Nonlinear dynamics and chaos simulation system analysis for improved design

Small errors proved catastrophic. Our purpose to remark that a very small cause which escapes our notice determined a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. Small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. When dealing with any kind of electrical device specification, it is important to note that there exists a pair of test conditions that define a test: the forcing function and the limit. Forcing functions define the external operating constraints placed upon the device tested. The actual test defines how well the device responds to these constraints. Forcing inputs to threshold for example, represents the most difficult testing because this put those inputs as close as possible to the actual switching critical points and guarantees that the device will meet the Input-Output specifications. ^ Prediction becomes impossible by classical analytical analysis bounded by Newton and Euclides. We have found that non linear dynamics characteristics is the natural state of being in all circuits and devices. Opportunities exist for effective error detection in a nonlinear dynamics and chaos environment. ^ Nowadays there are a set of linear limits established around every aspect of a digital or analog circuits out of which devices are consider bad after failing the test. Deterministic chaos circuit is a fact not a possibility as it has been revived by our Ph.D. research. In practice for linear standard informational methodologies, this chaotic data product is usually undesirable and we are educated to be interested in obtaining a more regular stream of output data. ^ This Ph.D. research explored the possibilities of taking the foundation of a very well known simulation and modeling methodology, introducing nonlinear dynamics and chaos precepts, to produce a new error detector instrument able to put together streams of data scattered in space and time. Therefore, mastering deterministic chaos and changing the bad reputation of chaotic data as a potential risk for practical system status determination. ^

Divisible quantum dynamics satisfies temporal Tsirelson's bound

We show that divisibility of qubit quantum processes implies temporal Tsirelson's bound. We also prove that the classical bound of the temporal Bell's inequality holds for dynamics that can be described by entanglement-breaking channels---a more general class of dynamics than that allowed by classical physics.

Actin dynamics provides membrane tension to merge fusing vesicles into the plasma membrane

Vesicle fusion is executed via formation of an Ω-shaped structure (Ω-profile), followed by closure (kiss-and-run) or merging of the Ω-profile into the plasma membrane (full fusion). Although Ω-profile closure limits release but recycles vesicles economically, Ω-profile merging facilitates release but couples to classical endocytosis for recycling. Despite its crucial role in determining exocytosis/endocytosis modes, how Ω-profile merging is mediated is poorly understood in endocrine cells and neurons containing small ∼30-300 nm vesicles. Here, using confocal and super-resolution STED imaging, force measurements, pharmacology and gene knockout, we show that dynamic assembly of filamentous actin, involving ATP hydrolysis, N-WASP and formin, mediates Ω-profile merging by providing sufficient plasma membrane tension to shrink the Ω-profile in neuroendocrine chromaffin cells containing ∼300 nm vesicles. Actin-directed compounds also induce Ω-profile accumulation at lamprey synaptic active zones, suggesting that actin may mediate Ω-profile merging at synapses. These results uncover molecular and biophysical mechanisms underlying Ω-profile merging.

Evolutionary dynamics under various modes of reproduction

Thesis (Ph.D.)--University of Washington, 2016-08

(Quantum-) critical dynamics of magnetoelectric materials

In this thesis the critical dynamics of several magnetoelectric compounds at their phase transition were examined. Mostly measurements of the dielectric properties in the frequency range of below 1 Hz up to 5 GHz were employed to evaluate the critical exponents for both magnetic field and temperature-dependent measurements. Most of the materials that are part of this work show anomalous behavior, especially at very low temperatures where quantum fluctuations are of the order of or even dominate those induced thermally. This anomalous behavior manifests in different forms. In Dy2Ti2O7 we demonstrate the existence of electric dipoles on magnetic monopoles. Here the dynamics at the critical endpoint located at 0.36K and in a magnetic field of 1T parallel to the [111] direction are of special interest. At this critical endpoint the expected critical slowing down of the dynamics could not only not be observed but instead the opposite, critical speeding-up by several orders of magnitude, could be demonstrated. Furthermore, we show that the phase diagram of Dy2Ti2O7 in this field direction can be reproduced solely from the dynamical properties, for example the resonance frequency of the observed relaxation that is connected to the monopole movement. Away from this point of the phase diagram the dynamics are slowing-down with reduction of temperature as one would expect. Additional measurements on Y2Ti2O7, a structurally identical but non-magnetic material, show only slowing down with reduction of temperature and no additional features. A possible explanation for the observed critical speeding-up is a coherent movement of magnetic monopoles close to the critical field that increases the resonance frequency by reducing the damping of the process. LiCuVO4 on the other hand behaves normally at its phase transition as long as the temperature is higher than 0.4 K. In this temperature regime the dynamics show critical slowing-down analogous to classical ferroelectric materials. This analogy extends also towards higher frequencies where the permittivity displays a ‘dispersion’ minimum that is temperature-dependent but of the order of 2 GHz. Below 0.4K the observed behavior changes drastically. Here we found no longer relaxational behavior but instead an excitation with very low energy. This low energy excitation was predicted by theory and is caused by nearly gapless soliton excitations within the 1D Cu2+ chains of LiCuVO4. Finally, in TbMnO3 the dynamics of the phase transition into the multiferroic phase was observed at roughly 27 K, a much higher temperature compared to the other materials. Here the expected critical slowing-down was observed, even though in low-frequency measurements this transition into the ferroelectric phase is overshadowed by the so-called c-axis relaxation. Therefore, only frequencies above 1MHz could be used to determine the critical exponents for both temperatureand magnetic-field-dependent measurements. This was done for both the peak frequency as well as the relaxation strength. In TbMnO3 an electromagnetic soft-mode with small optical weight causes the observed fluctuations, similar to the case of multiferroic MnWO4.

