Analytical Expressions Research Articles

Influence of magnetohydrodynamics and chemical reactions on oscillatory free convective flow through a vertical channel in a rotating system with variable permeability

This study investigates the impact of variable permeability as well as chemical reactions on the oscillatory free convective flow that passes parallel porous flat plates with fluctuating temperature and concentration in the presence of a magnetic field. A vertical channel is assumed to be rotating at an angular velocity [Formula: see text]. Periodic free stream velocity causes oscillations in one plate, while periodic suction velocity causes oscillations in the other plate. Complex variable notations are used to solve the governing equations. The perturbation technique is used to derive analytical expressions for the temperature, concentration, and velocity fields. In this study, various parameters were investigated in relation to mean velocity, mean temperature, mean concentration, amplitude, and phase difference. The study also examines the impact on secondary velocity, primary velocity, temperature, concentration, and heat transfer rate during transients. The outcomes are presented graphically for the physical parameters of the problem. The findings contribute to optimizing systems and improving efficiency in heat transfer, fluid dynamics, and environmental remediation.

Improving approximation accuracy in Godunov-type smoothed particle hydrodynamics methods

The study examines the origin of errors resulting from the approximation of the right hand sides of the Euler equations using the Godunov type contact method of smoothed particle hydrodynamics (CSPH). The analytical expression for the numerical shear viscosity in CSPH method is obtained. In our recent study the numerical viscosity was determined by comparing the numerical solution of momentum diffusion in the shear flow with theoretical one. In this study we deduce the analytical expression for the numerical viscosity which is found to be similar to numerical one, confirming the obtained results. To reduce numerical diffusion, diffusion limiters are typically applied to expressions for contact values of velocity and pressure, as well as higher-order reconstruction schemes. Based on the performed theoretical analysis, we propose a new method for correcting quantities at interparticle contacts in CSPH method, which can be easily extended to the MUSCL-type (Monotonic Upstream-centered Scheme for Conservation Laws) method. Original CSPH and MUSCL-SPH approaches and ones with aforementioned correction are compared.

Two-component nonlinear waves

The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary waves in the different areas of physics. Using the generalized perturbation reduction method the explicit analytical expressions for the shape and parameters of two-component nonlinear wave is presented. This nonlinear wave solution coincides with the vector 0π pulse of the self-induced transparency.

Physical understanding of a normally off p-GaN/AlGaN/GaN HEMT gate stack and a review of VTH measurement techniques

Abstract In this report a comprehensive review of the variations in threshold voltage (VTH) resulting from diverse VTH measurement bias conditions employed by leading manufacturers, as well as VTH extraction techniques is made. Notably, a standard deviation of 15% is observed in threshold voltage values due to variations in measurement bias conditions. This variation is attributed to the change in the lateral electic field conditions across gate and drain which occurs due to the change in bias conditions. Additionally, a simplified physical interpretation of the gate stack in p-GaN gate normally-off AlGaN/GaN on Si HEMTs is made. The formation of the two-dimensional electron gas (2DEG), the charge balance within the pGaN/AlGaN/GaN gate stack, and an analytical expression for threshold voltage are examined. Furthermore, various trapping mechanisms within the gate stack are reviewed to comprehend the dynamic conditions potentially contributing to threshold voltage instability during nominal operation.

Charge Carrier Density in Organic Semiconductors Modulates the Effective Capacitance: A Unified View of Electrolyte Gated Organic Transistors.

A framework for electrolyte-gated organic transistors (EGOTs) that unifies the view of interfacial capacitive coupling of electrolyte-gated organic field-effect transistors (EGOFETs) with the volumetric capacitive coupling in organic electrochemical transistors (OECTs) is proposed. The EGOT effective capacitance arises from in-series capacitances of the electrolyte/gate electrode and electrolyte/channel interfaces, and the chemical capacitance of the organic semiconductor channel whose weight with respect to the interfacial capacitance is modulated by the charge carrier density, hence by the gate voltage. The expression for chemical capacitance is derived from the DOS of the organic semiconductor, which it is assumed to exhibit exponential energy disorder in the HOMO-LUMO gap. The analytical expression of the EGOT current is assessed on experimental data and shown to accurately predict the shape of the whole transfer curve of an EGOT thus allowing to extract accurate values for the switch-on voltage and the interfacial transconductance, without assumptions on specific response regime and, in OECT, without invoking the volumetric capacitance. Interestingly, the EGOT model recovers EGOFET and OECT as limit cases and, in the latter case, explicitly represents the volumetric capacitance in terms of the energy disorder and the bandgap of the organic semiconductor.

