Equation Technique Research Articles

Stabilized explicit u-p_w solution in soil dynamic problems near the undrained-incompressible limit

Traditionally, Biot’s formulation is employed to model the behavior of saturated soils. The u-p_w (solid displacement–pore water pressure) formulation can be considered as the standard one, since involves a good computational performance together with excellent accuracy for slow and moderate speed phenomena. Dynamic processes can be studied even if the acceleration of the water is neglected, what occurs in the undrained limit. It is well-known that u-p_w formulation might display instabilities in the undrained-incompressible limit. Several techniques have been proposed to overcome this issue, principally within an implicit time integration scheme for small strains. In this paper, a robust implementation of the divergence of the momentum equation technique is presented for an explicit u-p_w approach within the framework of optimal transportation meshfree scheme at finite strain. Several examples are provided in order to assess the good performance of the proposed methodology.

A global bifurcation organizing rhythmic activity in a coupled network

We study a system of coupled phase oscillators near a saddle-node on invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the qualitative properties of collective dynamics. Using Ott–Antonsen reduction and geometric techniques for ordinary differential equations, we identify heteroclinic bifurcation in a family of vector fields on a cylinder, which explains the change in collective dynamics. Specifically, we show that heteroclinic bifurcation separates two topologically distinct families of limit cycles: contractible limit cycles before bifurcation from noncontractibile ones after bifurcation. Both families are stable for the model at hand.

Eco-Friendly UV Spectrophotometric Method for Simultaneous Estimation of Evogliptin and Metformin Hydrochloride in Bulk and Combined Tablet Dosage Form

Evogliptin (EGT) is used in fixed-dose combination with metformin hydrochloride (MFH) for a better glycemic control in Type 2 diabetes mellitus. To date, no method is available for simultaneous estimation of these drugs. In the present study, an UV spectrophotometric method was developed in distilled water, an environment-friendly solvent using the simultaneous equation technique to simultaneously determine EGT and MFH in bulk and tablet dosage form. The developed method was validated and applied to commercial tablet dosage forms containing EGT and MFH in combination. With a great correlation value (R2>0.998), the analytes displayed good linearity in the range of 10-100 μg mL-1. The low percent relative standard deviation proved the methods' precision. The methods' accuracy was demonstrated by excellent recovery. Thus, the developed method was found to be simple, environment-friendly, fast, specific, precise, and accurate, and it may be effectively used for routine analysis of EGT and MFH in bulk and their combined tablet dosage form.

Rate of convergence for particle approximation of PDEs in Wasserstein space

AbstractWe prove a rate of convergence for the N-particle approximation of a second-order partial differential equation in the space of probability measures, such as the master equation or Bellman equation of the mean-field control problem under common noise. The rate is of order $1/N$ for the pathwise error on the solution v and of order $1/\sqrt{N}$ for the $L^2$ -error on its L-derivative $\partial_\mu v$ . The proof relies on backward stochastic differential equation techniques.

Cutoff Boltzmann equation with polynomial perturbation near Maxwellian

In this paper, we consider the cutoff Boltzmann equation near Maxwellian, we proved the global existence and uniqueness for the cutoff Boltzmann equation in polynomial weighted space for all γ∈(−3,1]. We also proved initially polynomial decay for the large velocity in L2 space will induce polynomial decay rate, while initially exponential decay will induce exponential rate for the convergence. Our proof is based on newly established inequalities for the cutoff Boltzmann equation and semigroup techniques. Moreover, by generalizing the Lx∞Lv1∩Lx,v∞ approach, we prove the global existence and uniqueness of a mild solution to the Boltzmann equation with bounded polynomial weighted Lx,v∞ norm under some small condition on the initial Lx1Lv∞ norm and entropy so that this initial data allows large amplitude oscillations.

Bifurcation results for a non-local elliptic equation with a nonlinear boundary condition

In this paper we study a logistic elliptic equation with a nonlinear boundary condition and a nonlocal term. By employing the local and global bifurcation theories, a priori bounds for elliptic equations, blow-up techniques for parabolic equations and the properties of the principal eigenvalues, we establish some existence results for compact and unbounded connected components of the positive solutions set of the nonlocal problem.

Long-time behavior of several point particles in a 1D viscous compressible fluid

We study the long-time behavior of several point particles in a 1D viscous compressible fluid. It is shown that the velocities of the point particles all obey the power law $$t^{-3/2}$$ . This result extends author’s previous works on the long-time behavior of a single point particle. New difficulties arise in the derivation of pointwise estimates of Green’s functions due to infinite reflections of waves in-between the point particles. In particular, the differential equation technique used in previous works alone does not suffice. We overcome this by carefully analyzing the structure of Green’s functions in the Laplace variable, especially their asymptotic and analyticity properties.

