Integrable Perturbations Research Articles

Numerical investigation of two-dimensional fractional Helmholtz equation using Aboodh transform scheme

Purpose This paper aims to present a numerical investigation for two-dimensional fractional Helmholtz equation using the Aboodh integral homotopy perturbation transform scheme (AIHPTS). Design/methodology/approach The proposed scheme combines the Aboodh integral transform and the homotopy perturbation scheme (HPS). This strategy is based on an updated form of Taylor’s series that yields a convergent series solution. This study analyzes the fractional derivatives in the context of Caputo. Findings This study illustrates two numerical examples and calculates their approximate results using AIHPTS. The derived findings are also presented in tabular form and graphical representations. Research limitations/implications In addition, He’s polynomials are calculated using HPS, so the minimal computational outcome is a defining feature of this method and gives a competitive advantage over other series solution techniques. Originality/value Numerical data and graphical illustrations for different fractional order levels confirm the proposed method’s successful performance. The results show that the proposed approach is speedy and straightforward to execute on fractional-ordered models.

On the quadratic closeness of eigenfunctions of «unperturbed» and «perturbed» differentiation operators on an interval

The article considers the eigenvalue problem of the differentiation operator, when the spectral param- eter is also present in the boundary condition with an integral perturbation, where the integrand has the property of limited variation and has a value of unity at the ends of the segment [-1, 1]. The derivatives with respect to the time variable included in the boundary condition naturally arise when solving (by the Fourier method) initial boundary value problems for evolution equations. The conjugate operator is constructed. It is shown that the spectral questions of the conjugate operator have a similar structure. The characteristic determinant of the original direct spectral problem with an integral perturbation of the boundary condition and for the eigenvalue problem of a loaded first-order differential equation on a segment with a periodic boundary condition, which is an entire analytical function of the spectral parameter, is constructed. Based on the formula of the characteristic determinant, conclusions are drawn about the asymptotic behavior of the spectrum of the original «perturbed» differentiation operator and the loaded first-order differential equation on the segment. A special feature of the operator under consideration is the non-self-adjointness of the operator in L2(–1,1). The quadratic proximity of the systems of eigen functions of the «unperturbed» and «perturbed» differentiation operators and the Riesz basis property of these systems are proved. In this case, the system of eigenfunctions of the «perturbed» operator is not orthonormal.

An existence result for integro-differential degenerate sweeping process with convex sets.

In this paper, we study the well-posedness in the sense of existence and uniqueness of a solution of integrally perturbed degenerate sweeping processes, involving convex sets in Hilbert spaces. The degenerate sweeping process is perturbed by a sum of a singlevalued map satisfying a Lipschitz condition and an integral forcing term. The integral perturbation depends on two time-variables, by using a semi-discretization method. Unlike the previous works, the Cauchy’s criterion of the approximate solutions is obtained without any new Gronwall’s like inequality.

Lambda-ABF: Simplified, Portable, Accurate, and Cost-Effective Alchemical Free-Energy Computation.

We introduce the lambda-Adaptive Biasing Force (lambda-ABF) method for the computation of alchemical free-energy differences. We propose a software implementation and showcase it on biomolecular systems. The method arises from coupling multiple-walker adaptive biasing force with λ-dynamics. The sampling of the alchemical variable is continuous and converges toward a uniform distribution, making manual optimization of the λ schedule unnecessary. Contrary to most other approaches, alchemical free-energy estimates are obtained immediately without any postprocessing. Free diffusion of λ improves orthogonal relaxation compared to fixed-λ thermodynamic integration or free-energy perturbation. Furthermore, multiple walkers provide generic orthogonal space coverage with minimal user input and negligible computational overhead. We show that our high-performance implementations coupling the Colvars library with NAMD and Tinker-HP can address real-world cases including ligand-receptor binding with both fixed-charge and polarizable models, with a demonstrably richer sampling than fixed-λ methods. The implementation is fully open-source, publicly available, and readily usable by practitioners of current alchemical methods. Thanks to the portable Colvars library, lambda-ABF presents a unified user interface regardless of the back-end (NAMD, Tinker-HP, or any software to be interfaced in the future), sparing users the effort of learning multiple interfaces. Finally, the Colvars Dashboard extension of the visual molecular dynamics (VMD) software provides an interactive monitoring and diagnostic tool for lambda-ABF simulations.

