arXiv subjects

Grzegorz Litak

Publications and source records attributed to Grzegorz Litak.

31 records · Page 2Linked to original sources

arXiv2006

Chaotic Vibration of a Quarter-Car Model Excited by the Road Surface Profile

The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos in the case of a quarter car model excited kinematically by the road surface profile. By analyzing the potential an analytic expression is found for the homoclinic orbit. By introducing an harmonic excitation term and damping as perturbations, the critical Melnikov amplitude of the road surface profile is found, above which the system can vibrate chaotically.

nlin.CD↗

arXiv2006

Transition to Chaos in the Self-Excited System with a Cubic Double Well Potential and Parametric Forcing

We examine the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double well nonlinear potential. The system was subjected simultaneously to parametric periodic forcing and self excitation via negative damping term. Detailed numerical studies confirm the analytical predictions and show that transitions from regular to chaotic types of motion are often associated with increasing the energy of an oscillator and its escape from a single well.

nlin.CD↗

arXiv2006

Vibration of the Duffing Oscillator: Effect of Fractional Damping

We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a critical forcing amplitude above which the system may behave chaotically. The results have been verified by numerical simulations using standard nonlinear tools as Poincare maps and a Lyapunov exponent. Above the critical Melnikov amplitude $μ_c$, which is the sufficient condition of a global homoclinic bifurcation, we have observed the region with a transient chaotic motion.

nlin.CD↗

arXiv2004

Suppression of chaos by weak resonant excitations in a nonlinear oscillator with a non-symmetric potential

We examine the Mielnikov criterion for transition to chaos in case of one degree of freedom nonlinear oscillator with non symmetric potential. This system subjected to an external periodic force shows homoclinic transition from regular vibrations to chaos just before escape from the potential well. Especially we study the effect of a second resonant excitation with different phase on the system transition to chaos and propose a way of its control.

nlin.CD↗

arXiv2004

Variations of Pairing Potential and Charge Distribution in Presence of a Non-magnetic Impurity

Using an attractive Hubbard model we examine spatial variations of superconducting order parameter and local charge on a two dimensional lattice. For various band filling we show the effect of destruction of the order parameter around a non-magnetic impurity. In case of a half-filled system such destruction is accompanied by appearance of characteristic charge variations around the impurity with an isotropic distribution.

cond-mat.supr-con↗

arXiv2004

'Pi State' Induced by Impurities with a Repulsive Interaction

We study the properties of a quantum impurity embedded in a superconducting host. The superconductor is described by the negative U Hubbard model while the impurity introduces a repulsive interaction to the system. We discuss the influence of this `on-impurity' Coulomb repulsion on the local properties (density of states, electron pairing) of the superconductor. We show the condition of pi - like behaviour, defined as two subsystems having a phase difference of pi, in the system by using a proper combination of attractive pairing interaction and repulsive one located at impurity site.

cond-mat.supr-con↗

arXiv2004

Dynamics of a Gear System with Faults in Meshing Stiffness

Gear box dynamics is characterised by a periodically changing stiffness. In real gear systems, a backlash also exists that can lead to a loss in contact between the teeth. Due to this loss of contact the gear has piecewise linear stiffness characteristics, and the gears can vibrate regularly and chaotically. In this paper we examine the effect of tooth shape imperfections and defects. Using standard methods for nonlinear systems we examine the dynamics of gear systems with various faults in meshing stiffness.

nlin.CD↗

arXiv2004

Estimation of a Noise Level Using Coarse-Grained Entropy of Experimental Time Series of Internal Pressure in a Combustion Engine

We report our results on non-periodic experimental time series of pressure in a single cylinder spark ignition engine. The experiments were performed for different levels of loading. We estimate the noise level in internal pressure calculating the coarse-grained entropy from variations of maximal pressures in successive cycles. The results show that the dynamics of the combustion is a nonlinear multidimensional process mediated by noise. Our results show that so defined level of noise in internal pressure is not monotonous function of loading.

nlin.CD↗

arXiv2003

Specific Heat of Disordered Superconductors Induced by Negative Centers

We show that superconductors with inhomogeneous order parameters can show similar features as anisotropic ones. In this paper we study the low temperature specific heat dependence in such a system and we show that the disorder associated with randomly distributed attractive centers convert the BCS temperature exponential behaviour into a power law formula. To describe superconductivity we used a random version of the negative U Hubbard model, while the disorder was treated by means of the Coherent Potential Approximation (CPA).

cond-mat.supr-con↗

arXiv2003

Nonlinear Vibration in Gear Systems

Gear box dynamics is characterised by a periodically changing stiffness and a backlash which can lead to a loss of the contact between the teeth. Due to backlash, the gear system has piecewise linear stiffness characteristics and, in consequence, can vibrate regularly or chaoticaly depending on the system parameters and the initial conditions. We examine the possibility of a nonfeedback system control by introducing a weak resonant excitation term and through adding an additional degree of freedom to account for shaft flexibility on one side of the gearbox. We shall show that by correctly choosing the coupling values the system vibrations may be controlled.

nlin.CD↗

arXiv2002

Charge and Phase Fluctuations in Attractive Hubbard Model

Using the negative U Hubbard model we analyze normal state properties of a superconductor. In this model there exists a characteristic pairing temperature T_P above a superconducting critical temperature. Below T_P electrons start to form incoherent pairs. The fluctuations in charge and phase are precursors of charge density wave and superconductivity phases depending on band filling. They lead naturally to pseudogap opening in the density of states.

cond-mat.supr-con↗

arXiv2001

Effect of Disorder on a D-wave Superconductor

We apply the Coherent Potential Approximation (CPA) to an extended Hubbard model to describe disordered superconductors with d-wave pairing. We discuss the pair-breaking effect caused by non-magneticdisorder in presence of Van Hove Singularity.

cond-mat.supr-con↗

arXiv2001

Chaotic vibrations in a regenerative cutting process

We have analyzed vibrations generated in an orthogonal cutting process. Using a simple one degree of freedom model of the regenerative cutting we have observed the complex behaviour of the system. In presence of a shaped cutting surface, the nonlinear interaction between the tool and a worpiece leads to chatter vibrations of periodic, quasi-periodic or chaotic type depending on system parameters. To describe the profile of the surface machined by the first pass we used a harmonic function. We analysed the impact phenomenon between the tool and a workpiece after their contact loss.

nlin.CD↗