Analytical Relations Research Articles

Geomechanical risk assessment for CO2 storage in deep saline aquifers

We study CO2 injection into a saline aquifer intersected by a tectonic fault using a coupled modeling approach to evaluate potential geomechanical risks. The simulation approach integrates the reservoir and mechanical simulators through a data transfer algorithm. MUFITS simulates non-isothermal multiphase flow in the reservoir, while FLAC3D calculates its mechanical equilibrium state. We accurately describe the tectonic fault, which consists of damage and core zones, and derive novel analytical closure relations governing the permeability alteration in the fault zone. We estimate the permeability of the activated fracture network in the damage zone and calculate the permeability of the main crack in the fault core, which opens on asperities due to slip. The coupled model is applied to simulate CO2 injection into synthetic and realistic reservoirs. In the synthetic reservoir model, we examine the impact of formation depth and initial tectonic stresses on geomechanical risks. Pronounced tectonic stresses lead to inelastic deformations in the fault zone. Regardless of the magnitude of tectonic stress, slip along the fault plane occurs, and the main crack in the fault core opens on asperities, causing CO2 leakage out of the storage aquifer. In the realistic reservoir model, we demonstrate that sufficiently high bottomhole pressure induces plastic deformations in the near-wellbore zone, interpreted as rock fracturing, without slippage along the fault plane. We perform a sensitivity analysis of the coupled model, varying the mechanical and flow properties of the storage layers and fault zone to assess fault stability and associated geomechanical risks.

Decay Timescales of Chromospheric Condensations in Solar Flare Footpoints

Chromospheric condensations (CCs) are a prominent feature of flare footpoint heating in the solar flare standard model, yet their timescales and velocities are not well understood. Fisher derived several important analytical relationships, which have rarely been examined with modern spectral observations. The Interface Region Imaging Spectrograph (IRIS) provides a wealth of flare data with a high enough cadence to sufficiently capture CC evolution. We analyzed Doppler shifts in Mg ii 2791 and Fe ii 2814 from a sample of flare footpoint pixels observed by IRIS to compare with Fisher's analytics and recent flare models. We found a detection lifetime of 1 minute occurs in 50% of the sample, with Mg ii showing several pixels with longer values and Fe ii almost categorically shorter, and both growing with the maximum velocity, v max. The shifts’ half-life is commonly <40 s and is inversely related to v max, indicating that the first half of the CC evolution has more efficient kinetic energy loss. The lifetime’s wide range and growth with v max indicate that the footpoint atmospherics and heating scenarios can vary more widely than first postulated in Fisher. Around 90% of the sample had observable acceleration periods, lasting an average of 38 and 32 s for Mg ii and Fe ii, respectively. These acceleration periods, as well as serving as flare model diagnostics themselves, could potentially be used to calculate other model diagnostics such as the initially accelerated mass.

METHODS OF REDUCING THE INFLUENCE OF TEMPERATURE GRADIENTS ON THE SENSITIVITY OF FIBER-OPTIC GYROSCOPE

Thermally induced error is one of the main limitations of the sensitivity of fiber-optic gyroscopes (FOGs). The analysis of thermal sensitivity of FOG is based on the study of the Shupe effect and the elastic-optical effect in the fiber circuit. The main requirement in this case is to preserve the principle of reciprocity for rays propagating in opposite directions of the fiber circuit. It was determined that the thermally induced phase difference of these rays should not exceed ∆φ(t) ≈ 10-7 rad. To reduce the thermal sensitivity of FOG, various methods are used, including quadrupole methods of winding the fiber circuit, using frameless coils, as well as coils made of special materials. Considerable attention is paid to improving the properties of fiber and adhesive compounds to minimize the effect of temperature on the optical-physical characteristics of these components of the fiber circuit. The article examines the advantages and disadvantages of each of the methods of compensating the thermally induced error of FOG. Analytical relations characterizing the effect of temperature gradients on the sensitivity of measuring angular velocity and Sagnac phase when using FOG are given. Part of the methods for solving this problem are discussed in this article. However, the elemental base and FOG signal processing tools are constantly being improved, the transition to integrated optical technologies is being carried out, which opens up new ways to increase the sensitivity of the FOG with minimal costs. On the basis of the conducted research, practical recommendations are given to reduce the influence of temperature gradients on the sensitivity of FOG. The work can be useful for specialists working in the field of FOG design.

