Exploring Critical Points of Energy Landscapes: From Low-Dimensional Examples to Phase Field Crystal PDEs

In the present work we explore the application of a few root-finding methods to a series of prototypical examples. The methods we consider include: (a) the so-called continuous-time Nesterov (CTN) flow method; (b) a variant thereof referred to as the squared-operator method (SOM); and (c) the the joint action of each of the above two methods with the so-called deflation method. More traditional methods such as Newton's method (and its variant with deflation) are also brought to bear. Our toy examples start with a naive one degree-of-freedom (dof) system to provide the lay of the land. Subsequently, we turn to a 2-dof system that is motivated by the reduction of an infinite-dimensional, phase field crystal (PFC) model of soft matter crystallisation. Once the landscape of the 2-dof system has been elucidated, we turn to the full PDE model and illustrate how the insights of the low-dimensional examples lead to novel solutions at the PDE level that are of relevance and interest to the full framework of soft matter crystallization.Comment: 17 pages, 16 figure

Epidemiology of Myocardial Infarction

Coronary heart disease (CHD) is the leading cause of morbidity and mortality throughout the world. The most common form of CHD is the myocardial infarction. It is responsible for over 15% of mortality each year, among the vast majority of people suffering from non-ST-segment elevation myocardial infarction (NSTEMI) than ST-segment elevation myocardial infarction (STEMI). The prevalence of myocardial infarction (MI) is higher in men in all age-specific groups than women. Although the incidence of MI is decreased in the industrialized nations partly because of improved health systems and implementation of effective public health strategies, nevertheless the rates are surging in the developing countries such as South Asia, parts of Latin America, and Eastern Europe. The modifiable risk factors represent over 90% of the risk for acute MI. The risk factors such as dyslipidemia, smoking, psychosocial stressors, diabetes mellitus, hypertension, obesity, alcohol consumption, physical inactivity, and a diet low in fruits and vegetables were strongly associated with acute MI

Bifurcation analysis of thermoacoustic instability in a horizontal Rijke tube

A bifurcation analysis of the dynamical behavior of a horizontal Rijke tube model is performed in this paper. The method of numerical continuation is used to obtain the bifurcation plots, including the amplitude of the unstable limit cycles. Bifurcation plots for the variation of nondimensional heater power, damping coefficient and the heater location are obtained for different values of time lag in the system. Subcritical bifurcation was observed for variation of parameters and regions of global stability, global instability and bistability are characterized. Linear and nonlinear stability boundaries are obtained for the simultaneous variation of two parameters of the system. The validity of the small time lag assumption in the calculation of linear stability boundary has been shown to fail at typical values of time lag of system. Accurate calculation of the linear stability boundary in systems with explicit time delay models, must therefore, not assume a small time lag assumption. Interesting dynamical behavior such as co-existing multiple attractors, quasiperiodic behavior and period doubling route to chaos have been observed in the analysis of the model. Comparison of the linear stability boundaries and bifurcation behavior from this reduced order model are shown to display trends similar to experimental data

Snaking without subcriticality: grain boundaries as non-topological defects

Non-topological defects such as grain boundaries abound in pattern forming systems, arising from local variations of pattern properties such as amplitude, wavelength, orientation, etc. We introduce the idea of treating such non-topological defects as spatially localised structures that are embedded in a background pattern, instead of treating them in an amplitude-phase decomposition. Using the two-dimensional quadratic-cubic Swift--Hohenberg equation as an example we obtain fully nonlinear equilibria that contain grain boundaries which are closed curves containing multiple penta-hepta defects separating regions of hexagons with different orientations. These states arise from local orientation mismatch between two stable hexagon patterns, one of which forms the localised grain and the other its background, and do not require a subcritical bifurcation connecting them. Multiple robust isolas that span a wide range of parameters are obtained even in the absence of a unique Maxwell point, underlining the importance of retaining pinning when analysing patterns with defects, an effect omitted from the amplitude-phase description.Comment: 16 pages, 12 figures and 2 movies in mp4 forma

