Analytical Theory Research Articles

Phase control of nonlinear Breit-Wheeler pair creation

Electron-positron pair creation occurs throughout the universe in the environments of extreme astrophysical objects, such as pulsar magnetospheres and black hole accretion disks. The difficulty of emulating these environments in the laboratory has motivated the use of ultrahigh-intensity laser pulses for pair creation. Here we show that the phase offset between a laser pulse and its second harmonic can be used to control the relative transverse motion of electrons and positrons created in the nonlinear Breit-Wheeler process. Analytic theory and particle-in-cell simulations of a head-on collision between a two-color laser pulse and electron beam predict that with an appropriate phase offset, the electrons will drift in one direction and the positrons in the other. The resulting current may provide a collective signature of nonlinear Breit-Wheeler, while the spatial separation resulting from the relative motion may facilitate isolation of positrons for subsequent applications or detection. Published by the American Physical Society 2024

Three-Body Binary Formation in Clusters: Analytical Theory

Abstract Binary formation in clusters through triple encounters between three unbound stars, ‘three-body’ binary formation, is one of the main dynamical formation processes of binary systems in dense environments. In this paper, we use an analytical probabilistic approach to study the process for the equal mass case and calculate a probability distribution for the orbital parameters of three-body-formed binaries, as well as their formation rate. For the first time, we give closed-form analytical expressions to the full orbital parameter distribution, accounting for both energy and angular momentum conservation. This calculation relies on the sensitive dependence of the outcomes of three-body scatterings on the initial conditions: here we compute the rate of three-body binaries from ergodic interactions, which allow for an analytical derivation of the distribution of orbital parameters of the binaries thus created. We find that soft binaries are highly favoured in this process and that these binaries have a super-thermal eccentricity distribution, while the few hard three-body binaries have an eccentricity distribution much closer to thermal. The analytical results predict and reproduce simulation results of three-body scattering experiments in the literature well.

Inversion of the attenuated momenta ray transform of planar symmetric tensors

Abstract We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary value problem for a system of transport equations, which we solve by an extension of Bukhgeim's $A$-analytic theory. The method of proof is constructive. To illustrate the reconstruction method, we present results obtained in the numerical implementation for the non-attenuated case of 1-tensors.

NEW CONJECTURES FOR THE ENTIRE FUNCTIONS ASSOCIATED WITH FRACTIONAL CALCULUS

In this paper, we address the entire Fourier sine and cosine integrals related to the Mittag-Leffler function. We guess that the entire functions have the real zeros in the entire complex plane. They can be connected with the well-known conjectures in analytic number theory. They are considered as the special solutions for the time-fractional diffusion equation within the Caputo fractional derivative.

Critical study of the concept of scientific hybridization of islamic education and neuroscience

Critical study of Islamic Education Neuroscience is still not sufficiently carried out in accounting for its knowledge, in order to confirm and fill in gaps in its scientific development. The purpose of this study is to examine the various scientific varieties of Islamic Education Neuroscience using the epistemology of Islamic Education, in order to find, fill, and develop their scientific potential, also from the perspective of developing hybridization of other Islamic Education scholarships. The method used in this study uses a qualitative type of literature according to Creswell: 2015, meaning that it is processed from various kinds of analytical theory from various sources of literature. The results of the study show that Islamic Education Neuroscience in epistemology also refers to Islamic law. Epistemologically, Irfani refers to the background of the scientific dichotomy between neuroscience, education, and Islam. Epistemologically, Burhani refers to empirical facts about the importance of collaboration between Islamic educators and neurologists in designing curricula and learning that optimizes students' brains in achieving Islamic education goals. Referring to the hybridization of other disciplines such as anthropology and psychology of Islamic education, this scientific development can further deepen the derivatives and clusters knowledge and more adapted to the needs of students.

