand side is reduced to a Fredholm type integral-differential equation, in which there is no derivative of the desired function on the right side of the equation. Further, the obtained boundary value problem is solved by the parametrization method created by Professor D. Dzhumabaev. Based on this method, the problem is reduced to solving a special Cauchy problem with respect to the introduced new functions and to solving systems of linear algebraic equations with respect to the introduced parameters. An algorithm to find a solution is proposed. As is known, in contrast to the Cauchy problem for ordinary differential equations, the special Cauchy problem for systems of integral-differential equations is not always solvable. Necessary conditions for unique solvability of the special Cauchy problem were established. By using results obtained by Professor D. Dzhumabaev, necessary and sufficient conditions for the unique solvability of the original problem were established.