A direct approach for solving the cubic Szegö equation

AbstractWe study the cubic Szegö equation which is an integrable nonlinear nondispersive and nonlocal evolution equation. In particular, we present a direct approach for obtaining the multiphase and multisoliton solutions as well as a special class of periodic solutions. Our method is substantially different from the existing one which relies mainly on the spectral analysis of the Hankel operator. We show that the cubic Szegö equation can be bilinearized through appropriate dependent variable transformations and then the solutions satisfy a set of bilinear equations. The proof is carried out within the framework of an elementary theory of determinants. Furthermore, we demonstrate that the eigenfunctions associated with the multiphase solutions satisfy the Lax pair for the cubic Szegö equation, providing an alternative proof of the solutions. Last, the eigenvalue problem for a periodic solution is solved exactly to obtain the analytical expressions of the eigenvalues.

Mathematical Analysis of Four Fundamental Epidemiological Models for Monkeypox Disease Outbreaks: On the Pivotal Role of Human–Animal Order Parameters—In Memory of Hermann Haken

Four fundamental models that describe the spread of Monkeypox disease are analyzed: the SIR-SIR, SEIR-SIR, SIR-SEIR, and SEIR-SEIR models. They form the basis of most Monkeypox diseases models that are currently discussed in the literature. It is shown that the way the model subpopulations are organized in disease outbreaks and evolve relative to each other is determined by the relevant unstable system eigenvectors, also called order parameters. For all models, analytical expressions of the order parameters are derived. Under appropriate conditions these order parameters describe the initial outbreak phases of exponential increase in good approximation. It is shown that all four models exhibit maximally two order parameters and maximally one human–animal order parameter. The human–animal order parameter firmly connects the outbreak dynamics in the animal system with the dynamics in the human system. For the special case of the SIR-SIR model, it is found that the two possible order parameters completely describe the dynamics of infected humans and animals during entire infection waves. Finally, a simulation of a Monkeypox infection wave illustrates that in line with the aforementioned analytical results the leading order parameter explains most of the variance in the infection dynamics.

Quasi-Diabatization Based on Minimizing Derivative Couplings in a Limited Configuration Space: Elimination of Boundary Condition Dependence.

Due to the cuspidal ridges of adiabatic potential energy surfaces (PESs) and singularities of nonadiabatic couplings (NACs), obtaining an analytical expression for the adiabatic Hamiltonian is difficult. Thereby, nonadiabatic dynamics simulations are often carried out on-the-fly, which is time-consuming. This motivates us to construct quasi-diabatic representations, which have smooth PESs and diabatic couplings. In this study, we propose a new quasi-diabatization method based on minimizing derivative couplings (MDC) in a limited configuration space. The boundary conditions are first considered and finally released to obtain the adiabatic-to-diabatic rotation angles and transformation matrices. As demonstrated in representative one- and two-dimensional models and the widely studied linear H3 molecule, MDC performs significantly better than the direct integration quasi-diabatization approach. In particular, accurate diabatic potential energy matrices have been successfully obtained even when the NACs of all configurations in the considered space are nonnegligible.