Mapping intrapreneurship through the dimensions of happiness at work and internal communication

Mapping intrapreneurship through the dimensions of happiness at work and internal communication

Dynamics of a Particle in 3:1 Tesseral Resonance with the Dwarf Planet Haumea

The dynamics of a particle in 3:1 tesseral resonance with the dwarf planet Haumea is analysed. This resonance, three rotations of the primary per orbital period of the particle, is located inside the region where Haumea’s ring was observed. Thus, determining the effect of this resonance on a particle’s orbit reveals its relationship to the orbits that follow the particles of the ring. To analyse the effect, we propose four models of anisotropy; two of them are a reduced representation of the distribution of the mass of Haumea that we use to determine the centre of the resonance by means of the Hamiltonian formulation. After this, we analyse the effects of the four models on the resonance orbit by using the Lagrange planetary equations technique. The results show that the resonance centre has a high eccentricity value, meaning that a particle in 3:1 resonance with Haumea does not remain confined to the region that we consider to be the ring region.

Dynamical analysis on a size-structured population model of Daphnia with delayed birth process

In this paper, we investigate a size-structured population model of Daphnia coupled with an unstructured algal food source. We introduce a delay into the boundary condition of this model, where the delay describes the effect of competition for finding food or resource in short supply juvenile period. Following the semigroup theory, we transform our model into the abstract boundary delay problem and obtain the existence and uniqueness of a positive stationary solution. By means of the spectral analysis and the characteristic equation technique, the instability and linear stability results of stationary solutions are formulated in terms of the basic reproduction number ℛ(F). Some numerical simulation examples are presented to illustrate the feasibility of our main results.

A variety of solitons on the oceans exposed by the Kadomtsev Petviashvili-modified equal width equation adopting different techniques

The diverse patterns of waves on the oceans yielded by the Kadomtsev Petviashvili-modified equal width (KP-mEW) equation are highlighted in this paper. Two recent established approaches such as the improved auxiliary equation technique and the enhanced rational (G′/G)-expansion scheme are utilized to construct wave solutions of the proposed governing model. Numerous rational, trigonometric, exponential, and hyperbolic wave solutions bearing many free parameters are successfully acquired in appropriate form. The obtained solutions are plotted in various profiles as three-dimension, two-dimension, and contour to illustrate their physical appearances. The plotting outlines appear in the shapes of singular kink, anti-kink, kink, compacton, anti-compacton, bell, anti-bell, periodic, singular periodic etc. The computational software Maple is used for plotting and checking the validity of the found solutions. This paper claims to be novel for generating new results regarding the earlier results.

초급부사관의 군 인성과 조직몰입의 관계에서셀프리더십의 매개효과

This study, we investigate the mediation effect of the self-leadership in the relation between military character and the organizational commitment for junior NCOs(Non Commissioned Officers). This research target was 684 junior NCOs in the 00 unit located in Jeonbuk. The data was analyzed by using SPSS 18.0 and mediation effects were verified using structural equation techniques (Muthén & Muthén, 2010). First, as a result of correlation analysis of major variants showed the military character statically significantly and significantly correlated the organization commitment and the self-leadership. Also Self-leadership and organizational immersion appeared statically and significantly. Second, it was found that self-leadership mediates the relationship between military character and organizational commitment. These results mean that military character directly affect and increases theorganization commitment through the self-leadership. Therefore, it is suggested that there is a need for improving the education of the self-leadership and the military character in order to increase the organizational of junior NCOs.

Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard Equations

Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard Equations

Measurement of low Reynolds number flow emanating from a Turing pattern microchannel array using a modified Bernoulli equation technique

An experimental investigation of the air flow emanating from a Turing pattern microchannel array into an open atmosphere at very low Reynolds (Re) numbers is presented. As designed, the microchannel structure has channel sizes ranging between 0.6 mm and 1.5 mm with a depth of 0.6 mm. The development of a modified Bernoulli equation analysis method to determine fluid flow speed is introduced. Specifically, a low cost, large (11.11 mm inner diameter) flexible tube probe was employed to measure the fluid total pressure field distribution at a fixed distance from the outlets of the microchannel array. Using subsequent numerical modeling of the outlet-to-tube fluid flow interactions, a flow speed dependent correction factor for the determined dynamic pressure field is proposed. The experimentally measured fluid flow distribution is consistent with the expected flow field pattern obtained by additional computational modeling of flow through and exiting the entire Turing pattern microchannel manifold structure. The pressure measurement and post-processing technique for determining flow velocity may be adapted to a wide range of low-speed (e.g., Re≤100) fluid flow measurement scenarios.

