Search results for "equation"
showing 10 items of 4219 documents
A new calculation procedure for non-uniform residual stress analysis by the hole-drilling method
1998
The hole-drilling method is one of the most used semi-destructive techniques for residual stress analysis in mechanical parts. In the presence of non-uniform residual stress, the stress field can be determined from the measured relaxed strains using several calculation methods, but the most used one is the so-called integral method. This method is characterized by some simplifications that lead to approximate results, especially when the residual stress varies abruptly. In this paper a new calculation procedure called the spline methods is proposed, which allows these drawbacks to be overcome. Numerical simulations and an experimental test have corroborated the best performance of the prop…
A New Procedure for the Evaluation of Non-Uniform Residual Stresses by the Hole Drilling Method Based on the Newton-Raphson Technique
2010
The hole drilling method is one of the most used semi-destructive techniques for the analysis of residual stresses in mechanical components. The non-uniform stresses are evaluated by solving an integral equation in which the strains relieved by drilling a hole are introduced. In this paper a new calculation procedure, based on the Newton-Raphson method for the determination of zeroes of functions, is presented. This technique allows the user to introduce complex and effective forms of stress functions for the solution of the problem. All the relationships needed for the evaluation of the stresses are obtained in explicit form, eliminating the need to use additional mathematical tools. The t…
Generalized Camassa-Holm Equations: Symmetry, Conservation Laws and Regular Pulse and Front Solutions
2021
In this paper, we consider a member of an integrable family of generalized Camassa–Holm (GCH) equations. We make an analysis of the point Lie symmetries of these equations by using the Lie method of infinitesimals. We derive nonclassical symmetries and we find new symmetries via the nonclassical method, which cannot be obtained by Lie symmetry method. We employ the multiplier method to construct conservation laws for this family of GCH equations. Using the conservation laws of the underlying equation, double reduction is also constructed. Finally, we investigate traveling waves of the GCH equations. We derive convergent series solutions both for the homoclinic and heteroclinic orbits of the…
Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System
2012
In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and its double Hopf bifurcations are investigated. The general post-bifurcation and stability analysis are carried out using the normal form of the system obtained via the method of multiple scales. The dynamics of the orbits predicted through the normal form comprises possible regimes of periodic solutions, two-period tori, and three-period tori in parameter space. Moreover, we show how the hyperchaotic synchronization of this system can be realized via an adaptive control scheme. Numerical simulations are included to show the effectiveness of the designed control.
Cavity solitons in nondegenerate optical parametric oscillation
2000
Abstract We find analytically cavity solitons in nondegenerate optical parametric oscillators. These solitons are exact localised solutions of a pair of coupled parametrically driven Ginzburg–Landau equations describing the system for large pump detuning. We predict the existence of a Hopf bifurcation of the soliton resulting in a periodically pulsing localised structure. We give numerical evidence of the analytical results and address the problem of cavity soliton interaction.
Turing Instability and Pattern Formation for the Lengyel–Epstein System with Nonlinear Diffusion
2014
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel---Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we c…
How to Get a Model in Pedestrian Dynamics to Produce Stop and Go Waves
2016
Stop and go waves in granular flow can often be described mathematically by a dynamical system with a Hopf bifurcation. We show that a certain class of microscopic, ordinary differential equation-based models in crowd dynamics fulfil certain conditions of Hopf bifurcations. The class is based on the Gradient Navigation Model. An interesting phenomenon arises: the number of pedestrians in the system must be greater than nine for a bifurcation—and hence for stop and go waves to be possible at all, independent of the density. Below this number, no parameter setting will cause the system to exhibit stable stop and go behaviour. The result is also interesting for car traffic, where similar model…
Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
2013
We formulate the general approach based on the Lindblad equation to calculate the full counting statistics of work and heat produced by driven quantum systems weakly coupled with a Markovian thermal bath. The approach can be applied to a wide class of dissipative quantum systems driven by an arbitrary force protocol. We show the validity of general fluctuation relations and consider several generic examples. The possibilities of using calorimetric measurements to test the presence of coherence and entanglement in the open quantum systems are discussed. QC 20141010
Challenges in truncating the hierarchy of time-dependent reduced density matrices equations
2012
In this work, we analyze the Born, Bogoliubov, Green, Kirkwood, and Yvon (BBGKY) hierarchy of equations for describing the full time evolution of a many-body fermionic system in terms of its reduced density matrices (at all orders). We provide an exhaustive study of the challenges and open problems linked to the truncation of such a hierarchy of equations to make them practically applicable. We restrict our analysis to the coupled evolution of the one- and two-body reduced density matrices, where higher-order correlation effects are embodied into the approximation used to close the equations. We prove that within this approach, the number of electrons and total energy are conserved, regardl…
Validation of the Hungarian PHQ-15. A latent variable approach
2021
Somatic symptoms without a clear-cut organic or biomedical background, also called "medically unexplained" or "somatoform" symptoms, are frequent in primary and secondary health care. They are often accompanied by depression and/or anxiety, and cause functional impairment. The Patient Health Question-naire Somatic Symptom Scale (PHQ-15) was developed to measure somatic symptom distress based on the frequency and bothersomeness of non-specific somatic symptoms. The study aimed to (1) evaluate the Hungarian version of the PHQ-15 from a psychometric point of view; (2) replicate the bifactor structure and associations with negative affect described in the literature; and (3) provide the Hungari…