Assessment of Dynamic States of Railway Vehicles: Structural Mathematical Modeling

Introduction. The speed rise of railway transport and an increase in the loads on the axles of wheelsets necessitate the modernization of the existing fleet. Scientific studies in the field of rolling stock dynamics are aimed at taking into account the oscillatory processes that occur during the movement of railway vehicles in a traditional design. The attachment of supplementary elements was considered at the coupling level of two cars and the attachment of a third trolley in the center of gravity of the railway platform. The scientific literature has not paid enough attention to the construction of mathematical models that make it possible to assess the dynamic states of such constructive solutions. The objective of this study is to create a method for evaluating the dynamic conditions of a car. The situation is considered when an additional set of mass-inertial and elastic elements is introduced into its structure, and the general dynamic condition of the vehicle depends on the adjustment of their parameters.Materials and Methods. The basic research tool is the structural mathematical modeling, which is based on an approach where the source design scheme is a mechanical oscillatory system in the form of a solid body on elastic supports with supplementary typical elements introduced into its structure. The dynamic analogue of the calculation scheme used is the block diagram of the automatic control system, the use of which provides detailing the connections between typical elastic and mass-inertia elements.Results. A method for estimating the dynamic states of railway vehicles is proposed. It is based on the construction of mathematical models, taking into account the introduction of an additional structure of mass-inertia and elastic elements. The impact of additional parameters on the dynamic condition of the vehicle is investigated. Analytical relations have been obtained that provide reducing the dynamic loads on the major structural elastic elements when changing the corresponding parameters of a technical object. The transfer function of interpartial relations is given, which provides controlling the interaction between the coordinates of the vehicle movement under the action of two kinematic disturbances of the in-phase type.Discussion and Conclusion. The generated mathematical model provides for assessment, monitoring and control of the dynamic state of the vehicle under conditions of kinematic disturbances. The research results can be used to modernize existing vehicles and create new ones with improved dynamics.

Constructing mathematical models of thermal conductivity in individual elements and units of electronic devices at local heating considering thermosensitivity

This paper considers a heat conduction process for an isotropic medium with local external and internal thermal heating. It was necessary to construct linear and non-linear mathematical models for determining the temperature field, and consequently, for the analysis of temperature regimes in these heat-active environments. To solve the linear boundary value problems and the resulting linearized boundary value problems with respect to the Kirchhoff transformation, the Henkel integral transformation method was used, as a result of which the analytical solutions to these problems were obtained. For a heat-sensitive environment, as an example, a linear dependence of the coefficient of thermal conductivity of the structural material of the structure on temperature, which is often used in many practical problems, was chosen. As a result, analytical relations for determining the temperature distribution in this environment were established. To determine the numerical values of the temperature and analyze the heat exchange processes in the given structure, caused by the external heat load, a geometric image of the temperature distribution was constructed depending on spatial coordinates. The resulting linear and non-linear mathematical models testify to their adequacy to the real physical process. They make it possible to analyze heat-active media regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual nodes and their elements but the entire structure as well

Trajectory Approximation of a Low-Performance E-Sail with Fixed Orientation

The Electric Solar Wind Sail (E-sail) is a propellantless propulsion system that converts solar wind dynamic pressure into a deep-space thrust through a grid of long conducting tethers. The first flight test, needed to experience the true potential of the E-sail concept, is likely to be carried out using a single spinning cable deployed from a small satellite, such as a CubeSat. This specific configuration poses severe limitations to both the performance and the maneuverability of the spacecraft used to analyze the actual in situ thruster capabilities. In fact, the direction of the spin axis in a single-tether configuration can be considered fixed in an inertial reference frame, so that the classic sail pitch angle is no longer a control variable during the interplanetary flight. This paper aims to determine the polar form of the propelled trajectory and the characteristics of the osculating orbit of a spacecraft propelled by a low-performance spinning E-sail with an inertially fixed axis of rotation. Assuming that the spacecraft starts the trajectory from a parking orbit that coincides with the Earth’s heliocentric orbit and that its spin axis belongs to the plane of the ecliptic, a procedure is illustrated to solve the problem accurately with a set of simple analytical relations.