Optical phase and amplitude measurements of underwater turbulence via self-heterodyne detection

The creation of underwater optical turbulence is driven by density variations that lead to small changes in the water’s refractive index, which induce optical path length differences that affect light propagation. Measuring a laser beam’s optical phase after traversing these turbulent variations can provide insight into how the water’s turbulence behaves. The sensing technique to measure turbulent fluctuations is a self-heterodyne beatnote enhanced by light’s orbital angular momentum (OAM) to obtain simultaneous optical phase and amplitude information. Experimental results of this method are obtained in a water tank that creates a thermally driven flow called Rayleigh–Bénard (RB) convection. The results show time-varying statistics of the beatnote that depend on the incident OAM mode order and the strength of the temperature gradient. Beatnote amplitude and phase power spectral densities are compared to analytic theory to obtain estimates of the turbulent length scales using the Taylor hypothesis that include mean flow speed, turbulent strength, and length scales, and flow dynamics due to intermittency in the RB process.

On the Mode of Existence of Mute Law and the Inference of Cryptotypes

AbstractA widespread thesis in the analytical theory of law is that norms exist as linguistic entities. Rodolfo Sacco is one of the authors who have most fruitfully insisted, on the contrary, that there is no necessary correlation between norms and language, not even in the specific context of law. He thus extended the conceptualisation of legal normativity well beyond the boundaries of language through the notions of cryptotype and mute law. This paper takes into account two alternative hypotheses to the hypothesis that norms exist as linguistic entities, which are respectively based on the concepts of deontic state-of-affairs and deontic noema. Both hypotheses are tested for their applicability to the phenomena investigated by Sacco under the notion of mute law, notably with reference to cryptotypes. The question is raised then of how the existence of cryptotypes can be inferred from behaviour. The paper emphasizes the role that can be played in this context by nomotrophic behaviour, that is, the behaviour that consists in a reaction to the violation of a norm.

Fluid simulations of resistive drift-wave turbulence with diamagnetic flow in ZPED experiments

We derive a diamagnetic resistive fluid model (DRF) and develop an associated two-dimensional fluid simulation code (DRF-2D) to explore the dynamics of resistive drift modes within the plasmas of the Zheda Plasma Experiment Device (ZPED). The validation of the linear dispersion relation for the DRF-2D code revealed a harmonious agreement between analytical theory and linear numerical simulations. Leveraging plasma parameters obtained from the ZPED experiments, we conducted a comprehensive series of nonlinear simulations using the DRF-2D code. Our simulations successfully replicate the nonlinear trends in turbulent fluctuations and transport observed in the ZPED experiments, particularly demonstrating a remarkably accurate alignment of the turning point in the magnetic field. Notably, the DRF model sheds light on the observed frequency sign reversal from the electron diamagnetic direction to the ion diamagnetic direction in the ZPED experiments. This is demonstrated through well-matched turning points in the confining magnetic field between the nonlinear simulations and ZPED experiments. The fidelity of our model in capturing these phenomena underscores its efficacy in providing valuable insights and predictive capabilities for the intricate dynamics observed in the ZPED plasmas.

Analysis of the embedded cell method in 2D for the numerical homogenization of metal-ceramic composite materials

Abstract In this paper, we extend our analysis of the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials, from [W.-P. Düll, B. Hilder and G. Schneider, Analysis of the embedded cell method in 1D for the numerical homogenization of metal-ceramic composite materials, J. Appl. Anal. 24 2018, 1, 71–80]. We show the convergence of the iteration scheme of this algorithm and the coincidence of the material properties predicted by the limit with the effective material properties provided by the analytical homogenization theory for two-dimensional linear hyperelastic isotropic materials with constant shear modulus and slightly varying first Lamé parameter.

