Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach

<p style='text-indent:20px;'>We consider linear stability of steady states of 1<inline-formula><tex-math id="M1">\begin{document}$ \frac{1}{2} $\end{document}</tex-math></inline-formula> and 3DVlasov-Maxwell systems for collisionless plasmas. The linearized systems canbe written as separable Hamiltonian systems with constraints. By using ageneral theory for separable Hamiltonian systems, we recover the sharp linearstability criteria obtained previously by different approaches. Moreover, weobtain the exponential trichotomy estimates for the linearized Vlasov-Maxwellsystems in both relativistic and nonrelativistic cases.</p>

Steady-state thermodynamics for population dynamics in fluctuating environments with side information

Steady-state thermodynamics (SST) is a relatively newly emerging subfield of physics, which deals with transitions between steady states. In this paper, we find an SST-like structure in population dynamics of organisms that can sense their fluctuating environments. As heat is divided into two parts in SST, we decompose population growth into two parts: housekeeping growth and excess growth. Then, we derive the Clausius equality and inequality for excess growth. Using numerical simulations, we demonstrate how the Clausius inequality behaves depending on the magnitude of noise and strategies that organisms employ. Finally, we discuss the novelty of our findings and compare them with a previous study.

Dynamics of Mosquito Population Models with Spatial Diffusion

In this paper, we study some reaction-diffusion models of interactive dynamics of the wild and sterile mosquitoes. The well-posedness of the concerned model is proved. The stability of the steady states is discussed. Numerical simulations are presented to illustrate our theoretical results.

On the Existence of Linearly Oscillating Galaxies

We consider two classes of steady states of the three-dimensional, gravitational Vlasov-Poisson system: the spherically symmetric Antonov-stable steady states (including the polytropes and the King model) and their plane symmetric analogues. We completely describe the essential spectrum of the self-adjoint operator governing the linearized dynamics in the neighborhood of these steady states. We also show that for the steady states under consideration, there exists a gap in the spectrum. We then use a version of the Birman-Schwinger principle first used by Mathur to derive a general criterion for the existence of an eigenvalue inside the first gap of the essential spectrum, which corresponds to linear oscillations about the steady state. It follows in particular that no linear Landau damping can occur in the neighborhood of steady states satisfying our criterion. Verification of this criterion requires a good understanding of the so-called period function associated with each steady state. In the plane symmetric case we verify the criterion rigorously, while in the spherically symmetric case we do so under a natural monotonicity assumption for the associated period function. Our results explain the pulsating behavior triggered by perturbing such steady states, which has been observed numerically.

Cardiorespiratory kinetics in exercise physiology: estimates and predictions using randomized changes in work rate

Purpose Kinetics of cardiorespiratory parameters (CRP) in response to work rate (WR) changes are evaluated by pseudo-random binary sequences (PRBS testing). In this study, two algorithms were applied to convert responses from PRBS testing into appropriate impulse responses to predict steady states values and responses to incremental increases in exercise intensity. Methods 13 individuals (age: 41 ± 9 years, BMI: 23.8 ± 3.7 kg m−2), completing an exercise test protocol, comprising a section of randomized changes of 30 W and 80 W (PRBS), two phases of constant WR at 30 W and 80 W and incremental WR until subjective fatigue, were included in the analysis. Ventilation ($$\dot{V}_{{\text{E}}}$$ V ˙ E ), O2 uptake ($$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 ), CO2 output ($$\dot{V}{\text{CO}}_{2}$$ V ˙ CO 2 ) and heart rate (HR) were monitored. Impulse responses were calculated in the time domain and in the frequency domain from the cross-correlations of WR and the respective CRP. Results The algorithm in the time domain allows better prediction for $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 and $$\dot{V}{\text{CO}}_{2}$$ V ˙ CO 2 , whereas for $$\dot{V}_{{\text{E}}}$$ V ˙ E and HR the results were similar for both algorithms. Best predictions were found for $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 and HR with higher (3–4%) 30 W steady states and lower (1–4%) values for 80 W. Tendencies were found in the residuals between predicted and measured data. Conclusion The CRP kinetics, resulting from PRBS testing, are qualified to assess steady states within the applied WR range. Below the ventilatory threshold, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 and HR responses to incrementally increasing exercise intensities can be sufficiently predicted.