Analytical solutions for the free vibration of cross-ply composite laminated plates with arbitrary biaxial symmetric geometry

This paper presents an analytical model for the free vibration of composite laminated plates with arbitrary biaxial symmetric geometry under elastic boundary conditions, applicable to cross-ply fiber-reinforced composites. In this model, the domain segmentation integral method proposed by the authors is extended to the first-order shear deformation theory (FSDT) and the laminated plate theory. The energy integrals pertaining to the FSDT are analytically simplified by segmenting the integration domains and synthesizing orthogonal polynomial displacement functions over the plate domain coordinate intervals. This synthesis is achieved through the amalgamation of the penalty function method and the Gram-Schmidt orthogonalization process. Then, using the Rayleigh-Ritz procedure, a series solution for the free vibration problem of cross-ply fiber-reinforced composite laminated plates is obtained. The model provides an analytical mathematical relationship between the profile curve of composite laminated plates with arbitrary biaxial symmetric geometry and the strain energy, kinetic energy, and boundary potential energy during vibrational processes. The correctness and applicability of the method are validated by comparing the obtained results with those from the literatures. New results for laminated plates, such as hexagonal and astroid-shaped plates, were presented as references for future research. Taking a track shaped plate as an example, the effect of the number of layers on the vibration characteristics of cross-ply fiber-reinforced composite laminated plates with a certain thickness is studied.

Constraints on quasinormal modes from black hole shadows in regular non-minimal Einstein Yang–Mills gravity

This work deals with scalar quasinormal modes using the higher-order WKB method and black hole shadow in non-minimal Einstein–Yang–Mills theory. To validate the results of quasinormal modes, time domain profiles are also investigated. We find that with an increase in the magnetic charge of the black hole, the ringdown gravitational wave increases non-linearly and the damping rate decreases non-linearly. The presence of a magnetic charge also results in a non-linear decrease in the black hole shadow. For large values of the coupling parameter, the black hole becomes a soliton solution and the corresponding ringdown gravitational wave frequency increases slowly with a decrease in the damping rate. For the soliton solutions, the shadow is also smaller. The constraints on the model parameters calculated using shadow observations of M87* and Sgr A* and an approximate analytical relation between quasinormal modes and shadows at the eikonal limit are discussed.

Closed-form analytical relationships for pentamode metamaterials

Pentamode metamaterials are a class of extremal materials exhibiting fluid-like mechanical behavior. The mechanical properties of pentamode metamaterials arise from their unique micro-architecture, rather than their constituent material. In this research, we present closed-form analytical relationships for the elastic modulus and Poisson’s ratio of pentamode lattice structures with double-cone struts based on cubic diamond morphology. To validate our analytical solutions, we performed numerical simulations and experimental tests, which confirmed the accuracy of the derived relationships. Our findings indicate that increasing the smaller diameter (d) and the larger-to-smaller diameter ratio (α) of the double-cones increases the elastic modulus of pentamode metamaterials. However, within the considered range of d and α, the Poisson’s ratio is nearly constant and lies within the range of approximately 0.5. These analytical relationships provide valuable insight into the mechanical behavior of pentamode metamaterials, which can aid in the design and optimization of new materials with unique properties.

The collector current model of the IGBT based on the gate charge

In this study, a dynamic and static collector current (IC) model of the IGBT based on the gate charge is proposed. The gate charge could be easily obtained by measuring the voltage across the gate mirror circuit capacitance, and the transconductance obtained from the IC–VGE curve is mainly used. This model does not need the device structure parameters such as doping concentration, length, and thickness, thus is low cost and highly convenient. First, the gate charge is derived by integrating the currents of the variable capacitors CGE and CGC during the turn-on and turn-off transients, and an analytical relationship between the dynamic IC and QG is researched. Second, a static collector current IC is established, and the gate charge is obtained through current integration during the period of the Miller capacitance plateau. The influence of the temperature on the static transconductance is studied, and the accuracy of the static current model is improved. Finally, the performance of the model is optimized with various voltages, temperatures, and currents. The experimental results reveal that the proposed model achieves a collector current error of less than 5.6 % under various operating conditions, which verifies the accuracy of the proposed model.

