Higher Order, Planar Tangent-Line Envelope Curvature Theory

1979 ◽  
Vol 101 (4) ◽  
pp. 563-568 ◽  
Author(s):  
A. H. Soni ◽  
M. N. Siddhanty ◽  
K. L. Ting
Keyword(s):  
Fourth Order ◽  
Higher Order ◽  
Tangent Line ◽  
Path Generation ◽  
Tangency Point ◽  
Characteristic Numbers ◽  
New Concepts ◽  
Synthesis Of Mechanisms ◽  
Curvature Theory ◽  
Mathematical Relationships

Following the analogy of higher order point-path generation, new concepts for tangent-line higher order envelope curvature theory are introduced. Mathematical relationships are derived to define, using the instantaneous invariants and the stretch rotation concepts, the characteristic numbers λ1 and λ2 for third and fourth-order contacts at the tangency point of a tangent-line generating an envelope. The newly developed tangent-line higher order envelope curvature theory is applied to demonstrate its application in synthesis of mechanisms. Examples involving circular, elliptic and involute are generation using a mechanism are presented.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

HIGHER ORDER CELLULAR AUTOMATA

2005 ◽  
Vol 08 (02n03) ◽  
pp. 169-192 ◽  
Author(s):  
NILS A. BAAS ◽  
TORBJØRN HELVIK
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Level Structure ◽  
Higher Order ◽  
New Concepts ◽  
Multi Level

We introduce a class of dynamical systems called Higher Order Cellular Automata (HOCA). These are based on ordinary CA, but have a hierarchical, or multi-level, structure and/or dynamics. We present a detailed formalism for HOCA and illustrate the concepts through four examples. Throughout the article we emphasize the principles and ideas behind the construction of HOCA, such that these easily can be applied to other types of dynamical systems. The article also presents new concepts and ideas for describing and studying hierarchial dynamics in general.

REPRESENTATIONS AND IDENTIFICATIONS OF STRUCTURAL AND MOTION STATE CHARACTERISTICS OF MECHANISMS WITH VARIABLE TOPOLOGIES

2006 ◽  
Vol 30 (1) ◽  
pp. 19-40 ◽  
Author(s):  
Hong-Sen Yan ◽  
Chin-Hsing Kuo
Keyword(s):  
Topological Structure ◽  
Topological Analysis ◽  
State Machines ◽  
Matrix Representations ◽  
Motion State ◽  
New Concepts ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Finite State ◽  
State Graphs

A mechanism that encounters a certain changes in its topological structure during operation is called a mechanism with variable topologies (MVT). This paper is developed for the structural and motion state representations and identifications of MVTs. For representing the topological structures of MVTs, a set of methods including graph and matrix representations is proposed. For representing the motion state characteristics of MVTs, the idea of finite-state machines is employed via the state tables and state graphs. And, two new concepts, the topological homomorphism and motion homomorphism, are proposed for the identifications of structural and motion state characteristics of MVTs. The results of this work provide a logical foundation for the topological analysis and synthesis of mechanisms with variable topologies.

scholarly journals Influence of Even-Order Dispersion on Super-Sech Soliton Transmission Quality under Coherent Crosstalk

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
Aleksandra Panajotovic ◽  
Daniela Milovic ◽  
Anjan Biswas ◽  
Essaid Zerrad
Keyword(s):  
Fourth Order ◽  
Optical Network ◽  
Single Mode ◽  
Single Mode Fiber ◽  
Higher Order ◽  
Trailing Edges ◽  
Even Order ◽  
Transmission Quality ◽  
The Impact ◽  
Order Dispersion

The transmission speed of optical network strongly depends on the impact of higher order dispersion. In presence of coherent crosstalk, which cannot be otherwise controlled by optical filtering, the impact of higher order dispersions becomes more pronounced. In this paper, the general expressions, that describe pulse deformation due to second- and fourth-order dispersions in a single-mode fiber, are given. The responses for such even-order dispersions, in presence of coherent crosstalk, are characterized by waveforms with long trailing edges. The transmission quality of optical pulses, due to both individual and combined influence of second- and fourth-order dispersions, is studied in this paper. Finally, the pulse shape and eye diagrams are obtained.

