Exponential Law Research Articles

Some considerations of measuring temperature sensitivity in thermal ecology

Some considerations of measuring temperature sensitivity in thermal ecology

Schweizer‐Sklar operations based hybrid aggregation operator to dual hesitant q‐rung orthopair fuzzy set and its application on MCGDM

AbstractDual hesitant q‐rung orthopair fuzzy (DHq‐ROF) set appears as a powerful tool in compare to other variants of fuzzy sets to deal with uncertainties associated with available information in various real‐life decision‐making cases. In order to make DHq‐ROF aggregation information process flexible, at first some operations viz., addition, multiplication, scalar multiplication, exponential laws based on Schweizer‐Sklar class of t‐conorms and t‐norms are defined. Subsequently, using these operations, weighted average and geometric operators and ordered weighted average and geometric operators are introduced. But weighted average or geometric operators and ordered weighted average or geometric operators consider only the weight of the opinions and the weight of the ordered position of each given opinion respectively. To resolve weights of the arguments, hybrid aggregation operators viz., DHq‐ROF Schweizer‐Sklar hybrid averaging, DHq‐ROF Schweizer‐Sklar hybrid geometric operators are developed and their properties are discussed. Afterwards, a new method to deal with multicriteria group decision making problems under DHq‐ROF environment is framed. To illustrate the proposed method a decision making problem related to investment company selection is considered and solved. To show the advantages of the proposed study, a comparative analysis among the developed and existing studies is discussed.

Improvement of size effect simulation based on an energy-balanced exponential softening bond model and fracture energy regularization

Although the Mode I fracture of rock demonstrates a noticeable size effect, current contact models in the discrete element method cannot simulate the size effect very well. An exponential softening bond model is proposed to address this issue based on an exponential damage law and an elliptic yield criterion. Its basic formulas are established on energy balance to ensure that the total fracture energy of the normal and shear springs always equals the fracture energy dissipated by the resultant contact force. The simulations of uniaxial tensile and three-point bending tests were conducted to demonstrate the performances of the proposed model on the fracture simulations. The particle size dependency is successfully eliminated by fracture energy regularization, in which the force–displacement relationship is adjusted based on fracture energy and particle size. The simulation results show that the exponential softening bond model effectively simulates the whole load–displacement curves of experimental tests. It also demonstrates a perfect energy balance among external work, internal energy, and fracture energy. Besides, compared with the other two bond models, the exponential softening bond model is more precise in representing the fracture toughness, the fracture process zone, and the size effect of the Mode I fracture of limestone.

The ro-vibrational ν2 mode spectrum of methane investigated by ultrabroadband coherent Raman spectroscopy.

We present the first experimental application of coherent Raman spectroscopy (CRS) on the ro-vibrational ν2 mode spectrum of methane (CH4). Ultrabroadband femtosecond/picosecond (fs/ps) CRS is performed in the molecular fingerprint region from 1100 to 2000cm-1, employing fs laser-induced filamentation as the supercontinuum generation mechanism to provide the ultrabroadband excitation pulses. We introduce a time-domain model of the CH4 ν2 CRS spectrum, including all five ro-vibrational branches allowed by the selection rules Δv = 1, ΔJ = 0, ±1, ±2; the model includes collisional linewidths, computed according to a modified exponential gap scaling law and validated experimentally. The use of ultrabroadband CRS for in situ monitoring of the CH4 chemistry is demonstrated in a laboratory CH4/air diffusion flame: CRS measurements in the fingerprint region, performed across the laminar flame front, allow the simultaneous detection of molecular oxygen (O2), carbon dioxide (CO2), and molecular hydrogen (H2), along with CH4. Fundamental physicochemical processes, such as H2 production via CH4 pyrolysis, are observed through the Raman spectra of these chemical species. In addition, we demonstrate ro-vibrational CH4 v2 CRS thermometry, and we validate it against CO2 CRS measurements. The present technique offers an interesting diagnostics approach to in situ measurement of CH4-rich environments, e.g., in plasma reactors for CH4 pyrolysis and H2 production.

