Localized Elasticae for the Strut on the Linear Foundation

1993 ◽  
Vol 60 (4) ◽  
pp. 1033-1038 ◽  
Author(s):  
G. W. Hunt ◽  
M. K. Wadee ◽  
N. Shiacolas
Keyword(s):  
Classical Problem ◽  
Unbounded Solutions ◽  
Dynamical Phase ◽  
Linear Elastic ◽  
Localized Solutions ◽  
Numerical Experimentation ◽  
Indefinite Quadratic Form ◽  
Post Buckling ◽  
Indefinite Quadratic ◽  
Volume Preserving

Localized solutions, for the classical problem of the nonlinear strut (elastica) on the linear elastic foundation, are predicted from double-scale analysis, and confirmed from nonlinear volume-preserving Runge-Kutta runs. The dynamical phase-space analogy introduces a spatial Lagrangian function, valid over the initial post-buckling range, with kinetic and potential energy components. The indefinite quadratic form of the spatial kinetic energy admits unbounded solutions, corresponding to escape from a potential well. Numerical experimentation demonstrates that there is a fractal edge to the escape boundary, resulting in spatial chaos.

scholarly journals On Restriction Estimates for Discrete Quadratic Surfaces

2018 ◽  
Vol 2019 (23) ◽  
pp. 7139-7159 ◽  
Author(s):  
Kevin Henriot ◽  
Kevin Hughes
Keyword(s):  
Quadratic Form ◽  
Integer Matrix ◽  
Discrete Surfaces ◽  
Indefinite Quadratic Form ◽  
Indefinite Quadratic ◽  
Quadratic Surfaces

Abstract We obtain truncated restriction estimates of an unexpected form for discrete surfaces $$\begin{align*}S_N = \{\, ( n_1 , \dots , n_d , R( n_1 , \dots, n_d ) ) \,,\, n_i \in [-N,N] \cap {\mathbb{Z}} \,\},\end{align*}$$ where $R$ is an indefinite quadratic form with integer matrix.

Trust Your Data or Not—StQP Remains StQP: Community Detection via Robust Standard Quadratic Optimization

2020 ◽  
Author(s):  
Immanuel M. Bomze ◽  
Michael Kahr ◽  
Markus Leitner
Keyword(s):  
Community Detection ◽  
Optimization Problem ◽  
Quadratic Optimization ◽  
Quadratic Optimization Problem ◽  
Standard Quadratic Optimization ◽  
Uncertainty Sets ◽  
Indefinite Quadratic Form ◽  
Indefinite Quadratic ◽  
Order Intervals ◽  
Copositive Matrix

We consider the robust standard quadratic optimization problem (RStQP), in which an uncertain (possibly indefinite) quadratic form is optimized over the standard simplex. Following most approaches, we model the uncertainty sets by balls, polyhedra, or spectrahedra, more generally, by ellipsoids or order intervals intersected with subcones of the copositive matrix cone. We show that the copositive relaxation gap of the RStQP equals the minimax gap under some mild assumptions on the curvature of the aforementioned uncertainty sets and present conditions under which the RStQP reduces to the standard quadratic optimization problem. These conditions also ensure that the copositive relaxation of an RStQP is exact. The theoretical findings are accompanied by the results of computational experiments for a specific application from the domain of graph clustering, more precisely, community detection in (social) networks. The results indicate that the cardinality of communities tend to increase for ellipsoidal uncertainty sets and to decrease for spectrahedral uncertainty sets.

Surface virtual texturing of the journal bearings of a three-cylinder ethanol engine

2020 ◽  
Vol 72 (9) ◽  
pp. 1059-1073
Author(s):  
Gabriel Welfany Rodrigues ◽  
Marco Lucio Bittencourt
Keyword(s):  
Peer Review ◽  
Power Loss ◽  
Mathematical Formulation ◽  
Surface Texturing ◽  
Elastohydrodynamic Lubrication ◽  
Element Model ◽  
Content Type ◽  
Linear Elastic ◽  
Numerical Experimentation ◽  
Coupling Procedure

Purpose This paper aims to numerically investigate the surface texturing effects on the main bearings of a three-cylinder ethanol engine in terms of the power loss and friction coefficient for dynamic load conditions. Design/methodology/approach The mathematical formulation considers the Partir-Cheng modified Reynolds equation. The mass-conserving Elrod-Adams p-θ model with the JFO approach is used to deal with cavitation. A fluid-structure coupling procedure is considered for the elastohydrodynamic lubrication. Accordingly, a 3-D linear-elastic substructured finite element model obtained from Abaqus is applied Findings Simulations were carried out considering different dimple texture designs in terms of location, depth and radius. The results suggested that there are regions where texturing is more effective. In addition, distinct journal rotation speeds are studied and the surface texture was able to reduce friction and the power loss by 7%. Practical implications The surface texturing can be a useful technique to reduce the power loss on the crankshaft bearing increasing the overall engine efficiency. Originality/value The surface texturing performance in a three-cylinder engine using ethanol as fuel was investigated through numerical experimentation. The results are supported by previous findings. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-09-2019-0380/

