Constrained generalized mechanics. The second-order case

1985 ◽  
Vol 90 (1) ◽  
pp. 15-28 ◽  
Author(s):  
V. Tapia
Keyword(s):  
Second Order ◽  
Order Case ◽  
Generalized Mechanics

scholarly journals Numerical Approximation of the Space Fractional Cahn-Hilliard Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Zhifeng Weng ◽  
Langyang Huang ◽  
Rong Wu
Keyword(s):  
Numerical Approximation ◽  
Second Order ◽  
Differentiation Formula ◽  
Numerical Examples ◽  
Backward Differentiation Formula ◽  
Hilliard Equation ◽  
Order Case ◽  
Energy Stable ◽  
Cahn Hilliard Equation ◽  
Fourier Spectral Methods

In this paper, a second-order accurate (in time) energy stable Fourier spectral scheme for the fractional-in-space Cahn-Hilliard (CH) equation is considered. The time is discretized by the implicit backward differentiation formula (BDF), along with a linear stabilized term which represents a second-order Douglas-Dupont-type regularization. The semidiscrete schemes are shown to be energy stable and to be mass conservative. Then we further use Fourier-spectral methods to discretize the space. Some numerical examples are included to testify the effectiveness of our proposed method. In addition, it shows that the fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case.

scholarly journals On correctness of first and second order fast marching method

2011 ◽  
Vol 1 (2) ◽  
Author(s):  
Christoph Lass
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Unique Solution ◽  
Nonlinear Partial Differential Equations ◽  
Second Order ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Order Case ◽  
Upwind Discretization ◽  
Marching Method

AbstractIn this article we will discuss the Fast Marching Method which was introduced by James A. Sethian to solve some types of nonlinear partial differential equations efficiently. We will show that this method yields the unique solution to an upwind discretization. Furthermore we will present the correct algorithm for the second order case where existence and unicity of the solution will be proven as well.

scholarly journals Consensus Indices of Two-Layered Multi-Star Networks: An Application of Laplacian Spectrum

2021 ◽  
Vol 9 ◽  
Author(s):  
Da Huang ◽  
Jicheng Bian ◽  
Haijun Jiang ◽  
Zhiyong Yu
Keyword(s):  
Asymptotic Properties ◽  
Second Order ◽  
Graph Spectra ◽  
Layered Systems ◽  
First Order ◽  
Layered Networks ◽  
Order Case ◽  
Coordination Systems ◽  
Multi Agent ◽  
Agent Networks

In this article, the convergence speed and robustness of the consensus for several dual-layered star-composed multi-agent networks are studied through the method of graph spectra. The consensus-related indices, which can measure the performance of the coordination systems, refer to the algebraic connectivity of the graph and the network coherence. In particular, graph operations are introduced to construct several novel two-layered networks, the methods of graph spectra are applied to derive the network coherence for the multi-agent networks, and we find that the adherence of star topologies will make the first-order coherence of the dual-layered systems increase some constants in the sense of limit computations. In the second-order case, asymptotic properties also exist when the index is divided by the number of leaf nodes. Finally, the consensus-related indices of the duplex networks with the same number of nodes but non-isomorphic structures have been compared and simulated, and it is found that both the first-order coherence and second-order coherence of the network D are between A and B, and C has the best first-order robustness, but it has the worst robustness in the second-order case.

Fourth order exceptional points with spinning resonators

2022 ◽  
Author(s):  
Haoye Qin ◽  
Yiheng Yin ◽  
Ming Ding
Keyword(s):  
Fourth Order ◽  
Light Propagation ◽  
High Efficiency ◽  
Optical Resonators ◽  
Second Order ◽  
Exceptional Points ◽  
Enhanced Sensitivity ◽  
Order Case ◽  
Symmetric Systems

Abstract Investigation of exceptional points mostly focuses on the second order case and employs the gain-involved parity-time (PT) symmetric systems. Here, we propose an approach to implementing fourth order exceptional points (FOEPs) using directly coupled optical resonators with rotation. On resonance, the system manifests FOEP through tuning the spinning velocity to targeted values. Eigenfrequency bifurcation and enhanced sensitivity for nanoparticle have been presented. Also, near FOEP, nonreciprocal light propagation exhibits great boost and dramatic change, which may be applied to high-efficiency isolators and circulators.

NOTES ONω-INCONSISTENT THEORIES OF TRUTH IN SECOND-ORDER LANGUAGES

2013 ◽  
Vol 6 (4) ◽  
pp. 733-741 ◽  
Author(s):  
EDUARDO BARRIO ◽  
LAVINIA PICOLLO
Keyword(s):  
Classical Theory ◽  
Second Order ◽  
Revision Theory ◽  
Theories Of Truth ◽  
First Order ◽  
Order Case ◽  
Desirable Feature ◽  
Conceptual Problems ◽  
Inconsistent Theories

It is widely accepted that a theory of truth for arithmetic should be consistent, butω-consistency is less frequently required. This paper argues thatω-consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adoptingω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well knownω-inconsistent theories of truth are considered: the revision theory of nearly stable truthT#and the classical theory of symmetric truthFS. Briefly, we present some conceptual problems withω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.

scholarly journals The subdifferential of the sum of two functions in Banach spaces II. Second order case

1995 ◽  
Vol 51 (2) ◽  
pp. 235-248 ◽  
Author(s):  
Robert Deville ◽  
El Mahjoub El Haddad
Keyword(s):  
Hilbert Spaces ◽  
Type Theorem ◽  
Continuous Functions ◽  
Second Order ◽  
Infinite Dimensional ◽  
Jacobi Operators ◽  
Uniqueness Results ◽  
Lower Semi ◽  
Order Case ◽  
Jacobi Equations

We prove a formula for the second order subdifferential of the sum of two lower semi continuous functions in finite dimensions. This formula yields an Alexandrov type theorem for continuous functions. We derive from this uniqueness results of viscosity solutions of second order Hamilton-Jacobi equations and singlevaluedness of the associated Hamilton-Jacobi operators. We also provide conterexamples in infinite dimensional Hilbert spaces.

scholarly journals An efficient integrator that uses Gauss-Radau spacings

1985 ◽  
Vol 83 ◽  
pp. 185-202 ◽  
Author(s):  
Edgar Everhart
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Second Order ◽  
Double Precision ◽  
The Past ◽  
Fortran Code ◽  
Order Case ◽  
Speed And Accuracy ◽  
Second Order Equations

AbstractThis describes our integrator RADAU, which has been used by several groups in the U.S.A., in Italy, and in the U.S.S.R. over the past 10 years in the numerical integration of orbits and other problems involving numerical solution of systems of ordinary differential equations. First- and second-order equations are solved directly, including the general second-order case. A self-starting integrator, RADAU proceeds by sequences within which the substeps are taken at Gauss-Radau spacings. This allows rather high orders of accuracy with relatively few function evaluations. After the first sequence the information from previous sequences is used to improve the accuracy. The integrator itself chooses the next sequence size. When a 64-bit double word is available in double precision, a 15th-order version is often appropriate, and the FORTRAN code for this case is included here. RADAU is at least comparable with the best of other integrators in speed and accuracy, and it is often superior, particularly at high accuracies.

Sign in / Sign up

Export Citation Format

Share Document