Bianchi Type V Universe with Time Varying Cosmological Constant and Quadratic Equation of State in f(R,T) Theory of Gravity

In recent years, modified theories of gravity have been extensively studied because of the discovery and confirmation of the current phase of accelerated expansion of the universe. The f(R,T) theory of gravity is one such theory, proposed by Harko et al. in 2011, in which R is the Ricci scalar and T is the trace of the stress-energy tensor. In this paper, we study Bianchi type V universe in f(R,T) theory of gravity with time varying cosmological constant and a quadratic equation of state p=αρ2-ρ, where α≠0 is a constant. We obtain exact solutions of the field equations for two cases: one with a volumetric expansion law and the other with an exponential expansion law. The physical features of the two models are discussed by examining the behaviour of some important cosmological parameters such as the Hubble parameter, the deceleration parameter etc. We find that the models have initial singularity and the physical parameters diverge at the initial epoch. The model 1, corresponding to the volumetric expansion law does not resemble ΛCDM model while the model 2, corresponding to the exponential expansion law, resembles ΛCDM model. The energy conditions of the models are also examined and found to be consistent with recent cosmological observations.

Modeling of FGM beam under an extended exponential law

Modeling of FGM beam under an extended exponential law

Truncated generalized coherent states

A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label, and resolution of the identity operator with a positive weight function. Relying on this approach, in the present scenario, coherent states are generalized over the canonical or finite dimensional Fock space of the harmonic oscillator. A class of generalized coherent states is determined such that the corresponding distributions of the number of excitations depart from the Poisson statistics according to combinations of stretched exponential decays, power laws, and logarithmic forms. The analysis of the Mandel parameter shows that the generalized coherent states exhibit (non-classical) sub-Poissonian or super-Poissonian statistics of the number of excitations, based on the realization of determined constraints. Mittag-Leffler and Wright generalized coherent states are analyzed as particular cases.

A REPAIR REPLACEMENT PROBLEM FOR COLD STANDBY SYSTEM USING ALPHA SERIES AND GEOMETRIC PROCESS

The present paper studies a cold standby repairable system consisting of two identical components namely component 1, component 2 and onerepairman is studied. Assume that each component after repair is not 'as good as new' and also the successive working times form a decreasing a-series process, the successive repair time's form an increasing geometric process and both the processes are exposing to exponential failure law. Under these assumptions we study an optimal replacement policy N in which we replace the system when the number of failures of component 1 reaches N. It can be determined that an optimal repair replacement policy N* such that the long run average cost per unit time is minimized. It can also be derived an explicit expression of the long-run average cost and the corresponding optimal replacement policy N* can be determined analytically. Numerical results are provided to support the theoretical results

A model for gastrointestinal tract motility in a 4D imaging phantom of human anatomy.

Gastrointestinal (GI) tract motility is one of the main sources for intra/inter-fraction variability and uncertainty in radiation therapy for abdominal targets. Models for GI motility can improve the assessment of delivered dose and contribute to the development, testing, and validation of deformable image registration (DIR) and dose-accumulation algorithms. To implement GI tract motion in the 4D extended cardiac-torso (XCAT) digital phantom of human anatomy. Motility modes that exhibit large amplitude changes in the diameter of the GI tract and may persist over timescales comparable to online adaptive planning and radiotherapy delivery were identified based on literature research. Search criteria included amplitude changes larger than planning risk volume expansions and durations of the order of tens of minutes. The following modes were identified: peristalsis, rhythmic segmentation, high amplitude propagating contractions (HAPCs), and tonic contractions. Peristalsis and rhythmic segmentations were modeled by traveling and standing sinusoidal waves. HAPCs and tonic contractions were modeled by traveling and stationary Gaussian waves. Wave dispersion in the temporal and spatial domain was implemented by linear, exponential, and inverse power law functions. Modeling functions were applied to the control points of the nonuniform rational B-spline surfaces defined in the reference XCAT library. GI motility was combined with the cardiac and respiratory motions available in the standard 4D-XCAT phantom. Default model parameters were estimated based on the analysis of cine MRI acquisitions in 10 patients treated in a 1.5T MR-linac. We demonstrate the ability to generate realistic 4D multimodal images that simulate GI motility combined with respiratory and cardiac motion. All modes of motility, except tonic contractions, were observed in the analysis of our cine MRI acquisitions. Peristalsis was the most common. Default parameters estimated from cine MRI were used as initial values for simulation experiments. It is shown that in patients undergoing stereotactic body radiotherapy for abdominal targets, the effects of GI motility can be comparable or larger than the effects of respiratory motion. The digital phantom provides realistic models to aid in medical imaging and radiation therapy research. The addition of GI motility will further contribute to the development, testing, and validation of DIR and dose accumulation algorithms for MR-guided radiotherapy.

