Semi-analytical Results Research Articles

Nonleptonic B-meson decays to next-to-next-to-leading order

We compute next-to-next-to-leading order QCD corrections to the partonic processes b → cu¯d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ c\\overline{u}d $$\\end{document} and b → cc¯s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ c\\overline{c}s $$\\end{document}, which constitute the dominant decay channels in standard model predictions for B-meson lifetimes within the heavy quark expansion. We consider the contribution from the four-quark operators O1 and O2 in the ∆B = 1 effective Hamiltonian. The decay rates are obtained from the imaginary parts of four-loop propagator-type diagrams. We compute the corresponding master integrals using the “expand and match” approach which provides semi-analytic results for the physical charm and bottom quark masses. We show that the dependence of the decay rate on the renormalization scale is significantly reduced after including the next-to-next-to-leading order corrections. Furthermore, we compute next-to-next-to-leading order corrections to the Cabibbo-Kobayashi-Maskawa-suppressed decay channels b → uc¯s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ u\\overline{c}s $$\\end{document} and b → uu¯d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ u\\overline{u}d $$\\end{document}.

A perspective on conditional spectrum-based determination of response statistics of nonlinear systems

This work focuses on determining the stochastic response properties, in the frequency domain, of a general class of nonlinear systems with polynomial nonlinearities. Specifically, the results are presented in terms of the stationary power spectral densities of the system’s displacement and velocity. This is pursued by revisiting the conditional power spectrum concept, with the assumption that the response process is both ergodic and pseudo-harmonic and characterized by an amplitude, and a phase. A theoretical elucidation of an existing formula for the conditional spectrum is attempted. In particular, this concept is interpreted in conjunction with the time averaging approximation made in the definition of the stationary probability density function of a response amplitude quantity, associated with the original nonlinear system. It is shown that a proper definition of the stationary probability density of the response amplitude, along with a reasonable treatment of the distribution over the frequency domain of the amplitude contribution, lead to an improved approximation of the stationary response power spectral density. The treatment involves the averaging of a population of surrogate spectral densities of stationary random responses conforming with the system responses associated with individual values of the amplitudes of the responses. The semi-analytical results have been quite favourably juxtaposed with a large suite of à propos Monte Carlo simulations, both in terms of the shape and of the range of the involved germane frequencies, even for strongly nonlinear systems.

Dynamic Modelling and Performance Analysis of Deployable Telescopic Tubular Mast

AbstractThis work presents the longitudinal and transverse coupling vibrations of a deployable Telescopic Tubular Mast (TTM), a multi-stepped structure integrated into a spacecraft system, while considering the rigid-flexible coupling phenomenon. The model is derived using the principle of virtual work and discretized via the variable separation method. The von Kármán strain is employed to incorporate geometric nonlinear effects. Semi-analytical results for the shape functions and natural frequencies of the quasi-static multi-stepped boom are obtained using the extended transfer matrix method (ETMM). These natural frequencies are validated against results from Nastran, confirming the ETMM's accuracy. In addition, the model accounts for the continuously changing natural frequencies and shape functions during the deployment phase. Finally, the dynamic phenomena of the longitudinal and transverse displacements are analyzed at various deploying states, including locking and restart behaviors. The influence of the structural damping on the vibration evolution is also contained in the numerical analysis.

Dynamical and Secular Stability of Mutually Inclined Planetary Systems

Multiple analytical, semi-analytical, and empirical stability criteria have been derived in the literature for two-planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two-planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semimajor axis of the inner binary β = δ a 1/a 1 caused by perturbations from the companion. Stability criteria can be derived by setting a threshold on β. Focusing initially on circular orbits, we derive an analytical expression for β for coplanar prograde and retrograde orbits. For noncoplanar configurations, we evaluate a semi-analytical expression. We then generalize to orbits with arbitrary eccentricities and account for the secular effects. Our analytical and semi-analytical results are in excellent agreement with direct N-body simulations. In addition, we show that contours of β ∼ 0.01 can serve as criteria for stability. More specifically, we show that (1) retrograde orbits are generally more stable than prograde ones; (2) systems with intermediate mutual inclination are less stable due to von Ziepel–Lidov–Kozai (vZLK) dynamics; and (3) mean motion resonances (MMRs) can stabilize intermediate inclination secularly unstable regions in phase space, by quenching vZLK secular processes (4) MMRs can destabilize some of the dynamically stable regions. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems and their age.

