Set Of Equations Research Articles

Rearrangement and breakup amplitudes from the solution of Faddeev-AGS equations by pseudo-state discretization of the two-particle continuum

The AGS equations for rearrangement transition operators in the three-particle problem are turned into a set of effective multi-channel two-body equations using the pseudo-state discretization of the two-particle resolvent. The resulting effective equations are LS-type integral equations in the spectator degrees of freedom, much like the LS equations of multichannel inelastic scattering. In particular, the effective potential matrix is real, energy-independent and non-singular, while the propagator matrix has only simple poles. Difficulties associated with the moving singularities of the effective potential matrix in the usual separable-T approach to AGS equations are avoided. After regularization of the kernel via subtraction procedures well known from two-particle scattering, the set of coupled LS-type equations in the spectator momenta are solved rather straightforwardly by the Nyström method. Solutions of effective two-body equations are then used to calculate the breakup amplitudes using the well-known relationship between rearrangement and breakup amplitudes. Calculations using a local momentum-space basis on a benchmark model of the n+d collision show that rather accurate results for elastic and breakup amplitudes can be obtained with rather small bases.

Evolution of Tidal Disruption Event Disks with Magnetically Driven Winds

We present a time-dependent, one-dimensional, magnetically driven disk wind model based on magnetohydrodynamic (MHD) equations, in the context of tidal disruption events (TDEs). We assume that the disk is geometrically thin, is gas pressure dominated, and explicitly accounts for magnetic braking and turbulent viscosity through an extended α-viscosity prescription. We find a particular wind solution for a set of basic equations that satisfies the necessary and sufficient conditions for vertically unbound MHD flows. The solution shows that the disk evolves with mass loss due to wind and accretion from the initial Gaussian density distribution. We confirm that the mass accretion rate follows the power law of time t −19/16 at late times in the absence of wind, which matches the classical solution of J. K. Cannizzo et al. We find that the mass accretion rate is steeper than the t −19/16 curve when the wind is present. Mass accretion is also induced by magnetic braking, known as the wind-driven accretion mechanism, which results in a faster decay with time of both the mass accretion and mass-loss rates. In the disk emission, the ultraviolet (UV) luminosity is the highest among the optical, UV, and X-ray luminosities. While the optical and X-ray emission is observationally insignificant without magnetic braking, the X-ray emission is brighter at late times, especially in the presence of magnetic braking. This provides a possible explanation for observed delayed X-ray flares. Our model predicts that late-time bolometric light curves steeper than t −19/16 in UV-bright TDEs are potentially compelling indicators of magnetically driven winds.

A Fourth-Order Tensorial Wiener Filter Using the Conjugate Gradient Method

The recently developed iterative Wiener filter using a fourth-order tensorial (FOT) decomposition owns appealing performance in the identification of long length impulse responses. It relies on the nearest Kronecker product representation (with particular intrinsic symmetry features), together with low-rank approximations. Nevertheless, this new iterative filter requires matrix inversion operations when solving the Wiener–Hopf equations associated with the component filters. In this communication, we propose a computationally efficient version that relies on the conjugate gradient (CG) method for solving these sets of equations. The proposed solution involves a specific initialization of the component filters and sequential connections between the CG cycles. Different FOT-based decomposition setups are also analyzed from the point of view of the resulting parameter space. Experimental results obtained in the context of echo cancellation confirm the good behavior of the proposed approach and its superiority in comparison to the conventional Wiener filter and other decomposition-based versions.

Numerical Investigation of Two-Phase Shock Waves in CO2 Flows Using a Modified Hertz–Knudsen Model