Perturbation of azurophilic granule integrity drives NLRP3-independent IL-1b processing and release in neutrophils

Abstract IL-1β is an inflammatory cytokine secreted by myeloid cells in response to infection or sterile tissue damage. Non-canonical secretion of IL-1β from monocytes downstream of activated NLRP3 inflammasomes is the best-characterized model; this is mediated by caspase-1 cleavage of GSDMD and N-GSDMD plasma membrane (PM) pore formation to permit release of IL-1β and induction of pyroptosis. NLRP3 is a cytosolic sensor of cellular homeostasis including [K+]. In monocytes, K+ efflux mediated NLRP3 activation is triggered by agents that disrupt lysosomal integrity. Neutrophils assemble competent NLRP3 inflammasomes and release IL-1β via GSDMD-dependent mechanisms, but they resist N-GSDMD PM pore formation and pyroptosis. We tested whether lysosome-disrupting stimuli in neutrophils would phenocopy the monocyte mechanism of NLRP3-dependent IL-1β release. Surprisingly, our data indicates that lysosome disruption induces release of mature IL-1β and lytic cell death in an NLRP3-independent manner. Kinetic analysis demonstrates an alternate mechanism of release such that early phase IL-1β release is NLRP3-dependent, but prolonged stimulation leads to NLRP3-independent release. Collectively, our data supports a signaling mechanism by which azurophilic granule disruption and cytosolic accumulation of neutrophil serine proteases disrupt canonical NLRP3 inflammasome assembly and directly cleave proIL-1β as part of a novel neutrophil-specific signaling mechanism of IL-1β processing and export.

On a class of evolution problems driven by maximal monotone operators with integral perturbation

The present paper is dedicated to the study of a first-order differential inclusion driven by time and state-dependent maximal monotone operators with integral perturbation, in the context of Hilbert spaces. Based on a fixed point method, we derive a new existence theorem for this class of differential inclusions. Then, we investigate an optimal control problem subject to such a class, by considering control maps acting in the state of the operators and the integral perturbation.

BV Solutions to Evolution Inclusion with a Time and Space Dependent Maximal Monotone Operator

This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, existence of periodic and bounded variation right continuous (BVRC) solutions. Second-order evolution inclusions and fractional (Caputo and Riemann–Liouville) differential inclusions are also considered. A result of the Skorohod problem driven by a time- and space-dependent operator under rough signal and a Volterra integral perturbation in the BRC setting is given. The paper finishes with some results for fractional differential inclusions under rough signals and Young integrals. Many of the given results are novel.

C. elegans spermatocyte divisions show a weak spindle checkpoint response.

Male meiotic division exhibits two consecutive chromosome separation events without apparent pausing. Several studies have shown that spermatocyte divisions are not stringently regulated as in mitotic cells. In this study, we investigated the role of the canonical spindle assembly (SAC) pathway in Caenorhabditis elegans spermatogenesis. We found the intensity of chromosome-associated outer kinetochore protein BUB-1 and SAC effector MDF-1 oscillates between the two divisions. However, the SAC target securin is degraded during the first division and remains undetectable for the second division. Inhibition of proteasome-dependent protein degradation did not affect the progression of the second division but stopped the first division at metaphase. Perturbation of spindle integrity did not affect the duration of meiosis II, and only slightly lengthened meiosis I. Our results demonstrate that male meiosis II is independent of SAC regulation, and male meiosis I exhibits only weak checkpoint response.

Deciphering NF-kappaB pathways in smoking-related lung carcinogenesis.

One of the main causes of death worldwide is lung cancer, which is largely caused by cigarette smoking. The crucial transcription factor NF-κB, which controls inflammatory responses and various cellular processes, is a constitutively present cytoplasmic protein strictly regulated by inhibitors like IκB proteins. Upon activation by external stimuli, it undergoes phosphorylation, translocates into the nucleus, and modulates the expression of specific genes. The incontrovertible association between pulmonary malignancy and tobacco consumption underscores and highlights a public health concern. Polycyclic aromatic hydrocarbons and nitrosamines, potent carcinogenic compounds present in the aerosol emitted from combusted tobacco, elicit profound deleterious effects upon inhalation, resulting in severe perturbation of pulmonary tissue integrity. The pathogenesis of smoking-induced lung cancer encompasses an intricate process wherein NF-κB activation plays a pivotal role, triggered by exposure to cigarette smoke through diverse signaling pathways, including those associated with oxidative stress and pro-inflammatory cytokines. Unraveling the participation of NF-κB in smoking-induced lung cancer provides pivotal insights into molecular processes, wherein intricate crosstalk between NF-κB and pathways such as MAPK and PI3K-Akt amplifies the inflammatory response, fostering an environment conducive to the formation of lung cancer. This study reviews the critical function of NF-κB in the complex molecular pathways linked to the initiation and advancement of lung carcinogenesis as well as potential treatment targets. See also the graphical abstract(Fig. 1).

Distribution of eigenvalues of a perturbed differentiation operator on the interval

In this paper, we construct a characteristic determinant of the spectral problem of a first-order differential equation on an interval with an integral perturbation in the boundary value condition, which is an entire analytic function of the spectral parameter. Based on the formula for the characteristic determinant, conclusions are drawn about the asymptotic behavior of the spectrum of the perturbed spectral problem depending on the modulus of continuity of the subinteral function.

