SOME APPLICATIONS OF LINEAR PROGRAMMING TO THE INVERSE GRAVITY PROBLEM

Geophysics ◽  
1977 ◽  
Vol 42 (6) ◽  
pp. 1215-1229 ◽  
Author(s):  
Claude Safon ◽  
Guy Vasseur ◽  
Michel Cuer
Keyword(s):  
Linear Programming ◽  
Numerical Solutions ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Cylindrical Structures ◽  
All Solutions ◽  
Finite Set ◽  
Ideal Body ◽  
Programming Algorithms

An approach is presented for solving the inverse gravity problem in the presence of various constraints such as bounds on density. This approach takes into account the nonuniqueness of the solution: for a finite set of measurements, the region studied is divided into a great number of rectangular prisms of unknown density. The set of all solutions of this undetermined problem may be described through various convex diagrams of moments; plots of these moments give bounds on some physical parameters such as the partial and total mass or the position of the center of mass. Numerical solutions are obtained using linear programming algorithms. Also, particular solutions such as the so‐called ideal body may readily be obtained using this technique. Only two‐dimensional cylindrical structures are considered, but application of this technique to three‐dimensional bodies is straight‐forward.

Three-Dimensional Equilibria and Stability of Nonlinear Curved Beams Using Intrinsic Equations and Shooting

2012 ◽  
Author(s):  
Kyle N. Karlson ◽  
Michael J. Leamy
Keyword(s):  
Boundary Condition ◽  
Numerical Solutions ◽  
General Procedure ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Curved Beams ◽  
Equilibrium Solutions ◽  
Equilibrium Equations ◽  
All Solutions ◽  
Similar Solutions

This article describes a shooting method that provides numerical solutions to static equilibrium equations for intrinsically curved beams in three-dimensions. Notably, the method avoids iteration for cantilever beams subjected to distributed or point follower loads. This is due to the governing equations being given in first-order form such that the specification of a single boundary condition on the forced end results in automatic satisfaction of the fixed boundary condition. Also documented is a general procedure for finding all solutions to static beam problems with conservative loading. This is particularly useful in beam buckling problems where multiple stable and unstable solutions exist. The procedure for finding all solutions is built around the Picard-Lindelöf theorem on the uniqueness and existence of solutions to initial value problems. Using the presented approach, three-dimensional equilibrium solutions are generated for many loading cases and boundary conditions, including a three-dimensional helical beam, and are compared to similar solutions available in the literature. The stability of the generated solutions is assessed using a dynamic finite element code based on the same intrinsic beam equations. Due to the absent need for iteration, the presented approach may find application in model-based control for practical problems such as the control of equipment utilized in endoscopic surgeries and the control of spacecraft with robotic arms and long cables.

Numerical Simulations of Three-Dimensional Flows in a Cubic Cavity With an Oscillating Lid

1993 ◽  
Vol 115 (4) ◽  
pp. 680-686 ◽  
Author(s):  
Reima Iwatsu ◽  
Jae Min Hyun ◽  
Kunio Kuwahara
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Sinusoidal Oscillations ◽  
Dependent Flow

Numerical studies are made of three-dimensional flow of a viscous fluid in a cubical container. The flow is driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions are acquired by solving the time-dependent, three-dimensional incompressible Navier-Stokes equations by employing very fine meshes. Results are presented for wide ranges of two principal physical parameters, i.e., the Reynolds number, Re ≤ 2000 and the frequency parameter of the lid oscillation, ω′ ≤ 10.0. Comprehensive details of the flow structure are analyzed. Attention is focused on the three-dimensionality of the flow field. Extensive numerical flow visualizations have been performed. These yield sequential plots of the main flows as well as the secondary flow patterns. It is found that the previous two-dimensional computational results are adequate in describing the main flow characteristics in the bulk of interior when ω′ is reasonably high. For the cases of high-Re flows, however, the three-dimensional motions exhibit additional complexities especially when ω′ is low. It is asserted that, thanks to the recent development of the supercomputers, calculation of three-dimensional, time-dependent flow problems appears to be feasible at least over limited ranges of Re.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

scholarly journals Mass and spin for classical strings in dS3

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Klaas Parmentier
Keyword(s):  
Black Hole ◽  
Evolution Equation ◽  
Cosmic Strings ◽  
Center Of Mass ◽  
Open String ◽  
Conserved Quantities ◽  
Numerical Example ◽  
All Solutions

Abstract We demonstrate that all rigidly rotating strings with center of mass at the origin of the dS3 static patch satisfy the Higuchi bound. This extends the observation of Noumi et al. for the open GKP-like string to all solutions of the Larsen-Sanchez class. We argue that strings violating the bound end up expanding towards the horizon and provide a numerical example. Adding point masses to the open string only increases the mass/spin ratio. For segmented strings, we write the conserved quantities, invariant under Gubser’s algebraic evolution equation, in terms of discrete lightcone coordinates describing kink collisions. Randomly generated strings are found to have a tendency to escape through the horizon that is mostly determined by their energy. For rapidly rotating segmented strings with mass/spin < 1, the kink collisions eventually become causally disconnected. Finally we consider the scenario of cosmic strings captured by a black hole in dS and find that horizon friction can make the strings longer.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

scholarly journals Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 1077
Author(s):  
Muhammad Tamoor ◽  
Muhammad Kamran ◽  
Sadique Rehman ◽  
Aamir Farooq ◽  
Rewayat Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Convective Parameter ◽  
Momentum And Heat Transfer ◽  
Dimensional Boundary

In this study, a numerical approach was adopted in order to explore the analysis of magneto fluid in the presence of thermal radiation combined with mixed convective and slip conditions. Using the similarity transformation, the axisymmetric three-dimensional boundary layer equations were reduced to a self-similar form. The shooting technique, combined with the Range–Kutta–Fehlberg method, was used to solve the resulting coupled nonlinear momentum and heat transfer equations numerically. When physically interpreting the data, some important observations were made. The novelty of the present study lies in finding help to control the rate of heat transfer and fluid velocity in any industrial manufacturing processes (such as the cooling of metallic plates). The numerical results revealed that the Nusselt number decrease for larger Prandtl number, curvature, and convective parameters. At the same time, the skin friction coefficient was enhanced with an increase in both slip velocity and convective parameter. The effect of emerging physical parameters on velocity and temperature profiles for a nonlinear stretching cylinder has been thoroughly studied and analyzed using plotted graphs and tables.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

Calculation and Design Method Study of the Coil-Wound Heat Exchanger

2014 ◽  
Vol 1008-1009 ◽  
pp. 850-860 ◽  
Author(s):  
Zhou Wei Zhang ◽  
Jia Xing Xue ◽  
Ya Hong Wang
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Exchanger ◽  
Design Method ◽  
Fluid Velocity ◽  
Exchange Process ◽  
Three Dimensional ◽  
Simulation Method ◽  
Physical Parameters ◽  
Numerical Result

A calculation method for counter-current type coil-wound heat exchanger is presented for heat exchange process. The numerical simulation method is applied to determine the basic physical parameters of wound bundles. By controlling the inlet fluid velocity varying in coil-wound heat exchanger to program and calculate the iterative process. The calculation data is analyzed by comparison of numerical result and the unit three dimensional pipe bundle model was built. Studies show that the introduction of numerical simulation can simplify the pipe winding process and accelerate the calculation and design of overall configuration in coil-wound heat exchanger. This method can be applied to the physical modeling and heat transfer calculation of pipe bundles in coil wound heat exchanger, program to calculate the complex heat transfer changing with velocity and other parameters, and optimize the overall design and calculation of spiral bundles.

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