Search Results (1,125)

The electronic band structure of two-dimensional lithium is calculated using the Dirac equation. Lithium is modeled as a two-dimensional square lattice in which the two strongly bound inner electrons and the fixed nucleus are treated as a positively charged ion (+e), while the outer electron is assumed to be uniformly distributed within the cell. The electronic potential is obtained by considering Coulomb-type interactions between the charges inside the unit cell and those in the surrounding cells. A numerical method that divides the unit cell into small pieces is employed to calculate the potential and then the Fourier coefficients are obtained. The Bloch method is used to determine the energy bands, leading to an eigenvalue matrix equation (in momentum space) of infinite dimension, which is truncated and solved using standard matrix diagonalization techniques. Convergence is analyzed with respect to the key parameters influencing the calculation: the lattice period, the dimension of the eigenvalue matrix, the unit-cell partition used to compute the potential’s Fourier coefficients, and the number of neighboring cells that contribute to the electronic interaction. Full article

In this study, a three-dimensional Inverse Conjugate Heat Transfer Problem (ICHTP) is numerically and experimentally investigated to estimate the heat-source strength of multiple chips mounted on a printed circuit board (PCB) using the Conjugate Gradient Method (CGM) and infrared thermography. The interfaces between the PCB and the surrounding air domain are assumed to exhibit perfect thermal contact, establishing a fully coupled conjugate heat transfer framework for the inverse analysis. Unlike the conventional Inverse Heat Conduction Problem (IHCP), which typically only accounts for conduction within solid domains, the present ICHTP formulation requires the simultaneous solution of the governing continuity, momentum, and energy equations in the air domain, along with the heat conduction equation in the chips and PCB. This coupling introduces substantial computational complexity due to the nonlinear interaction between convective and conductive heat transfer mechanisms, as well as the sensitivity of the inverse solution to measurement uncertainties. The numerical simulations are conducted first with error-free measurement data and an inlet velocity of u_in = 4 m/s; the recovered heat-sources exhibit excellent agreement with the true values. The computed average errors for the estimated temperatures ERR1 and estimated heat sources ERR2 are as low as 0.0031% and 1.87%, respectively. The accuracy of the estimated heat sources is then experimentally validated under various prescribed inlet air velocities. During experimental verification at an inlet velocity of 4 m/s, the corresponding ERR1 and ERR2 values are obtained as 0.91% and 3.34%, while at 6 m/s, the values are 0.86% and 2.81%, respectively. Compared with the numerical results, the accuracy of the experimental estimations decreases noticeably. This discrepancy arises because the numerical simulations are free from measurement noise, whereas experimental data inherently include uncertainties due to thermal picture resolutions, environmental fluctuations, and other uncontrollable factors. These results highlight the inherent challenges associated with inverse problems and underscore the critical importance of obtaining precise and reliable temperature measurements to ensure accurate heat source estimation. Full article

As sustainable tourism gains global momentum, extended reality (XR) technologies have emerged as important tools for enhancing visitor experiences at overburdened World Heritage Sites while mitigating physical deterioration through non-consumptive engagement. However, existing research on immersive technologies in heritage tourism has largely relied on single-cultural samples and has paid limited attention to theoretically grounded boundary conditions in post-adoption behaviour. To address these gaps, this study extends the Expectation–Confirmation Model (ECM) by incorporating cultural distance (CD) and prior visitation experience (PVE) as moderating variables, and empirically tests the proposed framework using a mixed domestic–international sample exposed to an on-site XR application at the Badaling Great Wall World Heritage Site. Data were collected immediately after the XR experience and analysed using structural equation modelling. The results validate the core relationships of ECM while identifying significant moderating effects. Cultural distance attenuates the positive effects of confirmation on perceived usefulness as well as the effect of perceived usefulness on continuance intention, while prior visitation experience weakens the influences of enjoyment and visual appeal on satisfaction. These findings establish important boundary conditions for ECM in immersive heritage contexts. From a practical perspective, the study demonstrates that high-quality, culturally responsive XR can complement physical visitation and support sustainable conservation strategies at large-scale linear heritage sites. Full article

In recent years, a novel decomposition of fluid motion has been proposed, which mathematically defines a type of fluid rigid rotation distinct from vorticity, termed the Liutex quantity. Since its introduction, Liutex has been successfully applied to describe fluid vortices and has emerged as an internationally recognized third-generation vortex identification method. This new motion decomposition undoubtedly leads to a revised description of rotational and deformational motions, thereby necessitating a new description of dynamics. Therefore, based on the Stokes assumption and the novel Liutex decomposition, this paper constructs a new constitutive equation and derives a new set of fluid dynamic equations. The research findings reveal two key insights: first, the new shear stress in the fluid is no longer symmetric; second, in addition to traditional forces such as body force, pressure, and viscous force, an additional force induced by Liutex-based rigid rotation is identified. Furthermore, the new dynamic framework encompasses traditional fluid dynamics, with the latter being a special case when Liutex equals the traditional vorticity. It is anticipated that the proposed equations will find significant applications in the study of fluid vortices and turbulence and will undoubtedly stimulate research interest in the field of fluid mechanics. Full article