Impedance of nanocapacitors from molecular simulations to understand the dynamics of confined electrolytes

Nanoelectrochemical devices have become a promising candidate technology across various applications, including sensing and energy storage, and provide new platforms for studying fundamental properties of electrode/electrolyte interfaces. In this work, we employ constant-potential molecular dynamics simulations to investigate the impedance of gold-aqueous electrolyte nanocapacitors, exploiting a recently introduced fluctuation-dissipation relation. In particular, we relate the frequency-dependent impedance of these nanocapacitors to the complex conductivity of the bulk electrolyte in different regimes, and use this connection to design simple but accurate equivalent circuit models. We show that the electrode/electrolyte interfacial contribution is essentially capacitive and that the electrolyte response is bulk-like even when the interelectrode distance is only a few nanometers, provided that the latter is sufficiently large compared to the Debye screening length. We extensively compare our simulation results with spectroscopy experiments and predictions from analytical theories. In contrast to experiments, direct access in simulations to the ionic and solvent contributions to the polarization allows us to highlight their significant and persistent anticorrelation and to investigate the microscopic origin of the timescales observed in the impedance spectrum. This work opens avenues for the molecular interpretation of impedance measurements, and offers valuable contributions for future developments of accurate coarse-grained representations of confined electrolytes.

Assessment of factors affecting tourism policy implementation in businesses: A case study of Hanoi, Vietnam

Tourism policy plays a huge role in the tourism economy and contributes to the overall economic development of a region, locality, or country. And businesses play a key role in implementing policies to achieve those goals. In reality, the implementation of tourism policies in businesses still faces many inadequacies, is not thorough, and there are many conflicts. This study uses quantitative research methods with AHP analytical hierarchy theory to evaluate factors affecting the implementation of tourism policies in Vietnamese businesses in Hanoi. The results show that there are five main factors affecting policy implementation in businesses: “Enterprise resources”, “Enterprise awareness”, “State apparatus”, “Interdisciplinary factors” and “Society”. Among them, the factor “Enterprise awareness” has the strongest impact, followed by the factors “Enterprise resources”, “State apparatus”, “Interdisciplinary factors” and finally the “Society” factor.

Noncollinear electro-optic detection of terahertz waves: Advantages and limitations

Electro-optic sampling of terahertz waves by noncollinearly propagating femtosecond laser pulses in electro-optic crystals can provide high efficiency and high spectral resolution of terahertz detection with various types of crystals and laser wavelengths, unlike the conventional collinear scheme. We develop an analytical theory of noncollinear electro-optic sampling detection technique that describes the modulation of the probe laser beam polarization as a result of nonlinear interaction between the optical and terahertz fields. The theory accounts for finite widths of the terahertz and probe beams. It is found that noncollinear scheme operates as a low-pass terahertz filter with the frequency cut-off determined by the width of the probe beam and the crossing angle of the terahertz and probe beams. We apply the theory to two practical situations: sampling of terahertz waves by fiber laser pulses (1.55 μm wavelength) in a GaAs crystal and sampling by Ti:sapphire laser pulses (800 nm wavelength) in a LiNbO3 crystal.

Analytical solution to second-harmonic generation of ultrashort laser pulse

We present an analytical method to evaluate the second-harmonic generation (SHG) process of ultrashort laser pulses in a nonlinear medium within the small-signal regime. Building upon the broadband nonlinear coupled wave theory, we derive an analytical solution that allows one to investigate the fundamental physics and detailed dynamics of the nonlinear interaction between ultrashort laser pulses. We find that SHG for ultrashort laser pulses in a nonlinear crystal arises from a series of self-SHG and self sum-frequency generation processes involving different frequency components. We have applied the analytical method to investigate specific pulse profiles with Gaussian and sech functions and found good agreement between analytical theory and numerical simulations, validating the accuracy of the analytical approach. The analytical method enables one to explore the evolution of the second-harmonic wave under various pulse profiles, pulse widths, and crystal thicknesses, and offers a more efficient and insightful approach to study the nonlinear optical dynamics of ultrashort laser pulses.