Abstract Understanding the complex behavior of two-phase shocks in CO2 flows is essential for a variety of applications, including carbon capture and storage () and transcritical refrigeration cycles. This study presents a comprehensive numerical investigation of two-phase shock waves using the multispecies user-defined real gas model in Ansys Fluent. The simulations are performed for de-Laval nozzles, exploring the two-phase shock features for three-dimensional (3D), two-dimensional (2D), and two-dimensional axisymmetric geometries. The nonequilibrium condensation, subsequent evaporation, and denucleation occurring across the shock are modeled through a set of user-defined scalar transport equations implemented within Ansys Fluent. The two-phase computational fluid dynamics (CFD) simulations are carried out in proximity to the critical point where real gas effects are relevant. The CO2 real gas properties are computed using an in-house Python code and integrated into the solver via user-defined functions as external look-up tables. This study provides valuable insights into the physical processes underlying two-phase shocks in CO2 flows and their sensitivity to geometric variations and thermodynamic conditions. The findings contribute to the development and modification of predictive models and optimized designs for systems involving two-phase CO2 flows. The results highlight the influence of geometry configurations and thermodynamic conditions on shock location and intensity, providing comparisons for shock waves occurring in two-phase flows and supercritical single-phase flows.

Optimal Conversion of Food Packaging Waste to Liquid Fuel via Nonthermal Plasma Treatment: A Model-Centric Approach

The efficiency of employing a multifactorial approach to enhance the nonthermal plasma (NTP) chemical conversion of solid waste food packaging materials into liquid petroleum hydrocarbons was assessed for the first time in this study. The researchers adopted a hybrid approach which integrated the zero-dimensional (0-D) and response surface model (RSM) techniques. After their application, the researchers noted that these strategies significantly enhanced the model prediction owing to their accurate electrochemical description. Here, the researchers solved a set of equations to identify the optimisation dynamics. They also established experimental circumstances to determine the quantitative correlation among all process variables contributing to food plastic packaging waste degradation and the production of liquid fuels. The findings of the study indicate a good agreement between the numerical and experimental values. It was also noted that the electrical variables of NTP significantly influenced the conversion yield (Yconv%) of solid plastic packaging waste to liquid hydrocarbons. Similarly, after analysing the data, it was seen that factors like the power discharge rate (x1 ), discharge interval (x2), power frequency (x3), and power intensity (x4) could significantly affect the product yield. After optimizing the variables, the researchers observed a maximal Yconv% of approximately 86%. The findings revealed that the proposed framework could effectively scale up the plasma synergistic pyrolysis technology for obtaining the highest Yconv% of solid packaging plastic wastes to produce an aromatics-enriched oil. The researchers subsequently employed the precision of the constructed framework to upgrade the laboratory-scale procedures to industrial-scale processes, which showed more than 95% efficiency. The extracted oil showed a calorific value of 43,570.5 J/g, indicating that the liquid hydrocarbons exhibited properties similar to commercial diesel.

Generalized mathematical model applied to a silica sand laboratory-controlled mill: Derivation of simplified ceramic ball entrance flux, ball wear consumption, and mass distribution functions

A laboratory-controlled milling process of silica sand was carried out using aluminum oxide balls of three different sizes. The ball wear kinetic equations were experimentally obtained from the evolution curves of the ball diameter as a function of the operating time. From a generalized model, the ball entrance flux and ball wear consumption were calculated using exact two-parameter solution functions. One-parameter ball entrance flux and ball wear consumption functions were proposed to perform calculations that accurately describe the values provided by the two-parameter functions. In addition, a compact form of the ball mass distribution function is found. This set of simplified equations can be suitable for fast calculations in the milling industry.

Disentangling dynamic and stochastic modes in multivariate time series

A signal decomposition is presented that disentangles the deterministic and stochastic components of a multivariate time series. The dynamical component analysis (DyCA) algorithm is based on the assumption that an unknown set of ordinary differential equations (ODEs) describes the dynamics of the deterministic part of the signal. The algorithm is thoroughly derived and accompanied by a link to the GitHub repository containing the algorithm. The method was applied to both simulated and real-world data sets and compared to the results of principal component analysis (PCA), independent component analysis (ICA), and dynamic mode decomposition (DMD). The results demonstrate that DyCA is capable of separating the deterministic and stochastic components of the signal. Furthermore, the algorithm is able to estimate the number of linear and non-linear differential equations and to extract the corresponding amplitudes. The results demonstrate that DyCA is an effective tool for signal decomposition and dimension reduction of multivariate time series. In this regard, DyCA outperforms PCA and ICA and is on par or slightly superior to the DMD algorithm in terms of performance.