3D fracture study of cracked functionally graded biological materials by XIGA approach using Bézier extraction of NURBS

Functionally graded material (FGM) offers many varied engineering applications especially in biomedical implants and also used as biomaterials in orthopaedic implants such as hip & knee replacement and joint replacements and orthodontic applications. High risks are involved with revision surgery as orthopaedic prostheses suffer from limited lifetime. Commonly used bio materials consist of uniform and single constituent are vulnerable for their fabrication. Therefore, FGMs are developed to fabricate hybrid bio-material for overcoming these shortcomings. A long service life and safety of these hybrid bio-materials used in biomedical applications are one of the most important objective for their safe design and fabrications. In this paper, three-dimensional (3D) fracture problems in elastically graded biological materials by extended isogeometric analysis (XIGA) using Bézier extraction of NURBS are numerically simulated to understand the fracture behaviour. Bézier extraction of NURBS-based basis functions are implemented in discretization of domain for approximating both unknown field solution and geometries. The Bézier extraction operation decomposes the NURBS basis functions into a set of linear combination of Bernstein polynomials and a set of C0–continuity Bézier elements. For FGMs, exponential law has been implemented for grading the material property from left region (Material-A) to right region (Material-B). Few test cases based on penny-shaped crack problems have been solved to calculate fracture parameters, Von-Mises stress contours and deformation contours.

Hydrodynamic Characteristics of an Electric Eel-Like Undulating Fin

Taking the electric eel as a bionic object, a long undulatory fin is designed. The turbulent model standard k-ε is used to solve the N‒S equation of a three-dimensional unsteady incompressible fluid. The hydrodynamic characteristics of the undulatory fin are studied, and the influence of the swing angle, wave frequency and ground effects on the propulsion performance of the undulatory fin are discussed. The mathematical models of the average thrust and average lateral force of the undulatory fin are established by using multiple linear regression. The results show that the thrust and lateral force of the undulatory fin increase with increasing swing angle and swing frequency, but in a motion period, the number of fluctuations of the thrust is approximately twice that of the lateral force. The relationship between the average thrust force and the average lateral force of the undulatory fin and the wave frequency and the maximum swing angle satisfies a specific exponential law. When the undulating fin moves near the wall (d ≤0.2 W), due to the coupling between the vortex at the lower edge and the tail vortex where part of the vortex is transferred to the two sides, the total thrust decreases, and the lateral force increases.

Aging in binary-state models: The Threshold model for complex contagion.

We study the non-Markovian effects associated with aging for binary-state dynamics in complex networks. Aging is considered as the property of the agents to be less prone to change their state the longer they have been in the current state, which gives rise to heterogeneous activity patterns. In particular, we analyze aging in the Threshold model, which has been proposed to explain the process of adoption of new technologies. Our analytical approximations give a good description of extensive Monte Carlo simulations in Erdős-Rényi, random-regular and Barabási-Albert networks. While aging does not modify the cascade condition, it slows down the cascade dynamics towards the full-adoption state: the exponential increase of adopters in time from the original model is replaced by a stretched exponential or power law, depending on the aging mechanism. Under several approximations, we give analytical expressions for the cascade condition and for the exponents of the adopters' density growth laws. Beyond random networks, we also describe by Monte Carlo simulations the effects of aging for the Threshold model in a two-dimensional lattice.

A temperature-dependent elastoplastic damage model for frozen sandstone

Subzero temperature has a significant effect on mechanical behaviors of rocks. When a sandstone is in subzero temperature environments, the sandstone exhibits temperature-dependent mechanical characteristics due to the freezing of pore water and the shrinkage of mineral particles. To disclose the influence of subzero temperature on the mechanical behaviors of the frozen sandstone, triaxial compressive tests were carried out at four confining pressures (0 MPa, 1 MPa, 3 MPa, 5 MPa) and four subzero temperatures (0 °C, −5 °C, −10 °C, −15 °C). The laboratory tests show that the frozen sandstone undergoes four typical deformation stages from initial loading to failure: compaction, elasticity, yield and postpeak failure stage. With the temperature decreasing, the compaction stage gradually shortens, and the nonlinear behavior of yield stage weakens. The peak strength and initial yield stress of the frozen sandstone increase, and the initial and ultimate yield surfaces expand gradually with decreasing temperature. Based on the deformation features of the frozen sandstone, an elastoplastic damage model is established by considering the effect of subzero temperature on the yield process and deformation. The elastoplastic damage model was calibrated by the experimental data, and the comparisons demonstrate that the proposed constitutive model well agrees with the stress–strain curves at the four subzero temperatures. An exponential evolution law of the macroscopic damage is found in the elastoplastic model, which is totally consistent with the microscopic damage variation monitored by the acoustic emission (AE) technology. Therefore, the temperature-dependent elastoplastic model can well predict the whole deformation behaviors of the sandstone under different subzero temperatures and gives a quantitative description on the damage evolution, and may serve as theoretical references for the construction and safety operation of frozen rock masses in cold regions.