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

In this work, we take into account the (2+1)-Davey Stewartson equation (DSE) and the (2+1)-complex coupled Maccari system (CCMS) and their analytical solutions. Besides, we tackle the role of the problem parameters on the soliton behavior produced by the presented DSE. Exact traveling wave solutions are highly useful in numerical and analytical theories for such equations. While numerical methods are widely used, improving analytical approaches for obtaining analytical solutions is necessary for a deeper understanding of dynamics. This study marks a significant milestone by implementing the efficient analytical approach, enhanced modified extended tanh expansion method, for the first time to the (2+1)-DSE and (2+1)-CCMS equations, thereby making a notable contribution to the existing literature. We have shown that features of the soliton solutions can represent the spread of propagation on the wavefronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three- and two-dimensional arrangements can also be described in graphic representations of their behavior. With the help of the graphical depictions, bright, singular, and periodic singular soliton characters for the (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-DSE and singular, dark, bright, and periodic singular soliton characters for the (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-CCMS are acquired. The results show that the utilized analytical technique is easily applicable, efficient, reliable, robust, and categorical when it comes to finding analytical solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant influences on the behavior of the solitons of the DSE, and this examination is studied for the first time in this article.

Whistleblowing, Morality, Good Corporate Governance, The Role of Accountant as A Moderation Variable to Fraud Intention

Purposes - This study aims to investigate the problem solved and resolved by accountants in the country of Indonesia with various educational backgrounds, the scope of business, and experience in their job to examine fraud intention, with the whistleblowing system as a trigger and other variables like good corporate governance, Morality, the role of the accountant as additional variable moderate provides insights on the moderating effect to fraud intention. Design/methodology/Approach - Data was gathered using a questionnaire survey involving 291 respondents with accountant backgrounds. This study used quantitative research with smart pls 3.3 .3 and also the grand theory of agency theory and fraud triangle theory as a guide to conclude this study. Findings - The results show that there is a positive relationship between morality, Whistleblowing system, and Good Corporate Governance, to fraud intention. The moderate variables provide partial support that the role of accountants has a positive significant impact with good corporate governance to the fraud intention.  Research limitation/implications - The role of accountants in moderating whistleblowing against fraud in the future should be added with other dimensions such as professional skepticism, competence, and perceived behavior. Practical implications – this study contributes to the development of ideas to reduce fraud intention through critical studies of any variables including whistleblowing, Good Corporate Governance, Morality, also the role of accountants. Social Implications – this study argues that consistently by the major of morality personal is a must behave in a social environment, especially in the organization of a company or other society. Originality/Value – this study uses the role of the accountant as a proxy to contribute to the analytical fraud diamond theory. There is limited implication between whistleblowing the fraud intention because whistleblowing depends on practically system good corporate governance.

Positivity-hardness results on Markov decision processes

This paper investigates a series of optimization problems for one-counter Markov decision processes (MDPs) and integer-weighted MDPs with finite state space. Specifically, it considers problems addressing termination probabilities and expected termination times for one-counter MDPs, as well as satisfaction probabilities of energy objectives, conditional and partial expectations, satisfaction probabilities of constraints on the total accumulated weight, the computation of quantiles for the accumulated weight, and the conditional value-at-risk for accumulated weights for integer-weighted MDPs. Although algorithmic results are available for some special instances, the decidability status of the decision versions of these problems is unknown in general. The paper demonstrates that these optimization problems are inherently mathematically difficult by providing polynomial-time reductions from the Positivity problem for linear recurrence sequences. This problem is a well-known number-theoretic problem whose decidability status has been open for decades and it is known that decidability of the Positivity problem would have far-reaching consequences in analytic number theory. So, the reductions presented in the paper show that an algorithmic solution to any of the investigated problems is not possible without a major breakthrough in analytic number theory. The reductions rely on the construction of MDP-gadgets that encode the initial values and linear recurrence relations of linear recurrence sequences. These gadgets can flexibly be adjusted to prove the various Positivity-hardness results.