Boost heat transfer efficiency through thermal radiation and electrical conductivity in nanofluids

AbstractThermal radiation and electrical conductivity in nanofluids are crucial for their heat transfer characteristics, especially in applications with elevated temperatures or significant radiative heat transfer. The suspension of nanoparticles in suspension contributes to the fluid's electrical conductivity, which is essential for efficient heat dissipation in electronic cooling systems. Understanding the behavior of electroconductive nanofluids is particularly important in electronic cooling applications, where effective heat dissipation is crucial to prevent overheating. A study using a similarity parameter transformed a system of coupled PDEs into a set of nonlinear ordinary differential equations, revealing significant changes in key physical characteristics, such as temperature distribution, cubic concentration field, and velocity field. The study also examined the effects of parameters like Brownian motion, Rayleigh number, Peclet number, thermophoresis parameter, and buoyancy ratio parameter. The research provides valuable insights into the complex dynamics of magnetized non‐Newtonian nanofluids and offers practical implications for applications like microbial fuel cells and heat transmission equipment.

Impact of the Information and Communications Technologies (ICT) infrastructure on the returns to higher education in Mexico: A gender analysis

This paper aims to analyze the impact of access to Information and Communication Technologies (ICT) on the private returns to higher education (HE) focusing on gender inequality in 2020. Methodology: To evaluate the above impact a set of Mincerian equations will be estimated. The proposed approach mitigates biases associated with self-selection and individual heterogeneity. Data: The database comes from the National Household Income and Expenditure Survey (Encuesta Nacional de Ingresos y Gastos de los Hogares, ENIGH) from 2020. Results: Empirical evidence suggests that individuals that have HE have a positive and greater impact on their salary income compared to those with a lower educational level, being women that do not have access to ICT those with the lowest wage return. Policy: Access to ICT should be considered as one of the criteria that integrate social deprivation in the measurement of multidimensional poverty. Likewise, it is necessary to design public policies that promote the strengthening and creation of educational and/or training systems in technological matters for women. Limitations: No distinction was made between individuals that graduated from public or private schools, nor was income from sources other than work considered. Originality: This investigation evaluates the impact of access to ICT on the returns to higher education in Mexico, in 2020, addressing gender disparity.

Hydrodynamic equations for a U(N) invariant superfluid

Abstract In this paper, we develop an appropriate set of hydrodynamic equations for a U(N) invariant superfluid that couple the dynamics of superflow and magnetization. In the special case when both the superfluid and normal velocities are zero, the hydrodynamic equations reduce to a generalized version of Landau-Lifshitz equation for ferromagnetism with U(N) symmetry. When both velocities are non-zero, there appears couplings between the superflow and magnetization dynamics, and the superfluid velocity no longer satisfies the irrotational condition. On the other hand, the magnitude of magnetization is no longer a constant of motion as was the case for the standard Landau-Lifshitz theory. In comparison with the simple superfluid, the first and second sounds are modified by a non-zero magnetization through various thermodynamic functions. For U(2) invariant superfluid, we get both (zero-) sound wave and a spin wave at zero temperature. It is found that the dispersion of spin wave is always quadratic, which is consistent with microscopic analysis. In the Appendix, we
show that the hydrodynamic equation for a U(N) invariant superfluid can be obtained from the general hydrodynamic equation with arbitrary internal symmetries.

