Domain In Three-dimensional Space Research Articles

Modeling analysis of pulsatile non-Newtonian blood flow in a renal bifurcated artery with stenosis

A transient transport flow model is adopted in a renal bifurcated artery with different stenosis cases to examine the flow phenomena when the non-Newtonian blood flow regime within the three-dimensional space domain is chosen as a pulsatile nature. The nonlinear governing equations are solved using the Finite Element Method with suitable initial-boundary conditions. During numerical computation, distinct hemodynamic parameters including Wall shear stress, Reynolds number, power law index are evaluated based on different stenosis severities (0%, 25%, and 50%) and stenosis lengths (0mm, 0.5mm, and 1mm). For 0%, 25%, and 50% stenosis, the approximate values of velocity and pressure profiles are estimated at t = 5s at various positions, and achieved the highest velocities that were around 0.07m/s, 0.08m/s, and 0.13m/s respectively. The unsteady response of the stress due to stenosis-induced shear on the outside wall is described as a result of stenosis at t = 0.1s, 0.2s, 5s. The flow is severely restricted by constriction, which increases wall movement and produces stress, depending on the amount of stenosis. As pulsatile flow time increases due to the presence of stenosis, the wall shear stress decreases gradually. The impact of Reynolds numbers on pressure profiles and velocity profiles are displayed for Re = 100, 300, 500, and 700, and found that both velocity and pressure outlines increase significantly. In order to identify the flow phenomena, the influences of the power law index for n = 0.1, 0.3568, 0.5 are presented on the velocity and pressure profiles. Shear-thinning flow occurs for 0<n<1, pseudoplastic flow occurs for n = 0.1 and Bingham plastic flow occurs for n = 0.5. The modeling investigations of blood flow via arteries could assist in the diagnosis and treatment of arterial illnesses; as well as expand the knowledge about cardiovascular physiology and lead the development of revolutionary medical interventions to enhance patient treatment outcomes.

Aggregated space combat modeling

The use of aggregated combat modeling in the cislunar environment has been demonstrated to inform acquisition decisions for the United States Space Force (USSF). First, the cislunar space is hypothesized as a future strategic conflict environment. As such, Lanchester, Lotka–Volterra, and Brackney models could be appropriate to describe such conflict. All models encompass a system of differential equations which parametrically capture the dynamics between friendly and hostile forces. While the Brackney model was constructed to explain two-dimensional land battle, this article adapts it for the respective three-dimensional space domain and applies it to strategic procurement. The analysis demonstrates the pre-eminence of Space Domain Awareness (SDA) in certain contexts while recognizing conditions in which spacecraft survivability holds greater importance.

A new method for solving reachable domain of spacecraft with a single impulse

This paper develops a new approach to solve the reachable domain of a spacecraft with a single maximum available impulse. First, the distance in a chosen direction, started from a given position on the initial orbit, is formulated. Then, its extreme value is solved to obtain the maximum reachable distance in this direction. The envelop of the reachable domain in three-dimensional space is determined by solving the maximum reachable distance in all directions. Four scenarios are analyzed, including three typical scenarios (either the maneuver position or impulse direction is fixed, or both are arbitrary) and a new extended scenario (the maneuver position is restricted to an interval and the impulse direction is arbitrary). Moreover, the symmetry and the boundedness of the reachable domain are discussed in detail. The former is helpful to reduce the numerical computation, while the latter decides the maximum eccentricity of the initial orbit for a maximum available impulse. The numerical simulations verify the effectiveness of the proposed method for solving the reachable domain in all four scenarios. Especially, the reachable domain with a highly elliptical initial orbit can be determined successfully, which remains unsolved in the existing papers.

ЭФФЕКТИВНЫЕ КРИТЕРИИ ЭКСПОНЕНЦИАЛЬНОЙ УСТОЙЧИВОСТИ АВТОНОМНЫХ РАЗНОСТНЫХ УРАВНЕНИЙ

We obtain stability criteria for several classes of linear autonomous difference equations. The criteria are expressed in explisit analytic form, as well as in the form of belonging values of a vector function of the equation parameters to a domain in three-dimensional space.

Explicit moment integration algorithm and its application

The calculation of moment is often used in finite element method,volume calculation,moment of inertia calculation,etc. A discrete method of the computational domain in three-dimensional space was proposed firstly based on the superposition of moment. An explicit formula was derived in three-dimensional space and then extended to n-dimensional space,which can be easily implemented on the computer. Secondly,a parallel algorithm of moment calculation was designed and implemented with mixed Fortran and Python. Thirdly,a zero-order and second-order moment was calculated in a multi-fidelity example. The efficiency of the algorithm was compared with a serial algorithm and a successive dimensionality reduction algorithm. Meanwhile,efficiency analysis and error analysis were presented. The result shows that the explicit moment integration algorithm can be easily implemented with programs and runs faster than the serial algorithm. It is highly parallel and can also be easily extended to a higher dimensional space. The algorithm is highly parallel,whose error mainly comes from the discrete process of the computational domain.