Vibration and wave propagation in functionally graded beams with inclined cracks

This paper proposes an FEA method to study the vibration and wave propagation in functionally graded material (FGM) beams with multiple inclined cracks by introducing the local flexibility matrix caused by the cracks. The bending and tensile stiffnesses of the inclined cracks and their interaction are taken into consideration. Two-node (three degrees of freedom per node) beam element is used. The inclined cracks are equivalent to transversal cracks to calculate the additional flexibility matrix of the inclined cracked FGM beam element. The material properties of the FGM beam are supposed to satisfy the exponential law along its thickness. The governing equations of motion for the FGM beam with multiple inclined cracks are deduced in the frame of Euler-Bernoulli theory and Lagrange function, and numerically solved by the Newmark average acceleration method. Both theoretical and numerical comparisons are presented to validate the present method for the inclined cracked FGM beam with varying boundary conditions, arbitrary inclined crack angles as well as varying inclined crack lengths. The effects of the location, length, inclined angle and number of the inclined cracks as well as material property ratio on the fundamental frequencies and wave propagation characteristics of the inclined cracked cantilever FGM beams are comprehensively investigated.

ОБ ОЦЕНКЕ СНИЗУ РЕШЕНИЙ СЛАБО НЕЛИНЕЙНОГО ВОЛЬТЕРРОВА ИНТЕГРО-ДИФФЕРЕНЦИАЛЬНОГО УРАВНЕНИЯ ВТОРОГО ПОРЯДКА С ЗАПАЗДЫВАНИЯМИ

Sufficient conditions are established for lower bounds and tending to infinity as the argument of solutions to a weakly non-linear second-order Volterra integro-differential equation with delays on the half-axis grows unbounded. For this purpose, a non-standard method of reduction to a system, the method of transforming the equations of V. Volterra, the method of partial cutting, the method of integral inequalities with delays and the method of estimating solutions from below Yu.A. Ved are developed. It is shown that solutions with initial data from a certain manifold have lower bounds, and such solutions tend to infinity according to the exponential law with unlimited growth of the argument. This article proposes a technique for solving the problem of estimating from below on the half-line solutions of a weakly nonlinear Volterra-type integro-differential equation of the second order with delays, while the main role is played by the non-standard method of reduction to the system and the method of estimating solutions from below Yu.A.Ved (1965).

Mathematical modelling of the waning of anti-RBD IgG SARS-CoV-2 antibody titers after a two-dose BNT162b2 mRNA vaccination.

After exposure to SARS-CoV-2 and/or vaccination there is an increase in serum antibody titers followed by a non-linear waning. Our aim was to find out if this waning of antibody titers would fit to a mathematical model. We analyzed anti-RBD (receptor binding domain) IgG antibody titers and the breakthrough infections over a ten-month period following the second dose of the mRNA BNT162b2 (Pfizer-BioNtech.) vaccine, in a cohort of 54 health-care workers (HCWs) who were either never infected with SARS-CoV-2 (naïve, nHCW group, n=27) or previously infected with the virus (experienced, eHCW group, n=27). Two mathematical models, exponential and power law, were used to quantify antibody waning kinetics, and we compared the relative quality of the goodness of fit to the data between both models was compared using the Akaik Information Criterion. We found that the waning slopes were significantly more pronounced for the naïve when compared to the experienced HCWs in exponential (p-value: 1.801E-9) and power law (p-value: 9.399E-13) models. The waning of anti-RBD IgG antibody levels fitted significantly to both exponential (average-R2: 0.957 for nHCW and 0.954 for eHCW) and power law (average-R2: 0.991 for nHCW and 0.988 for eHCW) models, with a better fit to the power law model. In the nHCW group, titers would descend below an arbitrary 1000-units threshold at a median of 210.6 days (IQ range: 74.2). For the eHCW group, the same risk threshold would be reached at 440.0 days (IQ range: 135.2) post-vaccination. Two parsimonious models can explain the anti-RBD IgG antibody titer waning after vaccination. Regardless of the model used, eHCWs have lower waning slopes and longer persistence of antibody titers than nHCWs. Consequently, personalized vaccination booster schedules should be implemented according to the individual persistence of antibody levels.