Effects of Warping Constraints and Lateral Restraint on the Buckling of Thin-Walled Frames

2009 ◽  
Author(s):  
Marcello Pignataro ◽  
Giuseppe Ruta ◽  
Nicola Rizzi ◽  
Valerio Varano
Keyword(s):  
Critical Loads ◽  
Dead Load ◽  
Linear Elastic ◽  
Plane Frame ◽  
Post Buckling ◽  
Thin Walled ◽  
Lateral Restraint

We present the effect of warping constraints on the buckling of a thin-walled two-bar (‘Roorda’) plane frame subjected to a ‘dead’ load at the joint. The hinges with the ‘ground’ allow rotation with axis perpendicular to the frame plane; the joint is constrained in the same direction to simulate a 3D-frame. Warping constraints are considered; the restraint at the joint is first supposed rigid and fixed, then is supposed linear elastic to account for different lateral restraint. Critical loads are evaluated numerically; an analysis of the post-buckling behaviour will be part of future investigations.

scholarly journals H∞Fault Detection for Linear Discrete Time-Varying Descriptor Systems with Missing Measurements

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Guangfu Deng ◽  
Huihong Zhao
Keyword(s):  
Fault Detection ◽  
Discrete Time ◽  
Descriptor Systems ◽  
Necessary Condition ◽  
Time Varying ◽  
Missing Measurements ◽  
Indefinite Quadratic Form ◽  
Indefinite Quadratic ◽  
Matrix Differential ◽  
Binary Switching

This paper deals with the problem ofH∞fault detection for a class of linear discrete time-varying descriptor systems with missing measurements, and the missing measurements are described by a Bernoulli random binary switching sequence. We first translate theH∞fault detection problem into an indefinite quadratic form problem. Then, a sufficient and necessary condition on the existence of the minimum is derived. Finally, an observer-basedH∞fault detection filter is obtained such that the minimum is positive and its parameter matrices are calculated recursively by solving a matrix differential equation. A numerical example is given to demonstrate the efficiency of the proposed method.

The inhomogeneous minimum of quadratic forms of signature ± 1

1981 ◽  
Vol 89 (2) ◽  
pp. 225-235 ◽  
Author(s):  
Madhu Raka
Keyword(s):  
Quadratic Form ◽  
Quadratic Forms ◽  
Real Numbers ◽  
Inhomogeneous Minimum ◽  
Indefinite Quadratic Form ◽  
Indefinite Quadratic ◽  
Image Position

Let Qr be a real indefinite quadratic form in r variables of determinant D ≠ 0 and of type (r1, r2), 0 < r1 < r, r = r1 + r2, S = r1 − r2 being the signature of Qr. It is known (e.g. Blaney (3)) that, given any real numbers c1, c2,…, cr, there exists a constant C depending only on r and s such that the inequalityhas a solution in integers x1, x2, …, xr.

scholarly journals The arithmetically reduced indefinite quadratic form in n-variables

1931 ◽  
Vol 131 (816) ◽  
pp. 99-108 ◽  
Keyword(s):  
Quadratic Form ◽  
Real Number ◽  
Reduced Form ◽  
Indefinite Quadratic Form ◽  
Indefinite Quadratic

ƒ ( x 1 , x 2 , ... , x n ) = Ʃ n r,s = 1 a rs x r x s , or for brevity, say ƒ ( x ), where a rs = a sr and a rs is any real number, rational or irrational, be a quadratic form in n -variables. Suppose that the deter­minant ∆ = │ a rs │≠ 0, so that ƒ ( x ) cannot be expressed as a quadratic form with fewer than n variables. From (1) can be derived an infinity of forms g ( y 1 , y 2 , ... , y n ) = Ʃ n r,s = 1 b rs y r y s , say g ( y ), with b rs = b sr , by means of the linear substitutions x r = Ʃ n s = 1 λ rs y s , ( r = 1, 2, ..., n ), where the λ’s are integers and the determinant | λ rs | = 1. We consider throughout only such substitutions. All the forms g ( y ) have the same deter­minant ∆. They are said to be equivalent to ƒ ( x ) and to define a class of forms, the class including all the forms equivalent to ƒ ( x ) and only these. The problem of selecting a particular form as representing the class, i. e ., the so-called reduced form, is fundamental.

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