Efficient entanglement purification based on noise guessing decoding

In this paper, we propose a novel bipartite entanglement purification protocol built upon hashing and upon the guessing random additive noise decoding (GRAND) approach recently devised for classical error correction codes. Our protocol offers substantial advantages over existing hashing protocols, requiring fewer qubits for purification, achieving higher fidelities, and delivering better yields with reduced computational costs. We provide numerical and semi-analytical results to corroborate our findings and provide a detailed comparison with the hashing protocol of Bennet et al. Although that pioneering work devised performance bounds, it did not offer an explicit construction for implementation. The present work fills that gap, offering both an explicit and more efficient purification method. We demonstrate that our protocol is capable of purifying states with noise on the order of 10% per Bell pair even with a small ensemble of 16 pairs. The work explores a measurement-based implementation of the protocol to address practical setups with noise. This work opens the path to practical and efficient entanglement purification using hashing-based methods with feasible computational costs. Compared to the original hashing protocol, the proposed method can achieve some desired fidelity with a number of initial resources up to one hundred times smaller. Therefore, the proposed method seems well-fit for future quantum networks with a limited number of resources and entails a relatively low computational overhead.

Heavy-to-light form factors to three loops

We compute three-loop corrections of O(αs3) to form factors with one massive and one massless quark coupling to an external vector, axialvector, scalar, pseudoscalar, or tensor current. We obtain analytic results for the color-planar contributions, for the contributions of light-quark loops, and the contributions with two heavy-quark loops. For the computation of the remaining master integrals we use the “expand and match” approach which leads to semianalytic results for the form factors. We implement our results in a and a ortran code which allows for fast and precise numerical evaluations in the physically relevant phase space. The form factors are used to compute the hard matching coefficients in Soft-Collinear Effective Theory for all currents. The tensor coefficients at lightlike momentum transfer are used to extract the hard function in B¯→Xsγ to three loops. Published by the American Physical Society 2024

A perturbative treatment of the Yarkovsky-driven drifts in the 2:1 mean motion resonance

Aims. Our aim is to gain a qualitative understanding as well as to perform a quantitative analysis of the interplay between the Yarkovsky effect and the Jovian 2:1 mean motion resonance under the planar elliptic restricted three-body problem. Methods. We adopted the semi-analytical perturbation method valid for arbitrary eccentricity to obtain the resonance structures inside the Jovian 2:1 resonance. We averaged the Yarkovsky force so it could be applied to the integrable approximations for the 2:1 resonance and the ν5 secular resonance. The rates of Yarkovsky-driven drifts in the action space were derived from the quasi-integrable approximations perturbed by the averaged Yarkovsky force. Pseudo-proper elements of test particles inside the 2:1 resonance were computed using N-body simulations incorporated with the Yarkovsky effect to verify the semi-analytical results. Results. In the planar elliptic restricted model, we identified two main types of systematic drifts in the action space: (Type I) for orbits not trapped in the ν5 resonance, the footprints are parallel to the resonance curve of the stable center of the 2:1 resonance; (Type II) for orbits trapped in the ν5 resonance, the footprints are parallel to the resonance curve of the stable center of the ν5 resonance. Using the semi-analytical perturbation method, a vector field in the action space corresponding to the two types of systematic drifts was derived. The Type I drift with small eccentricities and small libration amplitudes of 2:1 resonance can be modeled by a harmonic oscillator with a slowly varying parameter, for which an analytical treatment using the adiabatic invariant theory was carried out.

Predicting delamination in composite laminates through semi-analytical dynamic analysis and vibration-based quantitative assessment

Delamination is a frequent failure mode of laminated fiber-reinforced polymer (FRP) composites structure in aeronautical and other industries, leading to changes in vibration characteristics. Vibration-based techniques evaluate and compare the dynamic response between damaged and undamaged structures, and guarantee the non-destructive measurement with reliability and repeatability. Previous studies typically concentrate on using finite element method to obtain vibration characteristics and enhance the database for intelligent algorithms. This paper presents a semi-analytical result using the Chebyshev−Ritz method to expand delamination prediction. Vibration frequency serves as a global damage indicator, and multi-order frequency characteristics are utilized to identify the delamination length and location of FRP composite plates. A database of natural frequencies corresponding to damage parameters for FRP laminated plates is generated based on the established model using the region approach. An intelligent approach, known as a genetic algorithm optimization-based back-propagation (GA-BP) artificial neural network, is utilized for system identification. The network model is subjected to a sensitivity analysis, where artificial noise is added to vibration frequency to distinguish between the actual structure and the numerical model. The results indicate that the GA-BP algorithm shows good accuracy and stable performance against the standard neural networks for delamination analysis.

