Min-protein oscillations in Escherichia coli with spontaneous formation of two-stranded filaments in a three-dimensional stochastic reaction-diffusion model

We introduce a three-dimensional stochastic reaction-diffusion model to describe MinD/MinE dynamical structures in Escherichia coli. This model spontaneously generates pole-to-pole oscillations of the membrane-associated MinD proteins, MinE ring, as well as filaments of the membrane-associated MinD proteins. Experimental data suggest MinD filaments are two-stranded. In order to model them we assume that each membrane-associated MinD protein can form up to three bonds with adjacent membrane associated MinD molecules and that MinE induced hydrolysis strongly depends on the number of bonds MinD has established.Comment: Corrected typos, changed conten

Design and Analysis of a Discrete, PCB-Level Low-Power, Microwave Cross-Coupled Differential LC Voltage-Controlled Oscillator

Radio Frequency (RF) and Microwave devices are typically implemented in Integrated Circuit (IC) form to minimize parasitics, increase precision and tolerances, and minimize size. Although IC fabrication for students and independent engineers is cost-prohibitive, an abundance of low-cost, easily accessible printed circuit board (PCB) and electronic component manufacturers allows affordable PCB fabrication. While nearly all microwave voltage-controlled oscillator (VCO) designs are IC-based, this study presents a discrete PCB-level cross-coupled, differential LC VCO to demonstrate this more affordable and accessible approach. This thesis presents a 65 mW, discrete component VCO PCB with industry-comparable RF performance. A phase noise of -103.7 dBc/Hz is simulated at a 100 kHz offset from a 4.05 GHz carrier. This VCO achieves a 532 MHz (13.25%) tuning bandwidth. A figure of merit, FOMP, [1] value of -177.7 dB (includes phase noise and power consumption) is calculated at 4.05 GHz. This surpasses the performance of an industry standard VCO (HMC430LPx, Analog Devices), -176.5 dB, and four other commercially available VCOs. Furthermore, this study presents novel discrete design implementations to minimize both power consumption and capacitive loading effects, while optimizing phase noise. Finally, this project serves as a reference for analyzing and implementing low-level, complex RF and Microwave circuits on a PCB accessible to all students and independent engineers

Overlapped KAM patterns for linearly coupled asymmetric oscillators

The pattern of energy dependence for the onset of chaos is investigated for conservative system of two linearly coupled asymmetric oscillators, harmonic oscillator and a two-well nonlinear oscillator. With increase of energy, the amount of chaoticity first grows up to a certain critical energy, according to the KAM scenario, and above this point, with a further increase of energy, the amount of chaoticity decreases according to the inverse KAM scenario. At the point of transition, there is an overlap of the two scenarios. The position of the critical energy increases with increasing value of the coupling strength between oscillators

Overlapping of two truncated crisis scenarios: Generator of peaks in mean lifetimes of chaotic transients

Maxima of mean transient time versus driving amplitude were found for weakly dissipated Duffing oscillator. In the neighborhood of peak of mean transient time an approximate power-law dependence was found. This behavior was compared with scaling in the vicinity of crisis point and interpreted as crossing of two neighboring crisis points which appears with decrease of driving amplitude. At this point chaotic attractor was destroyed and chaotic transient, exhibiting a maximum in the lifetime was borned. It was shown that the peak of mean lifetime has a regular behavior described by quadratic function

Missing preimages for chaotic logistic map with a hole

Chaotic transients and preimages are investigated for a new map proposed recently, having a hole in the unit interval of the r = 4 logistic map. This map is characterized by deviations from Frobenius-Perron equation for average lifetimes in dependence on hole position in the form of bursts of average lifetime. We present classification of these bursts on the basis of average lifetimes. Using time maps it is investigated how these bursts are caused by missing preimages of the hole interval I ^( 0 ). We derive approximate expression for the ratio of lifetimes deduced from Frobenius-Perron and from Kantz-Grassberger equations

conservative systems, linearly coupled harmonic and nonlinear oscillators, KAM scenario, inverse KAM scenario Preklapajući KAM-scenariji za linearno vezane asimetrične oscilatore