Centre-of-mass motion in multi-particle Schrodinger-Newton dynamics

We investigate the implication of the nonlinear and non-local multi-particle Schrodinger-Newton equation for the motion of the mass centre of an extended multi-particle object, giving self-contained and comprehensible derivations. In particular, we discuss two opposite limiting cases. In the first case, the width of the centre-of-mass wave packet is assumed much larger than the actual extent of the object, in the second case it is assumed much smaller. Both cases result in nonlinear deviations from ordinary free Schrodinger evolution for the centre of mass. On a general conceptual level we include some discussion in order to clarify the physical basis and intention for studying the Schrodinger-Newton equation.

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Exotic dynamics in a firing rate model of neural tissue with threshold accommodation

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognized that more realistic models of neural tissue can be obtained with the introduction of state-dependent dynamic thresholds. In this paper we treat a specific phenomenological model of threshold accommodation that mimics many of the properties originally described by Hill. Importantly we explore the consequences of this dynamic threshold at the tissue level, by modifying a standard neural field model of Wilson-Cowan type. As in the case without threshold accommodation classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps) in both one and two dimensions. Importantly an analysis of bump stability in one dimension, using recent Evans function techniques, shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. In the regime where a bump solution does not exist direct numerical simulations show the possibility of self-replicating bumps via a form of bump splitting. Simulations in two space dimensions show analogous localized and traveling solutions to those seen in one dimension. Indeed dynamical behavior in this neural model appears reminiscent of that seen in other dissipative systems that support localized structures, and in particular those of coupled cubic complex Ginzburg-Landau equations. Further numerical explorations illustrate that the traveling pulses in this model exhibit particle like properties, similar to those of dispersive solitons observed in some three component reaction-diffusion systems. A preliminary account of this work first appeared in S Coombes and M R Owen, Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters 94 (2005), 148102(1-4).

QuasiGeostrophic Diagnosis of Mixed-Layer Dynamics Embedded in a Mesoscale Turbulent Field

A quasigeostrophic model is developed to diagnose the three-dimensional circulation, including the vertical velocity, in the upper ocean from high-resolution observations of sea surface height and buoyancy. The formulation for the adiabatic component departs from the classical surface quasigeostrophic framework considered before since it takes into account the stratification within the surface mixed layer that is usually much weaker than that in the ocean interior. To achieve this, the model approximates the ocean with two constant stratification layers: a finite-thickness surface layer (or the mixed layer) and an infinitely deep interior layer. It is shown that the leading-order adiabatic circulation is entirely determined if both the surface streamfunction and buoyancy anomalies are considered. The surface layer further includes a diabatic dynamical contribution. Parameterization of diabatic vertical velocities is based on their restoring impacts of the thermal wind balance that is perturbed by turbulent vertical mixing of momentum and buoyancy. The model skill in reproducing the three-dimensional circulation in the upper ocean from surface data is checked against the output of a high-resolution primitive equation numerical simulation

Simulation of photoinduced processes in organic chromophores: mapping photochemically relevant states for accurate dynamics

The simulation of ultrafast photoinduced processes is a fundamental step towards the understanding of the underlying molecular mechanism and interpretation/prediction of experimental data. Performing a computer simulation of a complex photoinduced process is only possible introducing some approximations but, in order to obtain reliable results, the need to reduce the complexity must balance with the accuracy of the model, which should include all the relevant degrees of freedom and a quantitatively correct description of the electronic states involved in the process. This work presents new computational protocols and strategies for the parameterisation of accurate models for photochemical/photophysical processes based on state-of-the-art multiconfigurational wavefunction-based methods. The required ingredients for a dynamics simulation include potential energy surfaces (PESs) as well as electronic state couplings, which must be mapped across the wide range of geometries visited during the wavepacket/trajectory propagation. The developed procedures allow to obtain solid and extended databases reducing as much as possible the computational cost, thanks to, e.g., specific tuning of the level of theory for different PES regions and/or direct calculation of only the needed components of vectorial quantities (like gradients or nonadiabatic couplings). The presented approaches were applied to three case studies (azobenzene, pyrene, visual rhodopsin), all requiring an accurate parameterisation but for different reasons. The resulting models and simulations allowed to elucidate the mechanism and time scale of the internal conversion, reproducing or even predicting new transient experiments. The general applicability of the developed protocols to systems with different peculiarities and the possibility to parameterise different types of dynamics on an equal footing (classical vs purely quantum) prove that the developed procedures are flexible enough to be tailored for each specific system, and pave the way for exact quantum dynamics with multiple degrees of freedom.

