The non linear dynamics of retinal waves

Identifiability and indistinguishability of linear compartmental models

This paper addresses the coupling of flows of ice, till and water, and the issue of whether such coupling provides mechanisms for meso-scale (kilometres to tens of kilometres) variability in ice-sheet flow and texture. The question of whether effective pressures at the ice-bed interface are statically or hydraulically controlled is examined in this paper. The answer is scale dependent, and has a significant effect on the relationship between ice surface and basal topography.The consequences of these considerations on till flow, coupled ice–till flow and coupled ice, till and water flow are examined. An analysis of till-flow kinematics and shock formation is carried out. The linear stability of coupled long-wavelength ice-till flow is analysed, and regions in parameter space where this flow is unstable, with rather small rate constants are found. Upstream-moving ice surface waves are predicted. The linear stablity of coupled ice–till–water flow is examined, where water flow is modelled using a basal flow system with effective-pressure-dependent properties. Again, regions in parameter space where the system is linearly unstable are found, this time with relatively rapid rate constants. The water pressure exhibits “breather” modes.These analyses assume that there is a substantial basal traction. A problem with models of ice streams wholly restrained at the side is identified: they seem to predict erosion rates which are unfeasibly large.There appears to be sufficient variability in the ice–till– water system to potentially explain texture in ice-stream surfaces, variations in ice-stream thickness of tens of metres not directly relatable to topography, and waves moving upstream or downstream. Most importantly, the ice-stream–bed system is shown to exhibit meso-scale variability simply by coupling ice flow according to the shallow-ice approximation, till flow according to the hydrostatic thin-till approximation and water flow according to an effective-pressure-dependent hydraulics.

Nonlinear characteristics of the triggering combustion instabilities in solid rocket motors

Albeit occurring at zero temperature, quantum critical phenomena have a huge impact on the finite-temperature phase diagram of strongly correlated systems, giving experimental access to their observation. Indeed, the existence of a gapless, zero-temperature quantum critical point induces the existence of an extended region in parameter space—the quantum critical fan (QCF)—characterized by power-law temperature dependences of all observables. Identifying experimentally the QCF and its crossovers to other regimes (renormalized classical, quantum disordered) remains nonetheless challenging. Focusing on paradigmatic models of quantum phase transitions, here we show that quantum correlations—captured by the quantum variance of the order parameter—exhibit the temperature scaling associated with the QCF over a parameter region much broader than that revealed by ordinary correlations. The link existing between the quantum variance and the dynamical susceptibility paves the way to an experimental reconstruction of the QCF using spectroscopic techniques.

The stability and other physical properties of a class of regular black holes, quasiblack holes, and other electrically charged compact objects are investigated in the present work. The compact objects are obtained by solving the Einstein-Maxwell system of equations assuming spherical symmetry in a static spacetime. The spacetime is split in two regions by a spherical surface of coordinate radius $a$. The interior region contains a nonisotropic charged fluid with a de Sitter type equation of state, $p_r = -\rho_m$, $p_r$ and $\rho_m$ being respectively the radial pressure and the energy density of the fluid. The charge distribution is chosen as a well behaved power-law function. The exterior region is the electrovacuum Reissner-Nordstr\"om metric, which is joined to the interior metric through a spherical thin shell (a thin matter layer) placed at the radius $a$. The matter of the shell is assumed to be a perfect fluid satisfying a linear barotropic equation of state, ${\cal P}=\omega\sigma$, with ${\cal P}$ and $\sigma$ being respectively the pressure and energy density of the shell, with $\omega$ being a constant. The exact solutions obtained are analyzed in some detail by exploring the interesting regions of parameter space, complementing the analysis of previous works on similar models. This is the first important contribution of the present study. The stability of the solutions are then investigated considering perturbations around the equilibrium position of the shell. This is the second and the most important contribution of this work. We find that there are stable objects in relatively large regions of the parameter space. In particular, there are stable regular black holes for all values of the parameter $\omega$ of interest. Other stable ultracompact objects as quasiblack holes, gravastars, and even overcharged stars are allowed in certain regions of the parameter space.