Thermoelectric nonlinear vibration and buckling analysis of the smart porous core sandwich plate (SPCSP) resting on the elastic foundation

This paper analyses the vibration and buckling responses analysis of the smart porous core sandwich plate (SPCSP) resting on the elastic foundation under thermoelectric and thermomechanical loading. The plate is a constraint with conventional and unconventional boundary conditions. The thermo-mechanical properties of the plate are graded through the thickness direction with the sigmoid and exponential laws. The sandwich plate considered geometrical nonlinearity and assumed quadratic electric potential function across the thickness direction. The Hamilton principle derives the formulation with the first-order shear deformation theory (FSDT) displacement field. A nine-node quadratic element-based higher-order finite element method with seven degrees of freedom (DOFs) is used to convert the governing equation into a set of algebraic forms and solve it computationally (using MATLAB) with a modified Newton-Raphson scheme. Buckling and vibration responses are analysed under varying plate parameters like material exponent N, thickness ratio (a/h), porous exponent with different porosity dispersion, conventional and unconventional conditions, applied electric voltage V and temperature change [Formula: see text]. It is found that the presence of the Pasternak parameter gives additional stability to structures and overcomes the instability due to porosity. Also, the proposed work is not only precise but also simple in predicting the vibration and buckling response of smart sandwich porous plates under thermo-electric mechanical loading.

Lab-scale electrostatic droplet collection from a fog plume with droplet evaporation

The electrostatic droplet collection shows a great potential in harvesting water from fog. However, how and to what extent the droplet evaporation affects the droplet collection efficiency is unclear, which is a key problem to promote the industrial application of the electrostatic fog collection technology. A lab-scale electrostatic fog plume collector was proposed and a numerical model was developed to take the droplet evaporation into account. Experimental and numerical results demonstrated that the fluid transport process in the electrostatic device can be numerically predicted with reasonable accuracy. The ionic wind generated by the corona discharge inhibits the droplet dispersion, which aids the droplet collection. The water vapor mass fraction difference between the fog plume and the ambient air was proposed as the indicator of the droplet evaporation degree. It was found that the droplet collection efficiency decreases with the increasing water vapor mass fraction difference in an exponential law. Furthermore, the droplet collection efficiency loss caused by the droplet evaporation enhances with the decreasing droplet mass concentration in the plume and a loss of 85% occurs when the droplet mass concentration is 6 g/m3. The droplet collection efficiency decreases with the increasing fog plume velocity and a droplet collection efficiency loss of 28%∼43% exists when the plume velocity ranges from 1.3 to 5 m/s.

Size-dependent vibrations of bi-directional functionally graded porous beams under moving loads incorporating thickness effect

This article analyzes the forced and free vibrations of bi-directional functionally graded (BDFG) porous nanobeams under moving loads by considering the thickness effect based on the nonlocal strain gradient theory (NSGT). It is assumed that the material properties of the system are graded across the transverse and axial directions according to power and exponential laws, respectively. Various porosity models, including even, uneven, and asymmetric porosity distribution patterns, are considered to model the porosity effects. The dynamic equation of the system is derived by implementing the physical neutral surface concept. Analytical and numerical approaches are adopted to acquire the vibration response of the system. Mathematical closed-form expressions are provided for various dynamic phenomena, such as two types of cancelation, two types of resonance, maximum resonance, cancelation disappearance, and resonance disappearance. In addition, for the first time in this article, it is demonstrated that BDFG porous nanobeams under moving loads are prone to experience the double cancelation phenomenon. Several comparison studies with published data are conducted to validate the results. Also, comprehensive parametric studies are carried out to elucidate the impacts of system parameters such as thickness power index, axial gradient parameter, scale parameter ratio, axial force, porosity coefficient, and porosity distribution pattern on the dynamic magnification factor, critical load speed, and maximum free-response. The outcomes established that by considering the thickness effect, the stiffening behavior of the system is amplified depending on the slenderness ratio. Also, it is concluded that, among the considered porous models, the critical load speed for the system with an even porosity distribution is more dependent on the thickness power index.

Probabilistic Fitts' law and the likelihood of the Tunguska type of event

An analogy with the recently suggested probabilistic interpretation of the Fitts' law in the theory of human-computer interactions (HCI) is employed in this analysis to assess the likelihood that a Tunguska type meteorite hits Earth. Two extreme cases are considered: (1) a big asteroid travels within the solar system still far away from Earth (the probabilistic Fitts' law reduces in such a situation to the well-known exponential law of reliability) and (2) the asteroid has become a meteorite and is approaching Earth (the complete double-exponential probabilistic Fitts' law is employed in such a case). The addressed analogy can be used, in addition to other efforts, to design, conduct and interpret an inexpensive, but, of course, highly tentative HCI-theory-based imitation viewed as analogous to the vital space safety related problem.