Two-phase flow instability characteristics of HTGR Once Through Steam Generators

High Temperature Gas-cooled Reactors (HTGR) have the advantage of inherent safety compared with most Gen III reactors. They also have very high temperature, which make the plant have high electricity generation efficiency and have has the potential for hydrogen production. Once Through Steam Generator (OTSG) is responsible for transferring high temperature heat from primary loop helium to secondary loop composed of water and steam. The evaporation tubes of HTGR OTSG are very long due to the low heat transfer coefficient of helium convection over tube bundles. A Two-phase flow instability may occur in HTGR OTSG, which can cause pulsation of the mass flow rate, system pressure and temperature. This will not only interfere with the control system, but also cause thermal fatigue damage in the structures. Thus, it is important to predict and avoid two-phase flow instability in HTGR OTSG. Three types of flow instabilities are investigated for HTGR OTSG using both a linear analytical model and a nonlinear numerical model. They are flow excursion (or Ledinegg instability), density wave oscillation and pressure drop oscillation. For the nonlinear numerical model, RELAP5 software is adopted. Flow excursion and pressure drop oscillation are discussed based on the predicted hydraulic characteristic curve of HTGR OTSG (pressure drop vs. mass flow rate curve). Density wave oscillation is investigated using the transient variation of the outlet mass flow rate. For the linear analytical model, a set of ordinary differential equations are established using integration and small perturbation methods. The variables of differential equations are the length of the subcooling water region, the length of both the subcooling water and saturated two-phase regions, the average density of the saturated two-phase region and the inlet mass flux. The stability of OTSG is investigated using the eigenvalues of the coefficient matrix of the ordinary differential equations. Based on the results calculated using the linear analytical model and nonlinear numerical model, there is no flow excursion, pressure drop oscillation or density wave oscillation at the designed partial and full power levels (30%, 50%, 75% and 100%). Thus, HTGR OTSG can operate stably and have a sufficient safety margin at the designed power levels. Density wave oscillation will happen when decreasing system pressure. However, increasing inlet resistance coefficient can avoid density wave oscillation effectively. The tube lengths’ influences on the stability boundary of OTSG are also investigated and it shows no strong dependency.

On System of Root Vectors of Perturbed Regular Second-Order Differential Operator Not Possessing Basis Property

This article delves into the spectral problem associated with a multiple differentiation operator that features an integral perturbation of boundary conditions of one specific type, namely, regular but not strengthened regular. The integral perturbation is characterized by the function px, which belongs to the space L20,1. The concept of problems involving integral perturbations of boundary conditions has been the subject of previous studies, and the spectral properties of such problems have been examined in various early papers. What sets the problem under consideration apart is that the system of eigenfunctions for the unperturbed problem (when px≡0) lacks the property of forming a basis. To address this, a characteristic determinant for the spectral problem has been constructed. It has been established that the set of functions px, for which the system of eigenfunctions of the perturbed problem does not constitute an unconditional basis in L20,1, is dense within the space L20,1. Furthermore, it has been demonstrated that the adjoint operator shares a similar structure.

Speed Sensorless Control Method of Synchronous Reluctance Motor Based on Resonant Kalman Filter

When estimating the active back electromotive force (AEMF) of synchronous reluctance motor (SynRM) at medium and high speed, the traditional Kalman Filter (KF) will produce large phase delay due to the low-pass filter characteristics. A novel speed sensorless control scheme of SynRM based on resonant Kalman filter (RKF) is proposed in this paper. Firstly, the AEMF observer based on KF is designed and the bandwidth performance is analyzed. To solve the phase delay problem caused by KF, a generalized integral resonance perturbation estimator (GIRPE) is introduced to the framework of KF and the proposed RKF is formed. The estimation error of AEMF is compensated through GIRPE in the current error feedback loop of KF observer. In this way, the high-precision position estimation at high speed range is obtained. Finally, an improved dynamic position compensator (IDPC) is proposed to enhance the position estimation performance under dynamic case. The effectiveness of proposed scheme is validated at a 1.5kW SynRM drive, and the computational burden of the proposed method is assessed quantitatively.

Asymptotics of a Solution to an Optimal Control Problem with Integral Convex Performance Index, Cheap Control, and Initial Data Perturbations

Asymptotics of a Solution to an Optimal Control Problem with Integral Convex Performance Index, Cheap Control, and Initial Data Perturbations

Asymptotic forms of solutions of half-linear ordinary differential equations with integrable perturbations

Asymptotic forms of solutions of half-linear ordinary differential equations with integrable perturbations

Computing chemical potentials of adsorbed or confined fluids.