It is revealed that the material derivative of a variable in gravity field is its directional derivative, from which and energy/complementary-energy conservations with exterior derivatives, two sets of gauge equations of Newton’s dynamic gravity field are derived, which has same mathematical structure with the gauge ones for the Maxwell equations in electromagnetic fields, revealing that gravity force and curl momentum in Newton’s gravity field, respectively, play the roles like the electric $\mathit{E}$ and the magnetic $\mathit{B}$ of the Maxwell equations in the electromagnetic field. The gravity tensor of Newton’s gravitational field is constructed, and an example is given to validate it. This finding allows Newton’s gravity to be governed by a gauge theory, addressing the historic issue that “Newton’s gravitation is an exception to the Yang–Mills gauge theory”. Full article

Particle image velocimetry (PIV) flow measurements are common practice in laboratory settings in a wide variety of fields involving fluid dynamics, including biology, physics, engineering, and medicine. Dynamic fluid pressure is a notoriously difficult property to measure non-intrusively, yet its variation is a driving flow force and critical to model correctly. Techniques have been developed to estimate the pressure from velocity and velocity gradient measurements. Here, we highlight a novel application of boundary conditions when applying such pressure estimation techniques based on two-dimensional PIV data; the novel method is especially relevant to problems with complex boundary conditions. As such, it is demonstrated with PIV measurements of in vivo fish suction-feeding, which represents a challenging flow environment. Suction-feeding is a common method for capturing prey by aquatic organisms. Suction-feeding is a complex fish–fluid interaction governed by various hydrodynamic forces and the dynamic behavior of the fish (motion and forces). This study focuses on estimating the pressure within the flow field surrounding the mouth of a Bluegill sunfish (Lepomis macrochirus) during suction-feeding utilizing two-dimensional PIV measurements. High-speed imaging was used for measurements of the fish kinematics (duration and amplitude). Through the Poisson equation, the pressure field is estimated from the PIV velocity measurements. The boundary conditions for the pressure field are determined from the integral momentum equation, separately for three phases of the suction-feeding cycle. We demonstrate the utility of the technique with this case study on fish suction-feeding by quantifying the pressure field that drives the flow towards the buccal cavity, a feeding mechanism known to be dominated by pressure spatial variations over the feeding cycle. Full article

This article investigates the influence of wall permeability on channel flows and addresses the lack of studies that quantify entropy generation in magnetized Casson fluid models using wavelet-based numerical schemes. We introduce a Fibonacci Wavelet Collocation Method (FWCM) to efficiently solve the transformed nonlinear ordinary differential equations and demonstrate its applicability to the coupled momentum and energy equations. The analysis includes detailed graphical and numerical evaluations of entropy generation, temperature, and velocity fields, along with the Bejan number, Nusselt number, and skin-friction variations. The results reveal that entropy generation increases by approximately 18–22% with a higher Biot number and by nearly 15% with increasing Grashof number, while it decreases by about 12% for higher Eckert numbers. Magnetic field strength exhibits a dual effect, producing both suppressing and enhancing behaviors depending on parameter ranges. The FWCM solutions show strong agreement with previously published data, confirming both accuracy and robustness. Full article

The traditional way to model the statistics of turbulent flow and dispersion is through averaged conservation equations, in which the turbulent transport terms are described by semi-empirical expressions. A new development has been reported by Brouwers in a number of consecutive papers published over the last 15 years. The new development is that presented descriptions can be obtained through the application of fundamental principles of statistical physics and making use of the asymptotic structure of turbulence at a high Reynolds number. They no longer rely on empirical constructions, minimise calibration factors, and are not limited to specific flow situations. This article updates the contents of these works and presents them in coherent manner. The first derivations are presented as expressions for turbulent diffusion. These are subsequently implemented in a closed set of equations expressing the conservation of mean momentum, mean fluctuating energy, and energy dissipation rate. Predictions from these equations are shown to compare favourably with the results of direct numerical simulations (DNS) of the Navier–Stokes equations of highly anisotropic and inhomogeneous channel flow. The presented model equations provide a solid basis to calculate the main statistical parameters of turbulent flow and dispersion in engineering praxis and environmental analysis. Full article

