Stiff Stability of the Hydrogen atom in dissipative Fokker electrodynamics

We introduce an ad-hoc electrodynamics with advanced and retarded Lienard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem, i.e., the hydrogen atom. We perform the linear stability analysis of circular orbits for oscillations perpendicular to the orbital plane. In particular we study the normal modes of the linearized dynamics that have an arbitrarily large imaginary eigenvalue. These large eigenvalues are fast frequencies that introduce a fast (stiff) timescale into the dynamics. As an application, we study the phenomenon of resonant dissipation, i.e., a motion where both particles recoil together in a drifting circular orbit (a bound state), while the atom dissipates center-of-mass energy only. This balancing of the stiff dynamics is established by the existence of a quartic resonant constant that locks the dynamics to the neighborhood of the recoiling circular orbit. The resonance condition quantizes the angular momenta in reasonable agreement with the Bohr atom. The principal result is that the emission lines of quantum electrodynamics (QED) agree with the prediction of our resonance condition within one percent average deviation.Comment: 1 figure, Notice that Eq. (34) of the Phys. Rev. E paper has a typo; it is missing the square Brackets of eq. (33), find here the correct e

Stationary probability density of stochastic search processes in global optimization

A method for the construction of approximate analytical expressions for the stationary marginal densities of general stochastic search processes is proposed. By the marginal densities, regions of the search space that with high probability contain the global optima can be readily defined. The density estimation procedure involves a controlled number of linear operations, with a computational cost per iteration that grows linearly with problem size

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Periodic Host Absence Can Select for Higher or Lower Parasite Transmission Rates

This paper explores the effect of discontinuous periodic host absence on the evolution of pathogen transmission rates by using Ro maximisation techniques. The physiological consequence of an increased transmission rate can be either an increased virulence, i.e. there is a transmission-virulence trade-off or ii) a reduced between season survival, i.e. there is a transmission-survival trade-off. The results reveal that the type of trade-off determines the direction of selection, with relatively longer periods of host absence selecting for higher transmission rates in the presence of a trade-off between transmission and virulence but lower transmission rates in the presence of a trade-of between transmission and between season survival. The fact that for the transmission-virulence trade-off both trade-off parameters operate during host presence whereas for the transmission-survival trade-off one operates during host presence (transmission) and the other (survival) during the period of host absence is the main cause for this difference in selection direction. Moreover, the period of host absence seems to be the key determinant of the pathogens transmission rate. Comparing plant patho-systems with contrasting biological features suggests that airborne plant pathogen respond differently to longer periods of host absence than soil-borne plant pathogens

3D Bioprinted Human Skeletal Muscle Constructs for Muscle Function Restoration

A bioengineered skeletal muscle tissue as an alternative for autologous tissue flaps, which mimics the structural and functional characteristics of the native tissue, is needed for reconstructive surgery. Rapid progress in the cell-based tissue engineering principle has enabled in vitro creation of cellularized muscle-like constructs; however, the current fabrication methods are still limited to build a three-dimensional (3D) muscle construct with a highly viable, organized cellular structure with the potential for a future human trial. Here, we applied 3D bioprinting strategy to fabricate an implantable, bioengineered skeletal muscle tissue composed of human primary muscle progenitor cells (hMPCs). The bioprinted skeletal muscle tissue showed a highly organized multi-layered muscle bundle made by viable, densely packed, and aligned myofiber-like structures. Our in vivo study presented that the bioprinted muscle constructs reached 82% of functional recovery in a rodent model of tibialis anterior (TA) muscle defect at 8 weeks of post-implantation. In addition, histological and immunohistological examinations indicated that the bioprinted muscle constructs were well integrated with host vascular and neural networks. We demonstrated the potential of the use of the 3D bioprinted skeletal muscle with a spatially organized structure that can reconstruct the extensive muscle defects

Scaling Effects and Spatio-Temporal Multilevel Dynamics in Epileptic Seizures

Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of body control. In this paper, we aim to contribute towards a better understanding of the dynamical systems phenomena that cause seizures. Based on data analysis and modelling, seizure dynamics can be identified to possess multiple spatial scales and on each spatial scale also multiple time scales. At each scale, we reach several novel insights. On the smallest spatial scale we consider single model neurons and investigate early-warning signs of spiking. This introduces the theory of critical transitions to excitable systems. For clusters of neurons (or neuronal regions) we use patient data and find oscillatory behavior and new scaling laws near the seizure onset. These scalings lead to substantiate the conjecture obtained from mean-field models that a Hopf bifurcation could be involved near seizure onset. On the largest spatial scale we introduce a measure based on phase-locking intervals and wavelets into seizure modelling. It is used to resolve synchronization between different regions in the brain and identifies time-shifted scaling laws at different wavelet scales. We also compare our wavelet-based multiscale approach with maximum linear cross-correlation and mean-phase coherence measures

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase- or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). (...)Comment: 22 pages, 18 figure

Graz. Schloßberg.

Blick zum Schloßberg mit Hauptbrück