The chemical potential of adsorbed or confined fluids provides insight into their unique thermodynamic properties and determines adsorption isotherms. However, it is often difficult to compute this quantity from atomistic simulations using existing statistical mechanical methods. We introduce a computational framework that utilizes static structure factors, thermodynamic integration, and free energy perturbation for calculating the absolute chemical potential of fluids. For demonstration, we apply the method to compute the adsorption isotherms of carbon dioxide in a metal-organic framework and water in carbon nanotubes.

Coupled systems of subdifferential type with integral perturbation and fractional differential equations

This paper is mainly devoted to study a class of first-order differential inclusions governed by time-dependent subdifferential operators involving an integral perturbation. Employing then the constructive method used there, we also handle the associated second-order differential inclusion.
 Our final topic, accomplished in infinite-dimensional Hilbert spaces, is to develop some variants related to coupled systems by such differential inclusions and fractional differential equations.

Rate Decline of Acid Fracturing Stimulated Well in Bi-Zone Composite Carbonate Gas Reservoirs

This paper develops a model of the multi-wing finite-conductivity fractures considering stress sensitivity for low-permeability bi-zone composite gas reservoirs. A new semi-analytical solution in the Laplace domain is presented. The main solution includes the theory of source function, Laplace integral transformation, perturbation technique, and Stehfest numerical inversion. Wellbore pressure is obtained by coupling solutions of reservoirs and fractures. The results showed that the pressure and derivative curves generated by this model include a bi-linear flow stage. The model was validated by comparing its results with Wang’s results and the commercial well-test simulator; the results showed excellent agreement. This model illustrated the seepage characteristic of acid fracturing stimulated wells during refracturing treatment and how they are influenced by reservoir and hydraulic fractures parameters (asymmetrical factor and fractures distribution, etc.). The model is suitable to solve the solution of arbitrary-angle hydraulic fracture in refracturing and helpful to understand the transient production rate characteristic of the multi-wing fracturing well.

Rossby waves past the breaking point in zonally dominated turbulence

The spontaneous emergence of structure is a ubiquitous process observed in fluid and plasma turbulence. These structures typically manifest as flows which remain coherent over a range of spatial and temporal scales, resisting statistically homogeneous description. This work conducts a computational and theoretical study of coherence in turbulent flows in the stochastically forced barotropic$\beta$-plane quasi-geostrophic equations. These equations serve as a prototypical two-dimensional model for turbulent flows in Jovian atmospheres, and can also be extended to study flows in magnetically confined fusion plasmas. First, analysis of direct numerical simulations demonstrates that a significant fraction of the flow energy is organized into coherent large-scale Rossby wave eigenmodes, comparable with the total energy in the zonal flows. A characterization is given for Rossby wave eigenmodes as nearly integrable perturbations to zonal flow Lagrangian trajectories, linking finite-dimensional deterministic Hamiltonian chaos in the plane to a laminar-to-turbulent flow transition. Poincaré section analysis reveals that Lagrangian flows induced by the zonal flows plus large-scale waves exhibit localized chaotic regions bounded by invariant tori, manifesting as Rossby wave breaking in the absence of critical layers. It is argued that the surviving invariant tori organize the large-scale flows into a single temporally and zonally varying laminar flow, suggesting a form of self-organization and wave stability that can account for the resilience of the observed large-amplitude Rossby waves.

BDE-209 disrupted the blood-testis barrier integrity by inhibiting estrogen receptorα signaling pathway in Sprague-Dawley rats.

Deca brominated diphenyl ether (BDE-209) is a widely used flame retardant with endocrine-disrupting activity which reportedly caused sperm quality decline and damaged blood-testis barrier (BTB). However, whether BDE-209 exposure led to BTB integrity dysfunction through affecting microtubule cytoskeletal organization and junctions was not well-elucidated. This study aimed to investigate the role of estrogen receptor α (ERα) in BDE-209-mediated perturbation of BTB integrity. Male rats and primary culture Sertoli cells were co-treated with BDE-209 and propylpyrazoletriol (PPT). The data demonstrated that BDE-209 impaired BTB integrity by reducing crucial tight junction-related proteins with ZO-1 and Occludin. Furthermore, the data suggested that BDE-209 diminished the apical ectoplasmic specialization markers with Eps8 and Formin1. In addition, BDE-209 damaged BTB ultrastructure including tight junctions and ectoplasmic specialization structures with broken tight junctions and the absence of actin microfilaments. Further experiments revealed that ERα was triggered in BDE-209-treated Sertoli cells. Unexpectedly, we found that PPT rescued BDE-209-mediated disruption of BTB integrity including tight junction and apical ectoplasmic specialization by activating ERα in Sertoli cells. Taken together, these findings indicated that intratesticular BDE-209 exposure perturbed BTB integrity and destroyed BTB structure by blocking ERα pathway. Our findings provide a new therapeutic target for male reproductive dysfunction.