Artificial intelligence techniques for dynamic security assessments - a survey

The increasing uptake of converter-interfaced generation (CIG) is changing power system dynamics, rendering them extremely dependent on fast and complex control systems. Regularly assessing the stability of these systems across a wide range of operating conditions is thus a critical task for ensuring secure operation. However, the simultaneous simulation of both fast and slow (electromechanical) phenomena, along with an increased number of critical operating conditions, pushes traditional dynamic security assessments (DSA) to their limits. While DSA has served its purpose well, it will not be tenable in future electricity systems with thousands of power electronic devices at different voltage levels on the grid. Therefore, reducing both human and computational efforts required for stability studies is more critical than ever. In response to these challenges, several advanced simulation techniques leveraging artificial intelligence (AI) have been proposed in recent years. AI techniques can handle the increased uncertainty and complexity of power systems by capturing the non-linear relationships between the system’s operational conditions and their stability without solving the set of algebraic-differential equations that model the system. Once these relationships are established, system stability can be promptly and accurately evaluated for a wide range of scenarios. While hundreds of research articles confirm that AI techniques are paving the way for fast stability assessments, many questions and issues must still be addressed, especially regarding the pertinence of studying specific types of stability with the existing AI-based methods and their application in real-world scenarios. In this context, this article presents a comprehensive review of AI-based techniques for stability assessments in power systems. Different AI technical implementations, such as learning algorithms and the generation and treatment of input data, are widely discussed and contextualized. Their practical applications, considering the type of stability, system under study, and type of applications, are also addressed. We review the ongoing research efforts and the AI-based techniques put forward thus far for DSA, contextualizing and interrelating them. We also discuss the advantages, limitations, challenges, and future trends of AI techniques for stability studies.

Artificial neural network (ANN) approach in predicting the thermo-solutal transport rate from multiple heated chips within an enclosure filled with hybrid nanocoolant

This study focuses on enhancing heat and mass transfer in an electronic cooling system such as a rectangular cavity that contains equidistant heated chips along the bottom wall. The cavity of the present study is filled with ethylene glycol (30:70) based hybrid nano coolants of different volume fractions (ϕ) of Multi-walled Carbon Nanotube (MWCNT), Aluminum Oxide (Al2O3), and Copper Oxide (CuO). The set of equations controlling the thermo-solutal natural convection within the enclosure is simulated using the Galerkin weighted residual finite element method (FEM). The study has shown a good agreement of numerical results with different experimental reports within the framework of the present study. A solution space is constructed based on governing parameters such as Rayleigh number, buoyancy ratio, and Lewis number. A hybrid nano-coolant containing ϕMWCNT = 1.5 %, ϕCuO = 0.5 %, and ϕAl2O3 = 2 % showed a 3.11% improvement in heat transfer rate compared to the base fluid, highlighting its potential for thermal management applications. This study also investigates various machine learning models for predicting the heat and mass transfer rate, and an error analysis is conducted on the K-Nearest Neighbour Regressor, Random Forest Regressor, Decision Tree Regressor, and ANN model. The ANN model with 6-50-100-50-2 architecture showcases the best fit with the mean squared error of 0.8923 and an R² value of 99.96 % on testing data. The ANN model exhibits its capability to predict heat transfer and mass transfer rates within the error ranges from 1–2 % and 2–3 %, respectively, even at a strong thermal buoyancy force (Ra = 10⁵). This accuracy showcases a novel use of ANN to efficiently predict thermo-fluidic transport behaviors of hybrid nanofluids, offering a faster alternative to resource-intensive simulations. The present study opens new possibilities for real-time, cost-effective cooling solutions, particularly in microelectronics and renewable energy, while maintaining high prediction accuracy by integrating machine learning with the nanotechnology approach.

Analysis of thermophoretic and Brownian diffusions in hydromagnetic curvilinear flow of Carreau nanofluid with activation energy and heat generation

This study presents a theoretical analysis of the thermophoretic and Brownian diffusion effects on the magnetized flow of Carreau nanofluid over a stretchable curved surface. The investigation includes the impact of heat generation and activation energy, which are incorporated into the energy and concentration equations, respectively. The mathematical model of the boundary layer flow is formulated as a set of nonlinear partial differential equations using curvilinear coordinates. These equations are transformed into ordinary differential equations through the application of appropriate similarity variables. The resulting system is solved numerically by using the shooting method along with the Runge-Kutta technique. The accuracy of the numerical results is further verified by the Keller-box method, a finite difference technique. The obtained results are also checked by giving a comparison table with the published data in the literature. Furthermore, the convergence of the solutions is also checked by a convergent series method known as the homotopy analysis method (HAM). The study examines the influence of several key parameters, including the radius of curvature, Weissenberg number, Prandtl number, Lewis number, Brownian and thermophoretic diffusions parameters, Hartmann number, heat generation parameter, activation energy parameter, temperature difference parameter, chemical reaction parameter, and power law index. The effects of these parameters on momentum, temperature, concentration distributions, mass and heat transfer rates, and as well as the skin friction coefficient are examined through graphs and tables. Graphical observations declare that the velocity field diminishes against the rising values of the Hartmann number and Weissenberg number. However, the velocity profile rises with improved values of the radius of curvature parameter and power law index parameter. It is also noticed that the magnitude of the concentration field rises with growing values of the Brownian parameter, activation energy parameter and Lewis number, whereas it shows a decreasing manner against the enhanced values of the thermophoresis parameter and temperature difference parameter.