Three-dimensional icosahedral phase field quasicrystal

We investigate the formation and stability of icosahedral quasicrytalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state. We demonstrate that traits that promote the formation of two-dimensional quasicrystals are extant in three dimensions, and highlight the characteristics required for 3D soft matter quasicrystal formation

Structural crossover in a model fluid exhibiting two length scales: repercussions for quasicrystal formation

We investigate the liquid state structure of the two-dimensional (2D) model introduced by Barkan et al. [Phys. Rev. Lett. 113, 098304 (2014)], which exhibits quasicrystalline and other unusual solid phases, focussing on the radial distribution function $g(r)$ and its asymptotic decay $r\to\infty$. For this particular model system, we find that as the density is increased there is a structural crossover from damped oscillatory asymptotic decay with one wavelength to damped oscillatory asymptotic decay with another distinct wavelength. The ratio of these wavelengths is $\approx1.932$. Following the locus in the phase diagram of this structural crossover leads directly to the region where quasicrystals are found. We argue that identifying and following such a crossover line in the phase diagram towards higher densities where the solid phase(s) occur is a good strategy for finding quasicrystals in a wide variety of systems. We also show how the pole analysis of the asymptotic decay of equilibrium fluid correlations is intimately connected with the non-equilibrium growth or decay of small amplitude density fluctuations in a bulk fluid

Spatiotemporal chaos and quasipatterns in coupled reaction–diffusion systems

In coupled reaction–diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex steady patterns and time-varying states including spatiotemporal chaos. The interactions can take the form of two short waves with different orientations interacting with one long wave, or vice verse. We investigate the role of such three-wave interactions in a coupled Brusselator system. As well as finding simple steady patterns when the waves reinforce each other, we can also find spatially complex but steady patterns, including quasipatterns. When the waves compete with each other, time varying states such as spatiotemporal chaos are also possible. The signs of the quadratic coefficients in three-wave interaction equations distinguish between these two cases. By manipulating parameters of the chemical model, the formation of these various states can be encouraged, as we confirm through extensive numerical simulation. Our arguments allow us to predict when spatiotemporal chaos might be found: standard nonlinear methods fail in this case. The arguments are quite general and apply to a wide class of pattern-forming systems, including the Faraday wave experiment

COMPARATIVE EVALUATION OF ORAL MICROBIOTA OF CHILDREN WITH AND WITHOUT EARLY CHILDHOOD CARIES BORN TO CARIES FREE MOTHERS

Objectives: To compare the level of mutans streptococci in children with and without Early childhood caries (ECC) born to caries free mothers.Methods: Twenty children aged between 3 and 6 years were selected depending on their caries experience, and the mother should be caries free inboth the groups. The children were divided into two groups. Group I had an active carious lesion and Group II were caries free. Saliva samples werecollected from the child and the mother in a sterile tube and bacterial culture was carried out to estimate the colony count.Results: There was a highly significant difference in the colony forming unit (CFU) between the 2 groups, indicating higher CFU in children with ECC.Conclusions: Even though there are higher chances of vertical transmission of MS from mother to their child, this study provides a new view thatmother alone is not a potential factor for mutans streptococci transmission to their child.Keywords: Mutans streptocci, Early childhood caries, Colony forming unit

PMSG Based Stand Alone Wind Power System with Sensorless MPPT

ABSTRACT: In this paper, analyzing the operation of a Permanent Magnet Synchronous Generator (PMSG) based stand alone wind power system with Sensorless Maximum Power Point Tracking (MPPT) and a system for storing energy during wind speed and load variations. In standalone system, power, balance and power quality require the energy storage system. In conventional systems, MPPT depends on wind turbine parameters such as wind speed measurement and turbine generator speed. The proposed wind turbine and energy storage system supplies and delivers the power absorbed by the connected loads. Thus the resulting system has low cost and higher reliability. In order to obtain the maximum power point tracking, the duty cycle of DC-DC boost converter switch controlled by the measurement of DC current and DC voltage. Initially, the complete representation of entire system consists of PMSG, the boost converter and the storage system is achieved. Simulation results investigate the good performance of the proposed approach with the help of MATLAB/SIMULINK