Estimation of time delay by coherence analysis

Using coherence analysis (which is an extensively used method to study the correlations in frequency domain, between two simultaneously measured signals) we estimate the time delay between two signals. This method is suitable for time delay estimation of narrow band coherence signals for which the conventional methods cannot be reliably applied. We show by analysing coupled R\"ossler attractors with a known delay, that the method yields satisfactory results. Then, we apply this method to human pathologic tremor. The delay between simultaneously measured traces of Electroencephalogram (EEG) and Electromyogram (EMG) data of subjects with essential hand tremor is calculated. We find that there is a delay of 11-27 milli-seconds ($ms$) between the tremor correlated parts (cortex) of the brain (EEG) and the trembling hand (EMG) which is in agreement with the experimentally observed delay value of 15 $ms$ for the cortico-muscular conduction time. By surrogate analysis we calculate error-bars of the estimated delay.Comment: 21 pages, 8 figures, elstart.cls file included. Accepted for publication in Physica

Simulation of Laser Ablation in Aluminum: The Effectivity of Double Pulses

Lasers are becoming a more and more important tool in cutting and shaping materials. Improving precision and effectivity is an ongoing demand in science and industry. One possibility are double pulses. Here we study laser ablation of aluminum by the two-temperature model. There the laser is modeled as a source in a continuum heat conduction equation for the electrons, whose temperature then is transferred to a molecular dynamics particle model by an electron-phonon coupling term. The melting and ablation effectivity is investigated depending on the relative intensity and the time delay between two Gaussian shaped laser pulses. It turns out that at least for aluminum the optimal pulse shapes are standard Gaussian pulses. For double pulses with delay times up to 200 ps we find a behavior as observed in experiment: the ablation depth decreases beyond a delay of 10 ps even if one does not account for the weakening at the second pulse due to laser-plasma interaction.Comment: 18 pages, 6 figure

Numerical resolution of an exact heat conduction model with a delay term

In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.Peer ReviewedPostprint (published version

Random-matrix theory of Majorana fermions and topological superconductors

I. Introduction (What is new in RMT, Superconducting quasiparticles, Experimental platforms) II. Topological superconductivity (Kitaev chain, Majorana operators, Majorana zero-modes, Phase transition beyond mean-field) III. Fundamental symmetries (Particle-hole symmetry, Majorana representation, Time-reversal and chiral symmetry) IV. Hamiltonian ensembles (The ten-fold way, Midgap spectral peak, Energy level repulsion) V. Scattering matrix ensembles (Fundamental symmetries, Chaotic scattering, Circular ensembles, Topological quantum numbers) VI. Electrical conduction (Majorana nanowire, Counting Majorana zero-modes, Conductance distribution, Weak antilocalization, Andreev resonances, Shot noise of Majorana edge modes) VII. Thermal conduction (Topological phase transitions, Super-universality, Heat transport by Majorana edge modes, Thermopower and time-delay matrix, Andreev billiard with chiral symmetry) VIII. Josephson junctions (Fermion parity switches, 4{\pi}-periodic Josephson effect, Discrete vortices) IX. ConclusionComment: V1: 18 pages, 16 figures; pre-submission version, for feedback; V2: 33 pages, 31 figures; greatly expanded in response to feedback, thank you!; V3: minor corrections, version to be published in Reviews of Modern Physic

Ultrafast photodoping and effective Fermi-Dirac distribution of the Dirac particles in Bi2Se3

We exploit time- and angle- resolved photoemission spectroscopy to determine the evolution of the out-of-equilibrium electronic structure of the topological insulator Bi2Se. The response of the Fermi-Dirac distribution to ultrashort IR laser pulses has been studied by modelling the dynamics of the hot electrons after optical excitation. We disentangle a large increase of the effective temperature T* from a shift of the chemical potential mu*, which is consequence of the ultrafast photodoping of the conduction band. The relaxation dynamics of T* and mu* are k-independent and these two quantities uniquely define the evolution of the excited charge population. We observe that the energy dependence of the non-equilibrium charge population is solely determined by the analytical form of the effective Fermi-Dirac distribution.Comment: 5 Pages, 3 Figure

ECG patterns of left anterior fascicular block and conduction impairment in ventricular myocardium: a whole-heart model-based simulation study

Left anterior fascicular block (LAFB) is a heart disease identifiable from an abnormal electrocardiogram (ECG). It has been reported that LAFB is associated with an increased risk of heart failure. Non-specific intraventricular conduction delay due to the lesions of the conduction bundles and slow cell to cell conduction has also been considered as another cause of heart failure. Since the location and mechanism of conduction delay have notable variability between individual patients, we hypothesized that the impaired conduction in the ventricular myocardium may lead to abnormal ECGs similar to LAFB ECG patterns. To test this hypothesis, based on a computer model with a three dimensional whole-heart anatomical structure, we simulated the cardiac exciting sequence map and 12-lead ECG caused by the block in the left anterior fascicle and by the slow conduction velocity in the ventricular myocardium. The simulation results showed that the typical LAFB ECG patterns can also be observed from cases with slow conduction velocity in the ventricular myocardium. The main differences were the duration of QRS and wave amplitude. In conclusion, our simulations provide a promising starting point to further investigate the underlying mechanism of heart failure with LAFB, which would provide a potential reference for LAFB diagnosis