scholarly journals A New Methodology to Establish Upper Bounds on Open-Cell Foams Homogenized Properties

10.14311/652 ◽  
2004 ◽  
Vol 44 (5-6) ◽  
Author(s):  
Z. Dimitrovová
Keyword(s):  
Three Dimensional ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Geometrical Parameters ◽  
Open Cell ◽  
Linear Elastic ◽  
Internal Forces ◽  
Open Cell Foams ◽  
Necessary And Sufficient ◽  
First Time

The methodology for determining the upper bounds on the homogenized linear elastic properties of cellular solids, described for the two-dimensional case in Dimitrovová and Faria (1999), is extended to three-dimensional open-cell foams. Besides the upper bounds, the methodology provides necessary and sufficient conditions on optimal media. These conditions are written in terms of generalized internal forces and geometrical parameters. In some cases dependence on internal forces can be replaced by geometrical expressions. In such cases, the optimality of some medium under consideration can be verified directly from the microstructure, without any additional calculation. Some of the bounds derived in this paper are published for the first time, along with a proof of their optimality. 

A Time-Stepping Scheme for Quasistatic Multibody Systems

2005 ◽  
Author(s):  
J. C. Trinkle ◽  
Stephen Berard ◽  
J. S. Pang
Keyword(s):  
Three Dimensional ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Contact Forces ◽  
Global Optimal Solution ◽  
Convex Optimization Problem ◽  
Time Stepping ◽  
Global Optimal ◽  
Necessary And Sufficient ◽  
First Time

Two new instantaneous-time models for predicting the motion and contact forces of three-dimensional, quasistatic multi-rigid-body systems are developed; one linear and one nonlinear. The nonlinear characteristic is the result of retaining the usual quadratic friction cone in the model. Discrete-time versions of these models provide the first time-stepping methods for such systems. As a first step to understanding their usefulness in simulation and manipulation planning, a theorem defining the equivalence of solutions of a time-stepping method for the nonlinear model and a global optimal solution of a related convex optimization problem is given. In addition, a Proposition giving necessary and sufficient conditions for solution uniqueness of the nonlinear time-stepping method is given. Finally, a simple example is discussed to help develop intuition about quasistatic systems and to solidify the reader’s understanding of the theorem and proposition.

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

On the rate of growth of the overshoot and the maximum partial sum

1998 ◽  
Vol 30 (1) ◽  
pp. 181-196 ◽  
Author(s):  
P. S. Griffin ◽  
R. A. Maller
Keyword(s):  
Random Walk ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Strong Sense ◽  
Partial Sum ◽  
Order Of Magnitude ◽  
The Stability ◽  
Dominance Properties ◽  
Necessary And Sufficient ◽  
First Time

Let Tr be the first time at which a random walk Sn escapes from the strip [-r,r], and let |STr|-r be the overshoot of the boundary of the strip. We investigate the order of magnitude of the overshoot, as r → ∞, by providing necessary and sufficient conditions for the ‘stability’ of |STr|, by which we mean that |STr|/r converges to 1, either in probability (weakly) or almost surely (strongly), as r → ∞. These also turn out to be equivalent to requiring only the boundedness of |STr|/r, rather than its convergence to 1, either in the weak or strong sense, as r → ∞. The almost sure characterisation turns out to be extremely simple to state and to apply: we have |STr|/r → 1 a.s. if and only if EX2 < ∞ and EX = 0 or 0 < |EX| ≤ E|X| < ∞. Proving this requires establishing the equivalence of the stability of STr with certain dominance properties of the maximum partial sum Sn* = max{|Sj|: 1 ≤ j ≤ n} over its maximal increment.

scholarly journals On Embedding of the Morse-Smale Diffeomorphisms in a Topological Flow

2020 ◽  
Vol 66 (2) ◽  
pp. 160-181
Author(s):  
V. Z. Grines ◽  
E. Ya. Gurevich ◽  
O. V. Pochinka
Keyword(s):  
Invariant Manifolds ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Points ◽  
Topological Classification ◽  
Higher Dimension ◽  
Topological Information ◽  
Topology Of Manifolds ◽  
Necessary And Sufficient

This review presents the results of recent years on solving of the Palis problem on finding necessary and sufficient conditions for the embedding of Morse-Smale cascades in topological flows. To date, the problem has been solved by Palis for Morse-Smale diffeomorphisms given on manifolds of dimension two. The result for the circle is a trivial exercise. In dimensions three and higher new effects arise related to the possibility of wild embeddings of closures of invariant manifolds of saddle periodic points that leads to additional obstacles for Morse-Smale diffeomorphisms to embed in topological flows. The progress achieved in solving of Paliss problem in dimension three is associated with the recently obtained complete topological classification of Morse-Smale diffeomorphisms on three-dimensional manifolds and the introduction of new invariants describing the embedding of separatrices of saddle periodic points in a supporting manifold. The transition to a higher dimension requires the latest results from the topology of manifolds. The necessary topological information, which plays key roles in the proofs, is also presented in the survey.