STATISTICAL CHARACTERISTICS OF THE GEOPHYSICAL FIELDS DISTURBED BY WEATHER FRONTS

The Earth (internal spheres) — atmosphere — ionosphere — magnetosphere (EAIM) formation is a single integrated system with direct and reverse, positive and negative coupling, as well as with their combination. The high-energy sources of natural and anthropogenic origins activate coupling between the components of the EAIM. The effects that the sources of various physi- cal nature have on the EAIM system have been studied quite well, while the influence of the weather fronts and other powerful atmospheric sources on the EAIM system and its components has been studied only partly. The scientific objective of this study is to conduct a statistical analysis of variations in the basic parameters of the geophysical fields that accompany the movement of atmospheric fronts. The histograms have been constructed that show the atmospheric pressure difference, atmospheric tem- perature difference, duration of the action of the atmospheric front, and the rate of change in the pressure and temperature, as well as the histograms showing the distribution of variations in the atmospheric electric field, the atmospheric current density, and in the magnetic field. The analysis undertaken has shown that these parameters exhibit variations within a broad range of values. The mean values of these parameters are estimated to be 145 Pa, 6 °C, 70 min, 2.4 Pa/min, 0.23 °C/min, 3.2 kV/m, 63 nA/m2, and 20 nT, respectively. The analysis of the scatter diagrams shows that the correlation between the variation in physi- cal parameters is almost always absent. This means that a single governing parameter along the path of the atmospheric front does not exi st. A simplified analytical relation has been derived to estimate the perturbation in the electric field strength caused by the atmospheric front, which yields ~6–60 kV/m values that increase by an order of magnitude during thunderstorms. Under disturbed conditions, the atmospheric current density is shown to increase from 10 –12 A/m2 to 10–11—10–10 A/m 2. The fol- lowing three mechanisms of an increase in the magnetic induction under the influence of the atmospheric front are considered: the disturbances of the external current density, electromagnetic induction, and the magnetic effect of turbulence. All these mechanisms yield the value of the effect less than ~1 nT. Only the magnetic effect of the ionosphere can explain an increase of 10—70 nT in the magnetic field variations. The energetics of the pressure, temperature, electric, and magnetic fields has been estimated to be (~10 16—10 17 J, ~1013—1014 W), (~1018—1019 J, 1015—1016 W), (~109—1011 J, ~106—108 W), (~1010 — 10 11 J, 107—108 W), respectively. The following channels have been validated through which the components of the EAIM sys- tem couple under the action of atmospheric fronts: atmospheric pressure differences, ionospheric electron density differences, the generation of infrasound and gravity waves, the generation of electromagnetic waves by lightning flashes, and the perturba- tions in the global electric circuit.

Form-finding of thermal-adaptive pin-bar assemblies based on eigenvalue modification

Lattice structures with tunable expansion properties have been investigated in multidisciplinary fields to control the temperature effects of structures or materials. The expected thermal adaptivity can be achieved by optimizing the structural geometry. A novel method for the form-finding of thermal-adaptive pin-bar assemblies is developed in this paper by considering the control of structural temperature effects as the minimization of the potential energy of the system. Based on the stationarity condition of the potential energy with respect to the nodal coordinates, the compatibility relationship between the thermal elongations of members and the target nodal displacements is proven to be the sufficient and necessary condition for structural thermal adaptivity. The solvability of the compatibility equation is determined by the rank equality between the compatibility matrix and its augmented form, which can be measured by the number of nonzero eigenvalues of its Gramian matrix. The analytical relationship between the eigenvalues of the Gramian matrix and the nodal coordinates is established using the matrix perturbation theory. A numerical strategy based on Newton’s method is proposed in which the eigenvalues are gradually modified by adjusting the nodal coordinates until the rank equality is satisfied. To address the existence of multiple solutions with structural thermal adaptivity, structural symmetry and periodicity constraints are introduced to narrow the solution space. The thermal-adaptive configurations of three illustrative pin-bar assemblies are analyzed using the proposed form-finding method, and the expected thermal deformations are verified for the obtained configurations using the finite element software ABAQUS. Comparing the results obtained by the proposed method with those obtained by nonlinear programming and the genetic algorithm validates the advantages of the proposed method in terms of computational time, optimality of the obtained configuration and applicability to complex structural geometries.