Different States of water in α-Cyclodextrin hydrates

The pressure of saturated and unsaturated water vapor over α-CD·nH2O hydrates has been measured by static method with membrane-gauge manometer under conditions of complete loss of water. The temperature dependences of water vapor pressure have been obtained in the wide range of temperatures (287–469 K), pressures (0.04–34.95 kPa) and water content (0.17 ≤ n ≤ 6.0).The data obtained indicate the presence of water molecules with different volatility in α-CD·nH2O hydrates. Water molecules with lower volatility can be considered “external”, included in the network of intermolecular hydrogen bonds, while water molecules with higher volatility, discovered in our previous study, are considered “internal”, presumably located in the α-CD cavity. For each composition, the amount of “external” and “internal” water has been determined and the equations described the dependence of the content of each type of water on n in α-CD·nH2O have been obtained. The analytical expressions for the lnp – 1/T dependences as well as the values of enthalpy and entropy of processes studied have been calculated. Experimental data were used to obtain the Gibbs energy changes when “external” water molecules bind to the α-CD framework. The values obtained are differed from the values for “internal” water given in our previous study. The phase transition in α-CD·nH2O revealed in our previous study is also observed in this work and its thermodynamic characteristics are in good agreement with the results obtained earlier. The findings have been confirmed by 1H NMR studies.

An Improved Physics-Based Dual-Band Model for Satellite-Derived Bathymetry Using SuperDove Imagery

Shallow water bathymetry is critical for environmental monitoring and maritime security. Current widely used statistical models based on passive optical satellite remote sensing often rely on prior bathymetric data, limiting their application to regions lacking such information. In contrast, the physics-based dual-band log-linear analytical model (P-DLA) can estimate shallow water bathymetry without in situ measurements, offering significant potential. However, the quasi-analytical algorithm (QAA) used in the P-DLA is sensitive to non-ideal pixels, resulting in unstable bathymetry estimation. To address this issue and evaluate the potential of SuperDove imagery for bathymetry estimation in regions without prior bathymetric data, this study proposes an improved physics-based dual-band model (IPDB). The IPDB replaces the QAA with a spectral optimization algorithm that integrates deep and shallow water sample pixels to estimate diffuse attenuation coefficients for the blue and green bands. This allows for more accurate estimation of shallow water bathymetry. The IPDB was tested on SuperDove images of Dongdao Island, Yongxing Island, and Yongle Atoll. The results showed that SuperDove images are capable of estimating shallow water bathymetry in regions without prior bathymetric data. The IPDB achieved Root Mean Square Error (RMSE) values below 1.7 m and R2 values above 0.89 in all three study areas, indicating strong performance in bathymetric estimation. Notably, the IPDB outperformed the standard P-DLA model in accuracy. Furthermore, this study outlines four sampling principles that, when followed, ensure that variations in the spatial distribution of sampling pixels do not significantly impact model performance. This study also showed that the blue–green band combination is optimal for the analytical expression of the physics-based dual-band model.

Analytical expressions of the dynamic magnetic power loss under alternating or rotating magnetic field

Analytical methods are recommended for rapid predictions of the magnetic core loss as they require less computational resources and offer straightforward sensitivity analysis. This paper proposes analytical expressions of the dynamic magnetic power loss under an alternating or rotating magnetic field. The formulations rely on fractional derivative analytical expressions of trigonometric functions. The simulation method is validated on extensive experimental data obtained from state-of-the-art setups and gathered in the scientific literature. Five materials are tested for up to at least 1 kHz in both alternating and rotating conditions. The relative Euclidean distance between the simulated and experimentally measured power loss is lower than 5 % for most tested materials and always lower than 10 %. In standard characterization conditions, i.e., sinusoidal flux density, the dynamic power loss contribution under a rotating magnetic field is shown to be precisely two times higher than an alternating one. The knowledge of electrical conductivity reduces the dynamic magnetic power loss contribution to a single parameter (the fractional order). This parameter has the same value for a given material's rotational and alternating contribution. This study confirms the viscoelastic behavior of the magnetization process in ferromagnetic materials and, consequently, the relevance of the fractional derivative operators for their simulation.

Gravitational lensing in holonomy corrected spherically symmetric black holes with phantom global monopoles

In this paper, we address a theoretical investigation of the gravitational lensing phenomenon within the space-time framework of a holonomy-corrected spherically symmetric black hole (BH), incorporating both ordinary and phantom global monopoles. Our focus lies on the analysis of null geodesics within this BH background, examining the influence of ordinary and phantom global monopoles on the effective potential of null geodesics of the system. Afterwards, we derive analytical expressions for the deflection angle of photon light, considering weak field limit. The obtain expressions are presented up to the second order of the Loop Quantum Gravity parameter, enabling a thorough examination of the impact of ordinary and phantom global monopoles on the deflection angle.