Multiscale homogenized constrained mixture model of the bio-chemo-mechanics of soft tissue growth and remodeling.

Constrained mixture models have successfully simulated many cases of growth and remodeling in soft biological tissues. So far, extensions of these models have been proposed to include either intracellular signaling or chemo-mechanical coupling on the organ-scale. However, no version of constrained mixture models currently exists that includes both aspects. Here, we propose such a version that resolves cellular signal processing by a set of logic-gated ordinary differential equations and captures chemo-mechanical interactions between cells by coupling a reaction-diffusion equation with the equations of nonlinear continuum mechanics. To demonstrate the potential of the model, we present 2 case studies within vascular solid mechanics: (i) the influence of angiotensin II on aortic growth and remodeling and (ii) the effect of communication between endothelial and intramural arterial cells via nitric oxide and endothelin-1.

Resolving the Size and Charge of Small Particles: A Predictive Model of Nanopore Mechanics.

The movement of small particles and molecules through nanopore membranes is widespread and has far-reaching implications. Consequently, the development of mathematical models is essential for understanding these processes on a micro level, leading to deeper insights. In this endeavor, we suggested a model based on a set of empirical equations to predict the transport of substances through a solid-state nanopore and the associated signals generated during their translocation. This model establishes analytical relationships between the ionic current and electrical double-layer potential observed during analyte translocation and their size, charge, and mobility in an electrolyte solution. This framework allows for rapid interpretation and prediction of the nanopore system's behavior and provides a means for quantitatively determining the physical properties of molecular analytes. To illustrate the analytical capability of this model, ceria nanoparticles were investigated while undergoing oxidation or reduction within an original nanopore device. The results obtained were found to be in good agreement with predictions from physicochemical methods. This developed approach and model possess transferable utility to various porous materials, thereby expediting research efforts in membrane characterization and the advancement of nano- and ultrafiltration or electrodialysis technologies.

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.

Oblique Wave Scattering by a Pair of Asymmetric Inverse Π-Shaped Breakwater

Abstract The topic of wave scattering by different breakwaters has unfolded over the past few decades, largely driven by the profound impacts of global climate change. In this study, a completely new type of breakwater, inverse Π-shaped breakwater, has been taken into account for serving both purposes from analytical as well as an application point of view. During the formulation, the actual physical problem is transferred into a boundary value problem by employing the small amplitude water wave theory. With the aid of eigenfunction expansion, the problem is reduced to a set of integral equations having square-root singularities at the submerged edges of thin structures. To address such singularities, a multi-term Galerkin approximation technique is used along with Chebyshev polynomials (multiplied with suitable weights) as basis functions. The numerical methodology employed here validates with different previous literatures as special cases. Then, numerical solutions of the reflection and transmission coefficients, hydrodynamic forces are graphically illustrated across various dimensionless structural parameters. In summary, the present paper offers valuable insights into the dynamics of wave scattering by a pair of asymmetric inverse bottom-mounted Π-shaped breakwater, emphasizing the role of different non-dimensional parameters in this system.