Precise Determination of Reachable Domain for Spacecraft with Single Impulse

Reachable domain refers to the collection of all positions accessible for a spacecraft under a given initial orbit and fuel constraint with free time of flight. In this study, the fuel constraint is conveniently expressed by a single available velocity impulse. To solve the envelope of the reachable domain, the radius of an accessible target position in a given direction is formulated. By evaluating the extreme values of the accessible radius in the given direction, two reachable boundaries and a reachable line segment are solved. The reachable domain in three-dimensional space is determined by rotating the direction and tracing all the reachable boundaries. The proposed method successfully solves the envelope of the reachable domain for the remaining two unresolved scenarios: the reachable domain with an arbitrary maneuver point and arbitrary impulse direction and the reachable domain with an arbitrary maneuver point and fixed impulse direction. This is the first time the accurate envelope of the reachable domain has been described in three-dimensional space. A comparison of the results of the proposed numerical simulations with those of the existing method demonstrates the accuracy of the proposed method.

Regular asymptotics of a generalized solution of the stationary Navier-Stokes system

A regular asymptotic series is constructed for a generalized solution of the stationary system of Navier-Stokes equations in a bounded domain of three-dimensional space under a constraint on the generalized Reynolds number. A theorem on the approximation to any degree of accuracy of the exact solution of a homogeneous boundary value problem by partial sums of the series is proved.

Conformation of the HIV-1 Gag Protein in Solution

A single multi-domain viral protein, termed Gag, is sufficient for assembly of retrovirus-like particles in mammalian cells. We have purified the human immunodeficiency virus type 1 (HIV-1) Gag protein (lacking myristate at its N terminus and the p6 domain at its C terminus) from bacteria. This protein is capable of assembly into virus-like particles in a defined in vitro system. We have reported that it is in monomer–dimer equilibrium in solution, and have described a mutant Gag protein that remains monomeric at high concentrations in solution. We report that the mutant protein retains several properties of wild-type Gag. This mutant enabled us to analyze solutions of monomeric protein. Hydrodynamic studies on the mutant protein showed that it is highly asymmetric, with a frictional ratio of 1.66. Small-angle neutron scattering (SANS) experiments confirmed its asymmetry and yielded an Rg value of 34 Å. Atomic-level structures of individual domains within Gag have previously been determined, but these domains are connected in Gag by flexible linkers. We constructed a series of models of the mutant Gag protein based on these domain structures, and tested each model computationally for its agreement with the experimental hydrodynamic and SANS data. The only models consistent with the data were those in which Gag was folded over, with its N-terminal matrix domain near its C-terminal nucleocapsid domain in three-dimensional space. Since Gag is a rod-shaped molecule in the assembled immature virion, these findings imply that Gag undergoes a major conformational change upon virus assembly.

Analysis of a time-domain finite element method for 3-D Maxwell’s equations in dispersive media

We consider the time dependent Maxwell’s equations in dispersive media on a bounded domain in three-dimensional space. A fully discrete finite element scheme is developed to approximate the electric field equation derived from the Maxwell’s equations. Optimal energy-norm error estimates are proved for Nédélec curl-conforming edge elements. This is the first finite element error analysis for Maxwell’s equations in dispersive media.

Parallelization of three-dimensional spectral laser–plasma interaction code using High Performance Fortran

We present the results from a parallelization of sequential code used for investigating parametric instabilities in large-scale laser-produced plasmas. The physical model consists of a system of two nonstationary, nonlinear, second-order partial differential equations. The solver is semi-implicit in time and employs Fourier and Chebyshev discretization in a three-dimensional space domain. High Performance Fortran is used for the parallelization of the solver. A detailed performance analysis of the parallel code (speedup, scalability, and load balancing) has been carried out for implementation on an IBM RS/6000 SP system using the XL HPF compiler. © 1998 American Institute of Physics.

Analysis of a Finite Element Method for Maxwell’s Equations

The use of finite elements to discretize the time dependent Maxwell equations on a bounded domain in three-dimensional space is analyzed. Energy norm error estimates are provided when general finite element methods are used to discretize the equations in space. In addition, it is shown that if some curl conforming elements due to Nédélec are used, error estimates may also be proved in the $L^2 $ norm.

An adaptive characteristic petrov-galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in two space variables

This paper is a continuation of previous work of the authors [2]. An adaptive scheme for the analysis of time-dependent parabolic problems defined on two-dimensional or three-dimensional space domains is developed which is based on a Petrov-Galerkin method for spatial approximation and the method of characteristics for the temporal approximation. Numerical examples are discussed which illustrate the efficiency and effectiveness of the method.

On nonlinear neutron transport equations

The purpose of this paper is to investigate a class of time-dependent neutron transport equations in which the total and differential scattering cross sections are nonlinear functions of neutron density function. Sufficient conditions on the nonlinear cross sections are given to insure the existence, uniqueness and asymptotic stability of a solution in one, two, or three-dimensional space domains under various boundary and initial conditions. The approach to the problem is based on abstract analysis on nonlinear evolution equations which are closely related to nonlinear semigroup theory.