The diagrammatic coaction and cuts of the double box

The diagrammatic coaction encodes the analytic structure of Feynman integrals by mapping any given Feynman diagram into a tensor product of diagrams defined by contractions and cuts of the original diagram. Feynman integrals evaluate to generalized hypergeometric functions in dimensional regularization. Establishing the coaction on this type of functions has helped formulating and checking the diagrammatic coaction of certain two-loop integrals. In this talk we study its application on the fully-massless double-box diagram. We make use of differential equation techniques, which, together with the properties of homology and cohomology theory of the resulting hypergeometric functions, allow us to formulate the coaction on a range of cuts of the double box in closed form.

Resolving Missing Data from the Movement Disorder Society Unified Parkinson's Disease Rating Scale: Implications for Telemedicine.

Telemedicine has become standard in clinical care and research during the coronavirus disease 2019 pandemic. Remote administration of Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS) Part III (Motor Examination) precludes ratings of all items, because Rigidity and Postural Stability (six scores) require in-person rating. The objective of this study was to determine imputation accuracy for total-sum and item-specific MDS-UPDRS Motor Examination scores in remote administration. We applied multivariate imputation by chained equations techniques in a cross-sectional dataset where patients had one MDS-UPDRS rating (International Translational Program, n=8,588) and in a longitudinal dataset where patients had multiple ratings (Rush Program, n=396). Successful imputation was stringently defined as (1) generalized Lin's concordance correlation coefficient>0.95, reflecting near-perfect agreement between total-sum score with complete data and surrogate score, calculated without patients' actual Rigidity and Postural Stability scores; and (2) perfect agreement for item-level scores for Rigidity and Postural Stability items. For total-sum score when Rigidity and Postural Stability scores were withdrawn, using one or multiple visits, multivariate imputation by chained equations imputation reached near-perfect agreement with the original total-sum score. However, at the item level, the degree of perfect agreement between the surrogate and actual Rigidity items and Postural Stability scores always fell below threshold. The MDS-UPDRS Part III total-sum score, a key clinical outcome in research and in clinical practice, can be accurately imputed without the Rigidity and Postural Stability items that cannot be rated by telemedicine. No formula, however, allows for specific item-level imputation. When Rigidity and Postural Stability item scores are of key clinical or research interest, patients with PD must be scored in person. © 2022 International Parkinson and Movement Disorder Society.

The (3 + 1)-dimensional Benjamin–Ono equation: Painlevé analysis, rogue waves, breather waves and soliton solutions

In this paper, we analyzed the (3 + 1)-dimensional Benjamin–Ono (BO) equation. We first demonstrated that the governing model is not integrable in the Painlevé sense. The rogue wave and the breather wave solutions are then achieved with the use of bilinear form. Furthermore, using a combination of Lie symmetry analysis with the new Kudryshov method, and the Riccati equation technique, the abundant soliton and singular periodic solutions were derived. The criteria for existence of such solutions are also provided. Consequently, the derived solutions are presented graphically through 3D, 2D and contour plots, which describe useful physical phenomena due to existence of the free parameters. Corresponding to the one-reduction, power series solution of BO equation is also obtained.

An Improved Two-Grid Technique for the Nonlinear Time-Fractional Parabolic Equation Based on the Block-Centered Finite Difference Method

An Improved Two-Grid Technique for the Nonlinear Time-Fractional Parabolic Equation Based on the Block-Centered Finite Difference Method

Quantum thermal transport beyond second order with the reaction coordinate mapping.

Standard quantum master equation techniques, such as the Redfield or Lindblad equations, are perturbative to second order in the microscopic system-reservoir coupling parameter λ. As a result, the characteristics of dissipative systems, which are beyond second order in λ, are not captured by such tools. Moreover, if the leading order in the studied effect is higher-than-quadratic in λ, a second-order description fundamentally fails even at weak coupling. Here, using the reaction coordinate (RC) quantum master equation framework, we are able to investigate and classify higher-than-second-order transport mechanisms. This technique, which relies on the redefinition of the system-environment boundary, allows for the effects of system-bath coupling to be included to high orders. We study steady-state heat current beyond second-order in two models: The generalized spin-boson model with non-commuting system-bath operators and a three-level ladder system. In the latter model, heat enters in one transition and is extracted from a different one. Crucially, we identify two transport pathways: (i) System's current, where heat conduction is mediated by transitions in the system, with the heat current scaling as jq ∝ λ2 to the lowest order in λ. (ii) Inter-bath current, with the thermal baths directly exchanging energy between them, facilitated by the bridging quantum system. To the lowest order in λ, this current scales as jq ∝ λ4. These mechanisms are uncovered and examined using numerical and analytical tools. We contend that the RC mapping brings, already at the level of the mapped Hamiltonian, much insight into transport characteristics.

Error estimates for deep learning methods in fluid dynamics

In this study, we provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier–Stokes equations. In particular, we obtain explicit error estimates (in suitable norms) for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution, with a fixed complexity.