Three-loop corrections to Higgs boson pair production: reducible contribution

We compute three-loop corrections to the process gg → HH originating from one-particle reducible diagrams. This requires the computation of two-loop corrections to the gluon-gluon-Higgs vertex with an off-shell gluon. We describe in detail our approach to obtain semi-analytic results for the vertex form factors and present results for the two form factors contributing to Higgs boson pair production.

Semi-analytical results for transient poroelastic behavior of a functionally graded hollow sphere

This paper provides semi-analytical results for transient poroelastic behaviors of a functionally graded hollow sphere that are lacking in the present literature. The whole medium is theoretically approximated by a spherical multilayer structure. Each layer is treated as a homogeneous spherical shell. The solutions are first explicitly obtained in Laplace space, and then the advanced Stehfest’s inversion method is employed to transform these results into the time domain. Numerical examples are provided to demonstrate the validity of the proposed method against the most relevant results given in literature. These validations are for some particular cases where literature results exist, but the capacity of this model is beyond those validation cases. Besides, sensitivity analysis demonstrates the significant impact of radial variations in poroelastic properties on the resulting mechanical fields. These findings are extremely important for validating the correctness and the convergence of sophisticated 3D finite element/finite volume software.

A study using a semi-analytical approach to the reaction kinetics that describes the behavior of heterogeneous reaction–diffusion process with a glyoxyl-agarose immobilized enzyme (penicillin G acylase) in a batch reactor

This research article examines the reaction–diffusion process in a batch reactor by means of immobilized penicillin G acylase (PGA) with a glyoxyl-agarose matrix support. This study employs the Akbari-Ganji’s Method (AGM) when the system is under the internal (intra-particle) diffusional restrictions, and the external (film) diffusional restrictions is negligible. The semi-analytical approximations by the AGM technique are employed for computing the dimensionless steady-state solutions for a system of nonlinear differential equations to examine the impact of internal diffusional restrictions (IDR) as a function of catalyst enzyme loading and particle size. The model entails highly nonlinear components that adhere to the standard Michaelis-Menten kinetics. In addition to the proposed model, the dynamics for the mean integrated effectiveness factor (MIEF) of the dimensionless substrate concentration phenylglycine methyl ester (PGME) is presented. In light of this, there is a satisfactory level of agreement on the comparison of the semi-analytical result with the simulated numerical results across the whole concentration range where the dimensionless initial substrate and product concentrations are S1b=30,S2b=15, and P1b=60,P2b=100. The behavior of concentration profiles under the steady/unsteady state conditions for the effect of IDR on the overall reaction rates by immobilized biocatalyst PGA were examined. A sensitivity analysis is carried out to identify the effective parameter which can influence the diffusional restrictions on MIEF. An error analysis is performed on the dimensionless concentration equations to assess the amount of accuracy and the convergence of a solution.

Comparison of unsteady MHD flow of second grade fluid by two fractional derivatives

A study is conducted on the unsteady motion of a free convective flow of second grade fluid, energy transfer, and Darcy’s law over an oscillatory smooth vertical plate. The study compares two different approaches in developing a fractional model: the Caputo-Fabrizio operator with nonsingular kernel and the constant proportional Caputo fractional operator with Fourier’s and Fick’s laws. By applying the Laplace method and transforming the provided set of equations into nondimensional form, we obtained semi-analytical results and presented these results through graphical analysis. The study examines how different flow parameters, including the fractional parameters, affect the velocity, mass, and heat profiles of the physical system. The results suggest that the physical model using constant proportional Caputo derivative leads to higher temperature, stronger concentration, and increased velocity compared to the Caputo-Fabrizio model. This highlights the importance of selecting an appropriate fractional model when studying complex physical systems. It is also depicted from the whole analysis that field variables with novel hybrid fractional derivative constant proportional Caputo exhibits a more effective and declining tendency than Caputo-Fabrizio.