A modified perturbation method for global dynamic analysis of generalized mixed Rayleigh–Liénard oscillator with cubic and quintic nonlinearities

Deriving analytical relationship between the system parameters and amplitude of the limit cycle is a meaningful and challenging task. Currently, numerous existing analytical approximate methods struggle to achieve this goal when expressions of restoring force or nonlinear damping is complicated. To overcome this shortcoming, this study proposes a modified generalized harmonic function perturbation method. Using the proposed method, a generalized mixed RayleighLiénard oscillator with cubic and quintic nonlinearities was investigated. The analytical relationships between the system parameters and amplitude of the limit cycle, as well as the expression of its characteristic quantity, were derived. By employing these analytical relationships, the existence, stability, number, position, and amplitude of each limit cycle are quantitatively analysed. The homoclinic and heteroclinic bifurcations were also predicted using the above analytical relationships. Additionally, analytical approximate solutions for this oscillator were calculated using the proposed method. All results obtained in this study were subsequently confirmed numerically to demonstrate their feasibility and validity. Consequently, the proposed method can be considered an effective supplement to perturbation-based methods. This also implies that the work presented in this paper has a certain theoretical significance and application value in the research area of quantitative analysis methods for strongly nonlinear oscillators.

System analysis and optimization of antennas of radio electronic systems

The methodological foundations are formulated and the problems of system substantiation of antenna requirements based on the objective characteristics of radio electronic systems (RES) are considered. The contradictions of the indicator parameters of the objective characteristics of the RES in the formation of requirements for antennas are noted. For space-based airborne radar complexes, radar systems for measuring navigation parameters, and communication systems of repeater satellites servicing areas with a complex boundary shape, analytical relations have been obtained linking the characteristics and parameters of antennas with the objective characteristics of the RES. For the considered types of RES, the main directions for optimizing the characteristics and parameters of antennas are shown.

Signature of nonminimal scalar-gravity coupling with an early matter domination on the power spectrum of gravitational waves

The signal strength of primordial gravitational waves experiencing an epoch of early scalar domination, due to an oscillating scalar field, is reduced with respect to radiation domination. In this paper, we demonstrate that the specific pattern of this reduction is sensitive to the coupling between the dominant field and gravity. When this coupling is zero, the impact of early-matter domination on gravitational waves is solely attributed to the alteration of the Hubble parameter and the scale factor. In the presence of nonzero couplings, on the other hand, the evolution of primordial gravitational waves is directly affected as well, resulting in a distinct steplike feature in the power spectrum of the gravitational wave as a function of frequency. This feature serves as a smoking gun signature of this model. Although the aforementioned results are obtained numerically, we also provide an analytical expression of the power spectrum to illustrate its dependence on the model parameters and initial conditions. Furthermore, we provide analytical relations that specify the frequency interval in which the step occurs. We compare the analytical estimates with numerical analysis and show they match well. Published by the American Physical Society 2024

Accurate analytical evaluation of the generalized logarithmic and double Fermi–Dirac and Bose–Einstein functions

AbstractThe accurate definition and powerful evaluation modeling of the various generalized Fermi–Dirac and Bose–Einstein functions remain a challenging problem in various areas of physics. In this study, we develop a general analytical technique for accurately calculating logarithmic and double Fermi–Dirac and Bose–Einstein functions. The obtaining analytical formulae are established by considering the binomial expansion theorem. The obtained expressions are valid in chemical potential values between ‐∞ &lt;μ &lt;0 and have been designated as explicit form features, high precision, and less computing time. The calculation results are tabularly illustrated to show the consistency of the analytical relations analysis under the effect of parameters. Based on a comprehensive analysis of the results, they are potentially useful in applications to evaluate thermionic emission and astrophysics problems.

Perfect pulsed inline twin-beam squeezers

Perfect inline squeezers are both spectrally pure and have identical input and output temporal modes, allowing one to squeeze an arbitrary input quantum state in the sole input mode on which the device acts, while the quantum states of any other modes are unaffected. We study theoretically how to obtain a perfect pulsed inline squeezer in twin-beam systems by considering three commonly used configurations: unpoled single pass, poled single pass, and poled double pass. By obtaining analytical relations between the input and output temporal modes from the Bloch–Messiah decomposition of the discretized Heisenberg-picture propagator, we find that a double-pass structure produces a perfect pulsed inline squeezer when operated in a frequency degenerate, symmetric group-velocity matched type-II configuration.