scholarly journals Effect of the turning characteristics of underfloor wheel lathes on the evolution of wheel polygonisation

2018 ◽  
Vol 233 (5) ◽  
pp. 479-488 ◽  
Author(s):  
Dabin Cui ◽  
Boyang An ◽  
Paul Allen ◽  
Ruichen Wang ◽  
Ping Wang ◽  
...  
Keyword(s):  
Fourth Order ◽  
High Speed ◽  
Higher Order ◽  
Ride Quality ◽  
Sustained Use ◽  
High Speed Trains ◽  
Cut Quality ◽  
Multiple Unit ◽  
Component Failures

During both running and wheel cut operations, wheels of railway vehicles and the friction rollers that support and drive the wheelset on a typical wheel cut lathe are subject to wear and hence are likely to develop out-of-round characteristics after sustained use. The resulting out-of-round wheels can significantly affect the ride quality and can potentially increase the incidence of fatigue-related component failures due to the resulting higher intensity loading cycles. Furthermore, the corresponding out-of-round characteristics of the lathe's friction rollers will continue to degrade the subsequent cut quality of wheels. For the analysis of the out-of-round characteristics caused by an underfloor wheel lathe used for the high-speed trains in China, a mathematical model based on a typical electric multiple unit (EMU) vehicle's wheelsets and their interactions with the wheel lathe friction rollers was established. Factors influencing the cut quality of the wheels, including the number of cuts, eccentricity forms of the friction rollers and the longitudinal spacing of the two rollers, have been analysed. The results show that two cuts can effectively remove the higher order polygon on the wheel surface. The eccentricity and phase angle of the friction rollers have no influence on the cut quality of higher order polygons, whereas they are the primary cause for the fourth-order polygons. The severity of the fourth-order polygon depends on the level and the phase of the eccentricity of the friction rollers. The space of the two rollers can also significantly affect the cut quality. Obtaining the theoretical and practical value for the maintenance of polygonised wheels using the underfloor lathe is the main outcome of this study.

Assessing the Use of Tensor Closure Methods With Orientation Distribution Reconstruction Functions

Materials ◽  
2003 ◽  
Author(s):  
David A. Jack ◽  
Douglas E. Smith
Keyword(s):  
Distribution Function ◽  
Fourth Order ◽  
Lower Order ◽  
Series Representation ◽  
Orientation Distribution ◽  
Higher Order ◽  
Interaction Coefficients ◽  
Order Tensor ◽  
Orientation Tensor ◽  
Orientation Tensors

Orientation tensors are widely used to describe fiber distri-butions in short fiber reinforced composite systems. Although these tensors capture the stochastic nature of concentrated fiber suspensions in a compact form, the evolution equation for each lower order tensor is a function of the next higher order tensor. Flow calculations typically employ a closure that approximates the fourth-order orientation tensor as a function of the second order orientation tensor. Recent work has been done with eigen-value based and invariant based closure approximations of the fourth-order tensor. The effect of using lower order tensors tensors in process simulations by reconstructing the distribution function from successively higher order orientation tensors in a Fourier series representation is considered. This analysis uses the property that orientation tensors are related to the series expansion coefficients of the distribution function. Errors for several closures are investigated and compared with errors developed when using a reconstruction from the exact 2nd, 4th, and 6th order orientation tensors over a range of interaction coefficients from 10−4 to 10−1 for several flow fields.