In this paper, we investigate the stability and feasibility of an anisotropic stellar model under $f(R,T)$ gravity that embraces the Karmarkar condition. In order to develop the $f(R,T)$ gravity model, the functional form of $f(R,T)$ is taken into consideration as the linear function of the trace of the energy-momentum tensor T and the Ricci scalar R, respectively. This study proposes a well-known form of the radial metric function and finds another metric function by employing the Karmakar condition, which provides the exact solution to the field equation. The expression of the model parameters is derived by matching the obtained interior solutions with the Schwarzschild exterior metric over the bounding surface of a celestial object, along with the requirement that the radial pressure vanish at the boundary. The current estimated data of the star, pulsar 4U1608-52, is used to graphically explore the model. The physical attributes of the celestial object are thoroughly examined within the framework of the present model. Adjusting the model parameter, a detailed analysis of the stability criterion is presented that involves the adiabatic index, the Herrera cracking technique, and the causality condition. Furthermore, the Tolman–Oppenheimer–Volkhoff equation is used to analyze the stellar model’s equilibrium state. In order to maintain the stability condition of the anisotropic stellar structure, a suitable range for the model parameter is determined by the graphical analysis of the present model in this study. In addition, the numerical values of the physical parameters related to the compact stars Her X-1, LMC X-4, Cen X-3 and KS1731-207 are used to examine the model solution within the desired range of the model parameter. Full article

Molten salt heat exchangers are crucial components in systems requiring high-temperature heat transfer and energy storage, especially in renewable energy and advanced nuclear technologies. Their ability to operate efficiently at high temperatures while offering significant energy storage capacity makes them highly valuable in modern energy systems. They have high thermal stability. In the framework of this research, a computational fluid dynamics (CFD) simulation model of the HITEC molten salt cooling system has been developed. HITEC molten salt is a specialized heat transfer and thermal energy storage medium primarily used in industrial processes and solar thermal power plants. It is a eutectic blend of sodium nitrate, sodium nitrite, and potassium nitrate. COMSOL multi-physics code has been employed in this research. It simultaneously solves the fluid flow, energy, and heat conduction transport equations. Two cases have been investigated in this paper: a water flowing velocity of 1 [m/s] and a water flowing velocity of 10 [m/s]. The results indicate that the maximal surface temperature of the Crofer^®22 H reached 441.2 °C in the first case. The maximal surface temperature of the Crofer^®22 H reached 500 °C in the second case. Crofer^®22 H alloy provides excellent steam oxidation, high corrosion resistance, and thermal creep resistance. The proposed HITEC molten thermal system may be applied in the oil and gas industries and in power plants (such as the Organic Rankine Cycle). Full article

This research examines the approximate solutions to the system of atmospheric internal-wave (AIW) fuzzy fractional partial differential equations with the gH-Caputo derivative. Atmospheric internal waves are a type of wave that occurs within the Earth’s atmosphere, typically in the lower atmosphere or boundary layer. Vertical displacements of air parcels cause them to occur due to various factors such as wind shear, buoyancy, and topographic effects. These waves can propagate horizontally and vertically and play an important role in atmospheric dynamics, including energy transport, momentum, and pollutants. Using the residual power series method (RPSM), we obtained new effective numerical solutions to the AIW equation system with gH-Caputo derivatives and fuzzy initial conditions. The RPSM solutions are compared with other numerical methods to examine the suggested method’s accuracy and efficiency. Illustrative examples and a comparative analysis of our approach with present methods are given. Full article

Heat exchangers–adsorbers (HEX-As) are emerging as innovative technologies in many applications (CO₂ capture, gas purification and separation, thermal energy storage, etc). This review addresses the theoretical challenges within computational fluid dynamics (CFD) in modeling and simulating coupled heat and mass transfer within gas separation by using adsorbing porous media in fixed beds. Conservation equations of mass, momentum, and energy from different studies (1D, 2D-CFD, and 3D-CFD models) are presented and discussed with an emphasis on their ability to predict the complex multi-physics multi-scale heat and mass transfer phenomena involved, such as the adsorption kinematics, the thermal front propagation, and the multi-component fluid flow dynamics inside the beds. For the fist time, we show that mathematical theoretical modeling in CFD has been differently developed and applied by many authors in the literature in order to model the same physical phenomena. This sheds light on the present challenges and bottlenecks in theoretical and computational fluid dynamics when it comes to complex coupled heat and mass transfer in multi-component gas dynamics in porous media. This review make it easier for readers to understand the different models that exist in the literature for modeling and simulating HEX-As. It also opens questions on how accurately one can model multi-functional heat exchangers–adsorbers using CFD, e.g., physics multi-scale extrapolation from nano- to meso- and then to macro-scale behavior. Full article