Health assessment of TBM diversion tunnel structure based on AHP and AMV models

Health assessment is one of the important theoretical bases for deciding whether the diversion tunnel can operate safely and stably. A project of the TBM diversion tunnel is taken as the research object to ensure the normal operation of the diversion tunnel. Based on measured data and considering multiple safety aspects such as structural response, durability, and external factors of the diversion tunnel, a TBM diversion tunnel structural health evaluation index system is established. A new method for the TBM diversion tunnel structural health comprehensive evaluation based on Analytic Hierarchy Process-Matter Element Extension-Variable Weight Theory (AMV) is proposed to explore the impact of AMV fluctuation with the measured results of the indicators on the weight, closeness, and health grade of each evaluation index. The high sensitivity and high-risk evaluation indicators for the structural health of the diversion tunnels are identified. It is found that the variable weight varies with the changes in various indicator values, which can accurately evaluate the health status of tunnels in real-time. The characteristic values of the tunnel grade calculated by the AHP and the AMV are 1.589 and 1.695, respectively. The results of the corresponding interval diversion tunnel are the basic safety state of grade B. Except for the two evaluation indicators of concrete strength and slurry properties, the variable weight values and grade characteristic values of other evaluation indicators increase with the increase of indicator values. The four indicators of segment settlement, segment opening, segment misalignment, and segment cracks are more sensitive to the health of the TBM diversion tunnel. This AMV can accurately evaluate the health status of the diversion tunnel structure. The research results can provide references for later maintenance work and similar projects.

General analytical theory of three-photon decays for hydrogenic ions with Coulomb Sturmian basis functions

General analytical theory of three-photon decays for hydrogenic ions with Coulomb Sturmian basis functions

Analytical and experimental analysis of guided waves in an aluminum plate under bending load

Although guided waves offer great potential for monitoring various structures, interpreting signals from piezoelectric sensors remains a challenging task. One main reason is the significant influence of environmental conditions on the wave propagation. A lot of research has already been done on the influence of temperature effects and recently more attention has been shifted towards loads. While previous publications have mainly focused on uni- or bi-directional loads, this publication expands the developed models to include bending loads.After reviewing the analytical basis of acoustoelasticity, the derived equations are expanded to nonhomogeneous elastic bending loads using the partial wave method. The analysis is completed using recent results developed by C. Hakoda and C. J. Lissenden (2018) [1], that gave more physical insight in the propagation of guided waves in various frequency-bands.The focus of the experimental analysis is around the fundamental S0- and A0-Modes of Lamb waves. To validate the analytical results an aluminum plate is instrumented using piezoelectric transducers and loaded with varying bending loads. The experimental results are in good agreement with the analytical theory and demonstrate the influence of bending prestress on guided wave propagation. Based on these results an innovative measurement method for bending loads is developed, that is robust to small temperature changes.

Heat-flux-limited Cloud Activity and Vertical Mixing in Giant Planet Atmospheres with an Application to Uranus and Neptune

Storms operated by moist convection and the condensation of CH4 or H2S have been observed on Uranus and Neptune. However, the mechanism of cloud formation, thermal structure, and mixing efficiency of ice giant weather layers remains unclear. In this paper, we show that moist convection is limited by heat transport on giant planets, especially on ice giants where planetary heat flux is weak. Latent heat associated with condensation and evaporation can efficiently bring heat across the weather layer through precipitations. This effect was usually neglected in previous studies without a complete hydrological cycle. We first derive analytical theories and show that the upper limit of cloud density is determined by the planetary heat flux and microphysics of clouds but is independent of the atmospheric composition. The eddy diffusivity of moisture depends on the planetary heat fluxes, atmospheric composition, and surface gravity but is not directly related to cloud microphysics. We then conduct convection- and cloud-resolving simulations with SNAP to validate our analytical theory. The simulated cloud density and eddy diffusivity are smaller than the results acquired from the equilibrium cloud condensation model and mixing length theory by several orders of magnitude but consistent with our analytical solutions. Meanwhile, the mass-loading effect of CH4 and H2S leads to superadiabatic and stable weather layers. Our simulations produced three cloud layers that are qualitatively similar to recent observations. This study has important implications for cloud formation and eddy mixing in giant planet atmospheres in general and observations for future space missions and ground-based telescopes.