Decidability of fourth-order matching

2000 ◽  
Vol 10 (3) ◽  
pp. 361-372 ◽  
Author(s):  
VINCENT PADOVANI
Keyword(s):  
Fourth Order ◽  
Higher Order ◽  
General Situation ◽  
Finite Sets ◽  
Free Variables ◽  
Open Question

Higher Order Matching consists of solving finite sets of equations of the form u =βηv, where u, v are simply typed terms of λ-calculus, and v is a closed term. Whether this problem is decidable is an open question. In this paper its decidability is proved when the free variables of all equations are of order at most 4 – we actually extend this result to a more general situation in which in addition to equations, disequations are also considered.

scholarly journals Anisotropic compact stars in higher-order curvature theory

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
G. G. L. Nashed ◽  
S. D. Odintsov ◽  
V. K. Oikonomou
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Higher Order ◽  
Specific Form ◽  
Ricci Scalar ◽  
Spherically Symmetric ◽  
Curvature Theory ◽  
Anisotropic Star ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

AbstractIn this paper we shall consider spherically symmetric spacetime solutions describing the interior of stellar compact objects, in the context of higher-order curvature theory of the $${{\mathrm {f(R)}}}$$ f ( R ) type. We shall derive the non-vacuum field equations of the higher-order curvature theory, without assuming any specific form of the $${{\mathrm {f(R)}}}$$ f ( R ) theory, specifying the analysis for a spherically symmetric spacetime with two unknown functions. We obtain a system of highly non-linear differential equations, which consists of four differential equations with six unknown functions. To solve such a system, we assume a specific form of metric potentials, using the Krori–Barua ansatz. We successfully solve the system of differential equations, and we derive all the components of the energy–momentum tensor. Moreover, we derive the non-trivial general form of $${{\mathrm {f(R)}}}$$ f ( R ) that may generate such solutions and calculate the dynamic Ricci scalar of the anisotropic star. Accordingly, we calculate the asymptotic form of the function $${\mathrm {f(R)}}$$ f ( R ) , which is a polynomial function. We match the derived interior solution with the exterior one, which was derived in [1], with the latter also resulting to a non-trivial form of the Ricci scalar. Notably but rather expected, the exterior solution differs from the Schwarzschild one in the context of general relativity. The matching procedure will eventually relate two constants with the mass and radius of the compact stellar object. We list the necessary conditions that any compact anisotropic star must satisfy and explain in detail that our model bypasses all of these conditions for a special compact star $$\textit{Her X--1}$$ Her X - - 1 , which has an estimated mass and radius $$(mass = 0.85 \pm 0.15M_{\circledcirc }\ and\ radius = 8.1 \pm 0.41~\text {km}$$ ( m a s s = 0.85 ± 0.15 M ⊚ a n d r a d i u s = 8.1 ± 0.41 km ). Moreover, we study the stability of this model by using the Tolman–Oppenheimer–Volkoff equation and adiabatic index, and we show that the considered model is different and more stable compared to the corresponding models in the context of general relativity.

Relating renormalizability of D-dimensional higher-order electromagnetic and gravitational models to the classical potential at the origin

2017 ◽  
Vol 32 (08) ◽  
pp. 1750048 ◽  
Author(s):  
Antonio Accioly ◽  
Gilson Correia ◽  
Gustavo P. de Brito ◽  
José de Almeida ◽  
Wallace Herdy
Keyword(s):  
Fourth Order ◽  
Massive Gravity ◽  
Higher Order ◽  
Sixth Order ◽  
Gravity Models ◽  
Local Models ◽  
Order Model ◽  
Functional Generator ◽  
Classical Potential ◽  
Real Poles

Simple prescriptions for computing the D-dimensional classical potential related to electromagnetic and gravitational models, based on the functional generator, are built out. These recipes are employed afterward as a support for probing the premise that renormalizable higher-order systems have a finite classical potential at the origin. It is also shown that the opposite of the conjecture above is not true. In other words, if a higher-order model is renormalizable, it is necessarily endowed with a finite classical potential at the origin, but the reverse of this statement is untrue. The systems used to check the conjecture were D-dimensional fourth-order Lee–Wick electrodynamics, and the D-dimensional fourth- and sixth-order gravity models. A special attention is devoted to New Massive Gravity (NMG) since it was the analysis of this model that inspired our surmise. In particular, we made use of our premise to resolve trivially the issue of the renormalizability of NMG, which was initially considered to be renormalizable, but it was shown some years later to be non-renormalizable. We remark that our analysis is restricted to local models in which the propagator has simple and real poles.

Sign in / Sign up

Export Citation Format

Share Document