Size–mass relation of the brightest cluster galaxies at z ∼ 1

ABSTRACT We present the size–mass relation of the brightest cluster galaxies (BCGs) at 0.1 < z < 1.4 using the imaging data obtained by the Hyper Suprime-Cam Subaru Strategic Program. Our sample consists of 471 photometrically selected BCGs with stellar mass logM*/M⊙ = 11–12. We measure the size of the BCGs using i-band imaging and model fits based on a single Sérsic light profile. Stellar masses are determined through spectral energy distribution fitting using Sérsic-modelled photometry data across five optical bands (grizy). The size–mass scaling relation of BCGs is $r_\mathrm{ e}\propto M_*^{0.73-1.00}$ at z < 1, with a slope that does not evolve significantly. The slope of the size–mass relation for BCGs is steeper than other non-BCG galaxies, which implies that BCGs are a special galaxy population. The size of BCGs at a given stellar mass evolves rapidly as ∝ (1 + z)−1.58 ± 0.13 and increases with redshift by a factor of 2.5 from z ∼ 1.2 to z ∼ 0.2. The rapid size growth is in agreement with semi-analytical model results, indicating that the BCG growth is dominated by frequent minor mergers. Furthermore, we explore the size–mass relationship of BCGs with respect to the halo mass of the cluster and find there is no significant correlation, which might imply that a dependence on the environment predominantly affects the outer envelope of the BCGs.

Virialized profiles and oscillations of self-interacting fuzzy dark matter solitons

We investigate the effect of self-interactions on the shape and oscillations of the solitonic core profile of condensed fuzzy dark matter systems without the backdrop of a halo, revealing universal features in terms of an appropriately scaled interaction strength characterizing the crossover between the weakly and strongly interacting regimes. Our semianalytical results are further confirmed by spherically symmetric simulations of the Gross-Pitaevskii-Poisson equations. Inverting our obtained relations, we highlight a degeneracy that could significantly affect constraints on the boson mass in the presence of repulsive boson self-interactions and propose the simultaneous extraction of static and dynamical solitonic features as a way to uniquely constrain both the boson mass and self-interactions. Published by the American Physical Society 2024

Smoothing in linear multicompartment biological processes subject to stochastic input.

Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before the eventual accumulation and release of replicated virions. While such systems may have some control over the internal dynamics that make up this progression, a challenge for many is to regulate behavior under what are often highly variable external environments acting as system inputs. In this work, we study a simple analog of this problem through a linear multicompartment model subject to a stochastic input in the form of a mean-reverting Ornstein-Uhlenbeck process, a type of Gaussian process. By expressing the system as a multidimensional Gaussian process, we derive several closed-form analytical results relating to the covariances and autocorrelations of the system, quantifying the smoothing effect discrete compartments afford multicompartment systems. Semianalytical results demonstrate that feedback and feedforward loops can enhance system robustness, and simulation results probe the intractable problem of the first passage time distribution, which has specific relevance to eventual cell lysis in the viral replication cycle. Finally, we demonstrate that the smoothing seen in the process is a consequence of the discreteness of the system, and does not manifest in systems with continuous transport. While we make progress through analysis of a simple linear problem, many of our insights are applicable more generally, and our work enables future analysis into multicompartment processes subject to stochastic inputs.

Improving the rheological behavior of magnetiz couple stress Buongiorno's nanofluid through resilient wavy channel with curvature effect: Nonlinear analysis

In biological systems, fluids with complex rheological behavior often encounter complex microenvironments. Couple stress fluids can be applied to model the flow of biological fluids in micro-vessels, capillaries, and other intricate structures. Couple stress fluids can be employed to model drug transport in microfluidic devices and capillaries, providing insights into the behavior of pharmaceuticals at small scales. Studying the couple stress fluids is crucial, particularly when considering the impact of particle viscosity in the existence of induced magnetic fields and nanoparticles that might enhance the characteristic motion. So, we studied the moderate and magnetic Reynold numbers and curvature effects of magnetized couple stress Buongiorno's nanofluid model through resilient wavy channel. The governing equations of this model are formed in non-dimensional form without any approximation, i.e., in the companionship of moderate Reynolds number and curvature effect, which aren't studied in this form. Using the Adomian decomposition approach, it is possible to obtain a solution of nonlinear system of partial differential equations analytically. The semi-analytical results are obtained and represented graphically for characteristic motion and bio-thermal properties for temperature and concentration, as well as magnetic features. Physically, by rising the magnetic Reynolds number, the magnetic permeability raises, so the ability of the couple stress fluid to form an internal magnetic field within itself with the impact of an applied magnetic field increases, which increases the magnetic force.