Nonlinear effects of partitioning and diffusion limitation on the efficiency of three-layer enzyme bioreactors and potentiometric biosensors

The nonlinear effects of the partitioning and diffusion limitation on the efficiency of enzyme-based bioreactors and potentiometric biosensors are investigated analytically and numerically using a three-layer mathematical model involving the Michaelis–Menten type reaction in the transient and steady states. Analytical expressions of the steady state substrate and reaction product concentrations and the bioreactor effectiveness as well as biosensor output potential are presented for the first and zero-order reaction rates. Mathematical modelling of the diffusion limiting membrane and the conditions under which the same values of the steady state characteristics are obtained when simulating the treated system at different values of the diffusion and distribution coefficients are investigated. The effective diffusion coefficients in the total diffusion layer consisting of the diffusion limiting membrane and the outer diffusion (Nernst) layer are applied to reduce the three-layer model to the corresponding two-layer model. The dynamics and behaviour of the substrate consumption rate, product emission rate, effectiveness factor and the output potential are numerically investigated.

Two-photon absorption in silicon using the real density matrix approach.

Two-photon absorption in indirect gap semiconductors is a frequently encountered, but not well-understood phenomenon. To address this, the real-density matrix approach is applied to describe two-photon absorption in silicon through the excitonic response to the interacting fields. This approach produces an analytical expression for the dispersion of the two-photon absorption coefficient for indirect-gap materials and can be used to explain trends in reported experimental data for bulk silicon both old and new with minimal fitting.

Holographic bounce cosmological models induced by viscous dark fluid from a generalized non-singular entropy function

Bounce cosmological models containing a dark viscous fluid in a spatially flat Friedmann–Robertson–Walker (FRW) universe are considered. The universe’s evolution is described in terms of generalized equation of state (EoS) parameters, in the presence of the bulk viscosity. Entropic cosmology plays a key role in the discussion, and the matter bounce behavior is described based on a nonsingular, generalized entropy function, recently proposed by S. D. Odintsov and T. Paul. Three different forms of the scale factor are investigated: an exponential, a power-law and a double-exponential function, respectively. Appropriate bounce cosmological models are formulated, via the relevant parameters of the modified EoS, and analytical expressions for the corresponding infrared cut-off are obtained, via the particle horizon. Results are displayed in holographic form, making use of generalized holographic cut-offs first introduced by S. Nojiri and S. D. Odintsov. In addition, the viability of the corresponding bounce cosmological models is investigated, taking into account the actual thermodynamic properties of our universe, by means of a no-singular, generalized entropy function. In the asymptotic case, an expression for the generalized entropy is obtained, which remarkably has the additivity property.

Heterogeneous beliefs and short selling taxes: A note

Short selling is widespread in financial markets but regulators can ban short positions. The intermediate policy of taxing short sellers has been studied in an asset pricing model with evolutionary competition of two belief types (Anufriev and Tuinstra, 2013). We extend this approach to an arbitrary number of belief types H, giving 3H−2H cases to check each period in the worst-case scenario. We provide analytic expressions for asset prices along with conditions on beliefs (optimism) that determine which types take long, short or zero asset positions at the market-clearing price. We use these results to construct a fast solution algorithm (quadratic in H) which can solve models with hundreds or thousands of types in a matter of seconds. A numerical example with a short-selling tax and many heterogeneous beliefs in evolutionary competition shows that price dynamics can differ substantially relative to the benchmark of few types.

Optical Möbius strips in isotropic random non-paraxial light

Abstract The statistics of Möbius strips with various topologies, formed by the axes of polarization ellipses as they are traced along a closed circular contour of small size passing through the center of a solitary circular polarization singularity line (C-line), have been investigated both analytically and numerically in a random isotropic electromagnetic field. Found are the analytical expressions for the joint probability density function of the differential characteristics of the random isotropic electromagnetic field, which allow for the determination of the topological properties of diagrams of polarization ellipses and the normal vectors to them, as well as the optical strips that arise in the space around C-lines.