We introduce a concept of noise robustness in dynamical systems with noise and argue that this concept is essential to guarantee the reliability of physical random bit generators (RBGs). As an example of promising physical RBGs we consider a chaotic laser system and show that it has the property of noise robustness with respect to changes in the temporal correlation of the noise source. Moreover, employing a simple model of tangent space dynamics, we give a theoretical interpretation of the numerical results and in particular show that the Lyapunov exponent determines a theoretical boundary of a noise-robust region in parameter space. These theoretical results are expected to be significant not only for chaotic lasers, but also for a broad class of chaotic dynamical systems with correlated noise.

<p>Previous studies have suggested that fully nonlinear internal solitary waves (ISWs) are very soliton-like as the interaction of two ISWs results in only very small changes in amplitude of the interacting ISWs and in the production of a very small amplitude wave train. Previous studies have, however, considered ISWs with the polarity predicted by the sign of the quadratic nonlinear coefficient of the KdV equation. The Gardner equation, which is an extension of the KdV equation that includes a cubic nonlinear term, has ISWs of two polarities (i.e., waves of depression and elevation) when the cubic coefficient of the Gardner equation is positive. These waves are soliton solutions of the Gardner equations.  In this talk I will discuss the interaction of ISWs of opposite polarity in continuous asymmetric three layer stratifications. Regions in parameter space where ISWs of opposite polarity exist will be discussed and I will demonstrate via fully nonlinear numerical simulations that the interaction of ISWs of opposite polarity waves are far from soliton-like: their interaction can result in very large changes in wave amplitude and may produce a very complicated wave field with multiple large ISWs, a large linear wave field and breather-like waves.<span> </span></p>

Electron-acoustic waves (EAWs) as well as electron-acoustic solitary structures play a crucial role in thermalization and acceleration of electron populations in Earth's magnetosphere. These waves are often observed in association with whistler-mode waves, but the detailed mechanism of EAW and whistler wave coupling is not yet revealed. We investigate the excitation mechanism of EAWs and their potential relation to whistler waves using particle-in-cell simulations. Whistler waves are first excited by electrons with a temperature anisotropy perpendicular to the background magnetic field. Electrons trapped by these whistler waves through nonlinear Landau resonance form localized field-aligned beams, which subsequently excite EAWs. By comparing the growth rate of EAWs and the phase mixing rate of trapped electron beams, we obtain the critical condition for EAW excitation, which is consistent with our simulation results across a wide region in parameter space. These results are expected to be useful in the interpretation of concurrent observations of whistler-mode waves and nonlinear solitary structures and may also have important implications for investigation of cross-scale energy transfer in the near-Earth space environment.

The next-to-minimal supersymmetric Standard Model (NMSSM) with an extended Higgs sector offers at least one Higgs boson as the Standard Model (SM)-like Higgs with a mass around 125 GeV. In this work, we revisit the mass spectrum and couplings of non-SM-like Higgs bosons taking into consideration most relevant constraints and identify the relevant parameter space. The discovery potential of these non-SM-like Higgs bosons, apart from their masses, is guided by their couplings with gauge bosons and fermions which are very much parameter space sensitive. We evaluate the rates of productions of these non-SM-like Higgs bosons at the LHC for a variety of decay channels in the allowed region of the parameter space. Although [Formula: see text], [Formula: see text] modes appear to be the most promising decay channels, but for a substantial region of parameter space the two-photon decay mode has a remarkably large rate. In this study we emphasize that this diphoton mode can be exploited to find the non-SM-like Higgs bosons of the NMSSM and can also be a potential avenue to distinguish the NMSSM from the MSSM. In addition, we discuss briefly the various detectable signals of these non-SM Higgs bosons at the LHC.

It is shown that the method of steps for linear delay-differential equation can be formally used to find an infinite-dimensional linear map whose stability is equivalent to that of the delay equation. The truncated map can be used to estimate the spectrum of the discrete version of the evolution semigroup associated with the continuous equation. The method provides an efficient way to numerically determine stability regions in parameter space.