This paper investigates the validity of the long wavelength approximation in the calculation of two-photon decay of $2s_{1/2}$ level in hydrogen-like ions with nuclear charge $Z=1-100$ based on time-dependent second-order perturbation theory and angular momentum algebra. While the relativistic structure effects on the two-photon decay rates are highlighted in the literature, the role of slowing effects in the photon electric dipole operators are not discussed extensively. The rate is computed by the sum-over-states method, with bound-bound and bound-free electric dipole matrix elements obtained in the Babushkin and Coulomb gauges, which satisfy the Lorenz gauge condition, as well as their non-relativistic limits in the long-wavelength approximation (Length and Velocity forms, respectively). The present results explicitly show how this approximation breaks gauge invariance by overestimating the Babushkin values by ∼24%${\left(\alpha Z\right)}^2$ while underestimating the Coulomb rates by ∼$31\%{\left(\alpha Z\right)}^2$. Using analytical eigenfunctions of the Dirac equation, we found that the contributions of the negative continuum states to the rate scale are ∼$0.0134{\left(\alpha Z\right)}^4$ in the Babushkin gauge and ∼$1.46{\left(\alpha Z\right)}^4$ in the Coulomb gauge, making the latter gauge more susceptible to errors when attempting to achieve basis completeness in multiphoton calculations. The present results are useful in assessing the complexity requirements of radiative transition rates for atomic systems of interest. Full article

This manuscript examines the rotational dynamics of rigid bodies in five-dimensional Euclidean space. This results in ten coupled nonlinear differential equations for angular velocities. Restricting rotations along certain axes reduces the 5D equations to sets of 4D Euler equations, which collapse to the classical 3D Euler equations. This demonstrates consistency with established mechanics. For bodies with equal principal moments of inertia (e.g., hyperspheres and Platonic solids), the rotation velocities remain constant over time. In cases with six equal and four distinct inertia moments, the solutions exhibit harmonic oscillations with frequencies determined by the initial conditions. Rotations are stable when the body spins around an axis with the largest or smallest principal moment of inertia, thus extending classical stability criteria into higher dimensions. This study defines a 5D angular momentum operator and derives commutation relations, thereby generalizing the familiar 3D and 4D cases. Additionally, it discusses the role of Pauli matrices in 5D and the implications for spin as an intrinsic property. While mathematically consistent, the hypothesis of a fifth spatial dimension is ultimately rejected since it contradicts experimental evidence. This work is valuable mainly as a theoretical framework for understanding spin and symmetry. This paper extends Euler’s equations to five dimensions (5D), demonstrates their reduction to four dimensions (4D) and three dimensions (3D), provides closed-form and oscillatory solutions under specific inertia conditions, analyzes stability, and explores quantum mechanical implications. Ultimately, it concludes that 5D space is not physically viable. Full article

This paper analyzes the modified canonical Heisenberg commutation relations or GUP, from a standard Hamiltonian point of view. For a one-dimensional system, a such modified canonical Heisenberg commutation relation is defined by the commutator between a position $\widehat{x}$ and a momentum operator $\widehat{p}$ (called the deformed momentum), which becomes a function F of the same operators: $\left[\widehat{x},\widehat{p}\right]=F(\widehat{x},\widehat{p})$, that is, the Heisenberg algebra closes itself in general in a nonlinear way. The function F also depends on a parameter that controls the deformation of the Heisenberg algebra in such a way that for a null parameter value, one recovers the usual Heisenberg algebra $\left[\widehat{x},{\widehat{p}}_0\right]=i\hslash \mathbb{I}$. Thus, it naturally raises the following questions: What does a relation of this type mean in Hamiltonian theory from a standard point of view? Is the deformed momentum the canonical variable conjugate to the position in such a relation? Moreover, what are the canonical variables in this model? The answer to these questions comes from the existence of two different phase spaces: The first one, called the non-deformed phase (which is obtained for control parameter value equal to zero), is defined by the Cartesian $\widehat{x}$ coordinate and its non-deformed conjugate momentum ${\widehat{p}}_0$, which satisfies the standard quantum mechanical Heisenberg commutation relation. The second phase space, the deformed one, is given by the deformed momentum $\widehat{p}$ and a new position coordinate $\widehat{y}$, which is its canonical conjugate variable, so $\widehat{y}$ and $\widehat{p}$ also satisfy standard commutation relations. We construct a classical canonical transformation that maps the non-deformed phase space into the deformed one for a specific class of deformation functions F. Additionally, a quantum mechanical operator transformation is found between the two non-commutative phase spaces, which allows the Schrödinger equation to be written in both spaces. Thus, there are two equivalent quantum mechanical descriptions of the same physical process associated with a deformed commutation relation. Full article