Semi-analytic modeling and experimental verification of arbitrary aero-engine complex spatial pipeline

In-depth research is imperative for complex spatial pipelines with fluid-structure interaction. A comprehensive and universal three-dimensional semi-analytical modeling method is first established for complex fluid-conveying spatial pipelines under the base excitation with arbitrary connections and configurations under different boundary conditions. The virtual spring technology is used to connect the straight and curved pipeline segments with spatial angles and simulate boundary conditions. For a thorough analysis, the actual stiffness of the bracket-clamp system is experimentally measured for the first time. The multi-level coupling dynamic model of part, component, and system levels under actual boundary conditions is established. An efficient method for solving the fluid-structure coupling pipeline system dynamics considering the base excitation is proposed based on energy method. The mid-plane displacement function of the Fourier series is introduced and solved using the principle of modal superposition. Hammer impact modal experiments, ANSYS software and vibration response experiments are performed on spatial pipelines supported by flexible bracket-clamps; the numerical and experimental results support the semi-analytical results. The degenerate model is verified with the simple plane pipelines in other references, and the errors are less than 5 %. The proposed method exhibits broad applicability and generalizability, making it suitable for various configurations and boundary conditions.

Non-Fourier Heat Flux Model for the Magnetohydrodynamic Casson Nanofluid Flow Past a Porous Stretching Sheet using the Akbari-Gangi Method

The Casson fluid flow with porous material in magnetohydrodynamics is examined in this work. Additional semi-analytical results are investigated using the Silver-Water nanofluid. The Akbari-Ganji Method (AGM) is used to solve the semi-analytical Cattaneo-Christov heat flux model after taking thermal radiation into account. With the use of appropriate parameters, such as the relaxation time parameter, Prandtl number, radiation parameter, magnetic parameter, and so on, the normalized shear stress at the wall, temperature profile, and rate of heat flux may be examined. This issue has numerous industrial applications and technical procedures, such as the extrusion of rubber sheets and the manufacture of glass fiber. The main physical application is the discovery that a rise in the thermal relaxation parameter and Prandtl number maintains a constant fluid temperature.

Transient electrophoresis of a conducting cylindrical colloidal particle suspended in a Brinkman medium

The time-dependent electrophoresis of an infinitely cylindrical particle in an electrolyte solution, saturated in a charged porous medium after the sudden application of a transverse or tangential step electric field, is investigated semi-theoretically with an arbitrary double-layer thickness in an arbitrary direction relative to the cylinder. The time-dependent modified Brinkman equation with an electric force term, which governs the fluid flow field, is used to model the porous medium and is solved by using the Laplace transform technique. Explicit formulas, for the time-dependent electrophoretic velocity of the cylindrical particle in Laplace’s transform domain, have been derived for both axially and transversely when the uniform electric fields are imposed. They can also be linearly superimposed for an arbitrarily oriented relative to the electric field. Semi-analytical results for the electrophoretic velocities are presented as functions of the dimensionless elapsed time, the ratio of the particle radius to the Debye length, the particle-to-medium density ratio, and the permeability parameter of the porous medium. The results demonstrate, in general, that the growth of the electrophoretic velocities with the time scale are more slower for high permeability, and the effect of the relaxation time for unsteady electrophoresis is found to be negligible, regardless of the thickness of the double layer, the relative mass density or the permeability of the medium. The normalized transient electrophoretic velocities exhibit a consistent upward trend as the ratio of the particle radius to the Debye screening length increases. Conversely, they display a consistent downward trend as the particle-to-fluid density ratio increases, while all other parameters remain constant. The effect of the relaxation time for the transient electrophoresis is much more important for a cylindrical particle than for a spherical particle due to its smaller specific surface area.

Dynamic terahertz beamforming based on magnetically switchable hyperbolic materials

In this work, we introduce a concept to enable dynamic beamforming of terahertz (THz) wavefronts using applied magnetic fields (B). The proposed system exploits the magnetically switchable hyperbolic dispersion of the InSb semiconductor. This phenomenology, combined with diffractive surfaces and magnetic tilting of scattered fields, allows the design of a metasurface that works with either circularly or linearly polarized wavefronts. In particular, we demonstrate numerically that the transmitted beam tilting can be manipulated with the direction and magnitude of B. Numerical results, obtained through the finite element method, are qualitatively supported by semi-analytical results from the generalized dipole theory. Motivated by potential applications in future Tera-WiFi active links, a metasurface is simulated for the working frequency f = 300 GHz. The results indicate that the transmitted field can be actively tuned to point in five different directions with beamforming of ±45∘ , depending on the magnitude and direction of B. In addition to magnetic beamforming, we also demonstrate that our proposal exhibits magnetic circular dichroism, which can also find applications in magnetically tunable THz isolators for one-way transmission/reflection.