A minimal chain of two quantum dots (QDs) connected via a superconductor has been predicted to host perfectly localized zero-energy states, known as poor man's Majoranas (PMMs). These states are expected to be related to Majorana bound states (MBSs) in longer chains and that the tunable nature of this setup makes it a promising platform to study MBSs. However, realistic systems can only host highly, but not perfectly, localized near-zero-energy states, called imperfect PMMs. These imperfect PMMs have been shown to evolve into trivial states unrelated to MBSs when the chain is extended. Such states are called false PMMs, whereas PMMs that evolve into MBSs in long chains are called true PMMs. Here, using a microscopic model of QD-superconductor arrays, we consider properties of false PMMs and the circumstances under which they appear. In two-site systems, we find that the origin of many false PMMs can be related to zero-energy states occurring in the absence of superconductivity, and we use this analytic understanding to characterize the false PMMs that are typical for different regions of parameter space. In three-site systems, we show that false PMMs can occur via the same mechanism as for two-site systems, but we also find them in regions of parameter space where they are not predicted to exist, thus hinting that the physics of false PMMs can be richer in longer chains. Finally, we demonstrate that the PMMs most stable to perturbations in chemical potential and with the largest excitation gaps appear in a region of parameter space that also has a large ratio of false to true PMMs.

Bifurcation Structure of a Three-Species Food-Chain Model

In this work, the interesting dynamics of coupled nonlinear memristor-based oscillators in ring configuration are explored. The mathematical models are derived to describe the possible cases of employing identical or different nonlinearities. Analytical and numerical techniques, involving perturbation methods, normal forms, phase portraits, and Lyapunov exponents are used to investigate various types of dynamical behaviors along with their stability regions in parameters space. The effects of time-delayed coupling on the proposed system are numerically studied. It is demonstrated that the coupled oscillators show rich dynamics including periodic orbits, quasiperiodicity, two-dimensional, and three-dimensional tori.

Self-excited vibration often emerges in closed-loop systems due to parameter points out of the stable region in the parameter space. Consequently, based on control theory, various analysis methods have been developed to determine the parameter condition of equilibrium stability and to calculate the amplitude and the frequency of self-excited vibration in high-order closedloop systems, of which frequency method is a very useful tool. Particularly, for the transfer function is invariant in nonsingular linear coordinate transformation for a given dynamic system, it may be obtained in a simple manner either from system equations or experimentally. Usually, the block diagram is a convenient model for the frequency method. Thus, the contents arranged in this chapter are divided into five sections: the first is devoted to establishing mathematical models in frequency domain for closed-loop systems; the second provides a frequency criterion of equilibrium stability for linear closed-loop systems; the third recommends a frequency criterion of equilibrium stability for nonlinear closed-loop systems; the fourth introduces a well-known describing function method used to calculate the amplitude and the frequency of self-excited vibration in closed-loop systems; and the fifth gives a quadratic form optimal algorithm to determine the control parameters, which can prevent the controlled system from self-excited vibration.

We study a class of supersymmetric models with nonuniversal gaugino masses that could arise from $F$-terms in a general combination of the singlet and adjoint representations of $SU(5)$. We explore models that satisfy present Large Hadron Collider and other bounds, showing how the allowed parameter space is divided into distinct ``continents.'' Regions of parameter space that ameliorate the supersymmetric little hierarchy problem with a small $\ensuremath{\mu}$ parameter include the usual focus-point scenario, but also natural areas with much lighter squarks and sleptons. These models are continuously connected in parameter space to regions in which stau coannihilation or Higgs exchange is mostly responsible for dark matter annihilation, and to models in which the thermal relic abundance is achieved by slepton-mediated annihilation, reviving the bulk region that is severely restricted in minimal supergravity models. In hybrid or confluence regions, several mechanisms combine to give the requisite dark matter annihilation rate. In each case, we study the prospects for direct detection of dark matter. We also comment briefly on the impact of recent hints for ${M}_{h}$ near 125 GeV from the LHC.