Survival of weak-field seekers inside a TOP trap even beyond the adiabatic condition

2019 ◽  
Vol 35 (01) ◽  
pp. 1950347
Author(s):  
Nirupam Dutta ◽  
Anirban Dey ◽  
Prasanta K. Panigrahi
Keyword(s):  
Ground State ◽  
Survival Probability ◽  
Sufficient Conditions ◽  
Weak Field ◽  
Adiabatic Limit ◽  
Magnetic Trapping ◽  
Adiabatic Condition ◽  
Adiabatic Evolution ◽  
Necessary And Sufficient ◽  
First Time

In this paper, for the first time in the context of time orbiting potential (TOP) trap, the necessary and sufficient conditions for the adiabatic evolution of weak field seeking states have been quantitatively examined. It has been well accepted since decades that adiabaticity has to be obeyed by the atoms for successful magnetic trapping. However, we show, on the contrary, that atoms can also be confined beyond the adiabatic limit. For the demonstration, we have considered a toy model of a single weak field seeking atom in its ground state and have calculated its survival probability inside a TOP trap. Our findings open new possibilities to relax the restrictions of atom trapping in laboratories.

scholarly journals Coating of polydopamine on polyurethane open cell foams to design soft structured supports for molecular catalysts

2019 ◽  
Vol 55 (79) ◽  
pp. 11960-11963 ◽  
Author(s):  
Ahmed Ait Khouya ◽  
Miguel L. Mendez Martinez ◽  
Philippe Bertani ◽  
Thierry Romero ◽  
Damien Favier ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Open Cell ◽  
Covalent Grafting ◽  
Open Cell Foams ◽  
Molecular Catalysts

A covalent grafting strategy of molecular catalysts onto a polydopamine-coated flexible three dimensional macroscopic support is presented.

Vectors

1996 ◽  
Author(s):  
Gerhard Oertel
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Unit Vector ◽  
Cross Product ◽  
Nonzero Vector ◽  
Algebraic Representation ◽  
The Difference ◽  
Necessary And Sufficient ◽  
Three Dimensional Space

The reader, even if familiar with vectors, will find it useful to work through this chapter because it introduces notation that will be used throughout this book. We will take vectors to be entities that possess magnitude, orientation, and sense in three-dimensional space. Graphically, we will represent them as arrows with the sense from tail to head, magnitude proportional to the length, and orientation indicated by the angles they form with a given set of reference directions. Two different kinds of symbol will be used to designate vectors algebraically, boldface letters (and the boldface number zero for a vector of zero magnitude), and subscripted letters to be introduced later. The first problems deal with simple vector geometry and its algebraic representation. Multiplying a vector by a scalar affects only its magnitude (length) without changing its direction. Problem 1. State the necessary and sufficient conditions for the three vectors A, B, and C to form a triangle. (Problems 1–9, 12–14, 19–23, and 25 from Sokolnikoff & Redheffer, 1958.) Problem 2. Given the sum S = A + B and the difference D = A – B, find A and B in terms of S and D (a) graphically and (b) algebraically. Problem 3. (a) State the unit vector a with the same direction as a nonzero vector A. (b) Let two nonzero vectors A and B issue from the same point, forming an angle between them; using the result of (a), find a vector that bisects this angle. Problem 4. Using vector methods, show that a line from one of the vertices of a parallelogram to the midpoint of one of the nonadjacent sides trisects one of the diagonals. Two vectors are said to form with each other two distinct products: a scalar, the dot product, and a vector, the cross product.

Micromechanical Modeling of Three-dimensional Open-cell Foams

2012 ◽  
pp. 213-258
Author(s):  
Ke Li ◽  
Xin-Lin Gao
Keyword(s):  
Three Dimensional ◽  
Micromechanical Modeling ◽  
Open Cell ◽  
Open Cell Foams

scholarly journals Post-Lie algebra structures for nilpotent Lie algebras

2018 ◽  
Vol 28 (05) ◽  
pp. 915-933
Author(s):  
Dietrich Burde ◽  
Christof Ender ◽  
Wolfgang Alexander Moens
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Nilpotent Lie Algebras ◽  
Dimension Formula ◽  
Necessary And Sufficient

We study post-Lie algebra structures on [Formula: see text] for nilpotent Lie algebras. First, we show that if [Formula: see text] is nilpotent such that [Formula: see text], then also [Formula: see text] must be nilpotent, of bounded class. For post-Lie algebra structures [Formula: see text] on pairs of [Formula: see text]-step nilpotent Lie algebras [Formula: see text] we give necessary and sufficient conditions such that [Formula: see text] defines a CPA-structure on [Formula: see text], or on [Formula: see text]. As a corollary, we obtain that every LR-structure on a Heisenberg Lie algebra of dimension [Formula: see text] is complete. Finally, we classify all post-Lie algebra structures on [Formula: see text] for [Formula: see text], where [Formula: see text] is the three-dimensional Heisenberg Lie algebra.

Sign in / Sign up

Export Citation Format

Share Document