Hidden Schrödinger symmetry in FLRW and Bianchi I minisuperspace models of cosmology and black holes Schwarzschild dynamics

A broad sector of literature focuses on the relationship between fluid dynamics and gravitational systems. This thesis presents results that suggest the existence of a new kind of fluid/gravity duality not based on the holographic principle. The goal is to provide tools that allow us to systematically unearth hidden symmetries for reduced models of cosmology. The focus is on the field space of these models, i.e. the superspace. In fact, conformal isometries of the supermetric leave geodesics in the field space unaltered; this leads to symmetries of the models. An innovative aspect is the use of the Eisenhart-Duval’s lift. Using this method, systems constrained by a potential can be treated as free ones. Moreover, charges explicitly dependent on time, i.e. dynamical, can be found. A detailed analysis is carried out on three basic models of homogenous cosmology: i) flat Friedmann-Lemaître-Robertson-Walker’s isotropic universe filled with a massless scalar field; ii) Schwarzschild’s black hole mechanics and its extension to vacuum (A)dS gravity; iii) Bianchi’s anisotropic type I universe with a massless scalar field. The results show the presence of a hidden Schrödinger’s symmetry which, being intrinsic to both Navier-Stokes’ and Schrödinger’s equations, indicates a correspondence between cosmology and hydrodynamics. Furthermore, the central extension of this algebra explicitly relates two concepts. The first is the number of particles coming from the fluid picture; while the second is the ratio between the IR and UV cutoffs that weighs how much a theory has of “classical” over “quantum”. This suggests a spacetime that emerges from an underlying world which is described by quantum building blocks. These quanta statistically conspire to appear as gravitational phenomena from a macroscopic point of view.

Mechanical Properties And Fracture Dynamics Of Silicene Membranes.

As graphene has become one of the most important materials, there is renewed interest in other similar structures. One example is silicene, the silicon analogue of graphene. It shares some of the remarkable graphene properties, such as the Dirac cone, but presents some distinct ones, such as a pronounced structural buckling. We have investigated, through density functional based tight-binding (DFTB), as well as reactive molecular dynamics (using ReaxFF), the mechanical properties of suspended single-layer silicene. We calculated the elastic constants, analyzed the fracture patterns and edge reconstructions. We also addressed the stress distributions, unbuckling mechanisms and the fracture dependence on the temperature. We analysed the differences due to distinct edge morphologies, namely zigzag and armchair.

Site Specific Spin Dynamics In Bafe2as2: Tuning The Ground State By Orbital Differentiation.

The role of orbital differentiation on the emergence of superconductivity in the Fe-based superconductors remains an open question to the scientific community. In this investigation, we employ a suitable microscopic spin probe technique, namely Electron Spin Resonance (ESR), to investigate this issue on selected chemically substituted BaFe2As2 single crystals. As the spin-density wave (SDW) phase is suppressed, we observe a clear increase of the Fe 3d bands anisotropy along with their localization at the FeAs plane. Such an increase of the planar orbital content is interestingly independent of the chemical substitution responsible for suppressing the SDW phase. As a consequence, the magnetic fluctuations in combination with this particular symmetry of the Fe 3d bands are propitious ingredients for the emergence of superconductivity in this class of materials.

[between The Country And The Laboratory: The Dynamics Of The Production Of Knowledge At The Menopause Outpatients Clinic At Caism, Unicamp.]

This study investigates the practices involved in the production of knowledge about menopause at Caism, Unicamp, a reference center for public policies for women's health. Gynecological appointments and psychological support meetings were observed, and women and doctors were interviewed in order to identify what discourse circulates there and how different actors are brought in to ensure that the knowledge produced attains credibility and travels beyond the boundaries of the teaching hospital to become universal. The analysis is based on localized studies aligned with social studies of science and technology.

[between The Country And The Laboratory: The Dynamics Of The Production Of Knowledge At The Menopause Outpatients Clinic At Caism, Unicamp].

This study investigates the practices involved in the production of knowledge about menopause at Caism, Unicamp, a reference center for public policies for women's health. Gynecological appointments and psychological support meetings were observed, and women and doctors were interviewed in order to identify what discourse circulates there and how different actors are brought in to ensure that the knowledge produced attains credibility and travels beyond the boundaries of the teaching hospital to become universal. The analysis is based on localized studies aligned with social studies of science and technology.