Simulating adiabatic quantum computing with parameterized quantum circuits

Abstract Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term devices, a number of hybrid approaches have been pursued in which a parameterized quantum circuit prepares and measures quantum states and a classical optimization algorithm minimizes an objective function that encompasses the solution to the problem of interest. In this work, we propose a different approach starting by analyzing how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states. We derive a set of equations that allow us to compute the new minimum by solving a constrained linear system of equations that is obtained from measuring a series of observables on the unperturbed system. We then propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device while at the same time is insensitive to the initialization of the parameters and to other limitations hindered in the optimization part of variational quantum algorithms. We compare our proposed algorithm with the variational quantum eigensolver on two classical optimization problems, namely MaxCut and number partitioning, and on a quantum-spin configuration problem, the transverse-field ising chain model, and confirm that our approach demonstrates superior performance.

Galerkin’s Method and Multivariate Newton’s Method for the Nonlinear Deformation of the Magneto-Electro-Elastic Bi-Layered Laminates

In this paper, mathematical modelling for the large deformation of a magneto-electro-elastic rectangular bi-layered laminate with general boundary conditions is presented. Constitutive equations involving the magneto-electro-elastic (MEE) material properties are introduced, Maxwell equations accounts for the electric and magnetic effects are also utilized. First-order shear deformation theory (FSDT) considering the von Karman nonlinear strain is adopted, and the plain strain/stress assumption applicable for thin plate analysis is used. A rather compact set of governing equations related to kinematical variables, electric/magnetic potentials and the Airy stress function is obtained as a consequence of the preliminary condensation for the electro-magnetic state to the plate kinematics. Semi-analytic solution for a bi-layered BaTiO3-CoFe2O4 laminate with specified boundary conditions subjected to various external applied loads is performed. By employing the Bubnov-Galerkin method, the set of nonlinear partial differential equations is transformed to a set of third-order nonlinear algebraic equations for the static deformation due to applied load. Numerical results are carried out by using the multivariate Newton's method with respect to various volume fractions indicating the volume ratio between piezoelectric BaTiO3 layer and piezomagnetic CoFe2O4. From the result, the nonlinearity of the von Karman strain appears to enhance system rigidity as smaller deformations will be detected when external load is applied. Also, some other interesting results are obtained which could be useful to future analysis and design of multiphase composite plates.

MHD double diffusive convective squeezing ternary nanofluid flow between parallel plates with activation energy and viscous dissipation

Purpose This study aims to present the consequences of activation energy and the chemical reactions on the unsteady MHD squeezing flow of an incompressible ternary hybrid nanofluid (THN) comprising magnetite (FE3O4), multiwalled carbon nano-tubes (MWCNT) and copper (Cu) along with water (H2O) as the base fluid. This investigation is performed within the framework of two moving parallel plates under the influence of magnetic field and viscous dissipation. Design/methodology/approach Due to the complementary benefits of nanoparticles, THN is used to augment the heat transmit fluid’s efficacy. The flow situation is expressed as a system of dimensionless, nonlinear partial differential equations, which are reduced to a set of nonlinear ordinary differential equations (ODEs) by suitable similarity substitutions. These transformed ODEs are then solved through a semianalytical technique called differential transform method (DTM). The effects of several changing physical parameters on the flow, temperature, concentration and the substantial measures of interest have been deliberated through graphs. This study verifies the reliability of the results by performing a comparison analysis with prior researches. Findings The enhanced activation energy results in improved concentration distribution and declined Sherwood number. Enhancement in chemical reaction parameter causes disparities in concentration of the ternary nanofluid. When the Hartmann number is zero, value of skin friction is high, but Nusselt and Sherwood numbers values are small. Rising nanoparticles concentrations correspond to a boost in overall thermal conductivity, causing reduced temperature profile. Research limitations/implications Due to its firm and simple nature, its implications are in various fields like chemical industry and medical industry for designing practical problems into mathematical models and experimental analysis. Practical implications Deployment of the squeezed flow of ternary nanofluid with activation energy has significant consideration in nuclear reactors, vehicles, manufacturing facilities and engineering environments. Social implications This study would be contributing significantly in the field of medical technology for treating cancer through hyperthermia treatment, and in industrial processes like water desalination and purification. Originality/value In this problem, a semianalytical approach called DTM is adopted to explore the consequences of activation energy and chemical reactions on the squeezing flow of ternary nanofluid.