METHODOLOGY FOR NUMERICAL MODELING OF DETERMINING THE VALUES OF CONDITIONAL PROBABILITIES OF HITTING AIR TARGETS WHEN FIRING A MISSILE WITH A TELEVISION OPTICAL SIGHT OF A COMBAT VEHICLE

The article presents a methodology for numerical modeling of determining the values of conditional probabilities of hitting air targets when firing a missile with a combat vehicle's television optical sight. The conditional probabilities of hitting air targets are associated with the sloping range to the far limit of the kill zone of an anti-aircraft missile system. The effectiveness of the use of an anti-aircraft missile system with a television optical sight depends on the plane of air targets, the picture plane of firing, and the conditions of missile firing. The following factors were taken into account in the modeling: the color of air targets, the meteorological range of atmospheric visibility, the quality of combat performance of the combat vehicle personnel, and sunlight. The calculations take into account the technical characteristics of the stations and systems of the combat vehicle and missile. The values of the first kind of missile firing errors are presented, namely, the systematic components of the first kind of missile firing errors and their standard deviations of errors depending on the far limit of the kill zone of the anti-aircraft missile system. It is shown that the systematic component of the dynamic first-order missile firing errors increases due to the maneuvering of air targets, provided that the standard deviation of the first-order missile firing errors during the maneuvering of air targets remains unchanged. The values of the standard deviations of the first kind of missile firing errors depending on the far limit of the kill zone of the anti-aircraft missile system are given, taking into account the influence of interference on the combat vehicle's reconnaissance radar station and optical interference on the channel of the combat vehicle's television optical sight. The parameters of the first kind of missile firing errors, i.e., the values of the probabilities of the missile passing through the “tube” of the required radius of operation of the missile's radio fuse, were found. The values of the second kind of missile firing errors, namely the conditional probabilities of the missile's radio fuse, are considered. The mathematical expectation of the random value of the radius of the missile's radio fuse, which corresponds to air targets under the specified conditions, is established. The values of conditional probabilities of hitting various air targets under various conditions of firing at the far edge of the kill zone of the anti- aircraft missile system are analyzed and calculated. The obtained analytical expressions for the numerical modeling technique and the corresponding graphical material are presented.

Spin dynamics of 2-DEG Rashba-Dresselhaus spin-orbit systems: Quantum propagators and semi-analytical analysis in low electron density.

Abstract The spin dynamics in space and time for Dresselhaus and Rashba spin-orbit interaction 2-DEG systems can be studied for any value of their β and α coefficients by using quantum propagators. With the development of analytical expressions for the quantum propagators and numerical solutions of the wave function, it has been possible to simulate the spin propagation in space-time and analyze the spin dynamics for different α/β ratios. In the present paper, the effects of the spin diffusion for large collision time τp, was performed by using quantum propagators for different α/β ratios. It was found that the largest degree of spin polarization is achieved when |α| = |β|.

Prestressed concrete slabs subjected to low-velocity impact: Theoretical analysis model and design method

Bidirectional bonded prestressed concrete (PS) structures are widely used in energy engineering structures due to their excellent impermeability. Owing to the particularity of the structure and the severity of damage consequences, the impact dynamic performance of bidirectional bonded PS structures has been widely concerned. Nonetheless, the existing researches focus on the test and finite element, and lacks the theoretical analysis model that can consider the whole process of load action, let alone the corresponding anti-impact design method. Therefore, based on the existing test and finite element results, the resistance function model of bidirectional bonded PS slab is proposed in this paper, and the anti-impact design method is formed. Firstly, the performance of specimens under low-velocity impact loading and quasi-static loading conditions is compared, and the effects of inertia force and material strain rate on the dynamic performance of specimens under low-velocity impact are further explored. Then, a resistance function theoretical analysis model that can consider the whole process of load action is proposed with a quadrilinear form, and the analytical expressions of resistance and stiffness at characteristic points are derived. Subsequently, the accuracy of the resistance function model is verified based on the existing test results. Furthermore, based on the resistance function model, the influence laws of compressive strength of concrete, prestressing degree, reinforcement ratio of reinforcement and slab thickness on slab resistance are analyzed. Finally, an anti-impact design method considering perforation and scabbing failure is proposed, and the feasibility of the design method is verified by impact test results.