Quantitative assessment of full-width at half-maximum and detector energy threshold in X-ray imaging systems

BackgroundThe response function of imaging systems is regularly considered to improve the qualified maps in various fields. More the accuracy of this function, the higher the quality of the images. MethodsIn this study, a distinct analytical relationship between full-width at half-maximum (FWHM) value and detector energy thresholds at distinct tube peak voltage of 100 kV has been addressed in X-ray imaging. The outcomes indicate that the behavior of the function is exponential. The relevant cut-off frequency and summation of point spread function S(PSF) were assessed at large and detailed energy ranges. ResultsA compromise must be made between cut-off frequency and FWHM to determine the optimal model. By detailed energy range, the minimum and maximum of S(PSF) values were revealed at 20 keV and 48 keV, respectively, by 2979 and 3073. Although the maximum value of FWHM occurred at the energy of 48 keV by 224 mm, its minimum value was revealed at 62 keV by 217 mm. Generally, FWHM value converged to 220 mm and S(PSF) to 3026 with small fluctuations. Consequently, there is no need to increase the voltage of the X-ray tube after the energy threshold of 20 keV. ConclusionThe proposed FWHM function may be used in designing the setup of the imaging parameters in order to reduce the absorbed dose and obtain the final accurate maps using the related mathematical suggestions.

Изотермическое прессование в конической матрице релаксирующего материала

The relations for calculating the deformation mode and force conditions of isothermal extrusion of blanks made of high-strength metallic alloys are proposed. Under isothermal deformation, the material is hardened and softened, which is associated with the manifestation of the viscous properties of the material (creep). In this regard, the state of viscoplasticity is taken on. The deformation state is accompanied by stress relaxation, which is greater the lower the speed (longer duration) of the operation. Based on the mechanics of deformation, the dependence of moulding conditions (deformation, force, damage to the work material) is expressed by analytical relations. The power balance of activity of forces results in a pressure estimation for isothermal exposure. In this case, a discontinuous field of path velocities is used, which consists of a block of deformations and rigid blocks. The blocks are separated by slip surfaces. Deformations occur in the deformation block and on slip surfaces. Since pressing leads to the occurrence of micro-damages, the damage rate of the coating material was estimated. In this case, the criteria of fracture kinetics are used: energy and deformation equations. The damage rate of the material depends on the speed and degree of deformation, or solely on the degree of deformation. For a number of materials, reducing the speed helps to reduce damage and, consequently, the possibility of increasing the degree of shaping of the primary blank. The relations for stiffness analysis of the stress pattern are given, on which the damage also depends. Calculations of the pressure and damage of the material under compaction for blanks made of titanium and high-strength aluminum alloys have been performed. It is shown that at low operation speeds on the appropriate hydraulic forging equipment, the exposure pressure decreases significantly. The aluminum alloy damaging is also reduced, and for titanium it depends only on the degree of forming.

Thermomechanical behavior of auxetic lattices

This study investigates the thermomechanical behavior of auxetic square-grid lattice structures through analytical, numerical, and experimental approaches. These structures have gained prominence in biomedical applications due to their ability to mimic the structural behavior of surrounding tissue, even if the natural tissue is not auxetic. First, analytical relations are derived for elastic modulus, Poisson’s ratio, and yield strength of lattice structures, as well as their thermomechanical behavior under different loading conditions. The mechanical properties of lattice structures are validated using both finite element and experiments. Several 3D-printed specimens with varying thickness-to-length dimensions are heated in a heat chamber to measure their deformations. Results also demonstrate excellent accuracy of the derived analytical relationships, which show that elastic modulus and yield strength increase exponentially with an increase in the thickness-to-length (t/l) ratio, while Poisson’s ratio is largely independent of t/l. Furthermore, it is found that the coefficient of thermal expansion is equivalent to that of the constituent solid material and that thermal stress has a linear relationship with temperature change. These findings have important implications for analyzing lattice structures based on other unit cell types and can be extended to macro-geometries such as tubular or spherical shapes commonly used in biomedical applications.