The pattern of energy dependence for the onset of chaos is investigated for conservative system of two linearly coupled asymmetric oscillators, harmonic oscillator and a two-well nonlinear oscillator. With increase of energy, the amount of chaoticity first grows up to a certain critical energy, according to the KAM scenario, and above this point, with a further increase of energy, the amount of chaoticity decreases according to the inverse KAM scenario. At the point of transition, there is an overlap of the two scenarios. The position of the critical energy increases with increasing value of the coupling strength between oscillators.Struktura energijske ovisnosti evolucije kaosa istražuje se za konzervativni sustav dvaju linearno vezanih asimetričnih oscilatora, harmonijskog oscilatora i nelinearnog oscilatora s dvije jame. S porastom energije stupanj kaotičnosti najprije raste do određene kritične vrijednosti energije, sukladno KAM scenariju, a iznad te energije, s daljnjim porastom energije, udio kaotičnosti pada sukladno inverznom KAM scenariju. Pri prijelazu iz jednog scenarija u drugi dolazi do njihovog preklopa. Vrijednost kritične energije raste s porastom jakosti vezanja među oscilatorima

conservative systems, linearly coupled harmonic and nonlinear oscillators, KAM scenario, inverse KAM scenario Preklapajući KAM-scenariji za linearno vezane asimetrične oscilatore

The pattern of energy dependence for the onset of chaos is investigated for conservative system of two linearly coupled asymmetric oscillators, harmonic oscillator and a two-well nonlinear oscillator. With increase of energy, the amount of chaoticity first grows up to a certain critical energy, according to the KAM scenario, and above this point, with a further increase of energy, the amount of chaoticity decreases according to the inverse KAM scenario. At the point of transition, there is an overlap of the two scenarios. The position of the critical energy increases with increasing value of the coupling strength between oscillators.Struktura energijske ovisnosti evolucije kaosa istražuje se za konzervativni sustav dvaju linearno vezanih asimetričnih oscilatora, harmonijskog oscilatora i nelinearnog oscilatora s dvije jame. S porastom energije stupanj kaotičnosti najprije raste do određene kritične vrijednosti energije, sukladno KAM scenariju, a iznad te energije, s daljnjim porastom energije, udio kaotičnosti pada sukladno inverznom KAM scenariju. Pri prijelazu iz jednog scenarija u drugi dolazi do njihovog preklopa. Vrijednost kritične energije raste s porastom jakosti vezanja među oscilatorima

Nedostajuće predslike za kaotičnu logističku mapu s rupom

Chaotic transients and preimages are investigated for a new map proposed recently, having a hole in the unitinterval of the r 4 logistic map. This map is characterized by deviations from Frobenius-Perron equation for average lifetimes in dependence on hole position in the form of bursts of average lifetime. We present classification of these bursts on the basis of average lifetimes. Using time maps it is investigated how these bursts are caused by missing preimages of the hole interval I 0 . We derive approximate expression for the ratio of lifetimes deduced from Frobenius-Perron and from Kantz-Grassberger equationsKaotični tranzijenti i predslike istražuju se za novu mapu koja ima rupu unutar jediničnog intervala logističke mape za r 4. Ovu mapu karakteriziraju odstupanja od Frobenius-Perronove jednadžbe za vrijeme poluraspada u ovisnosti o položaju rupe, u obliku skokova u vremenu poluraspada. Primjenom vremenske mape istražuje se kako ti skokovi nastaju kao posljedica nedostajućih predslika rupnog intervala. Izvodi se približan izraz za omjer vremena poluraspada dobivenog pomoću Frobenius-Perronove i Kantz-Grassbergerove jednadžbe

Nedostajuće predslike za kaotičnu logističku mapu s rupom

Chaotic transients and preimages are investigated for a new map proposed recently, having a hole in the unitinterval of the r 4 logistic map. This map is characterized by deviations from Frobenius-Perron equation for average lifetimes in dependence on hole position in the form of bursts of average lifetime. We present classification of these bursts on the basis of average lifetimes. Using time maps it is investigated how these bursts are caused by missing preimages of the hole interval I 0 . We derive approximate expression for the ratio of lifetimes deduced from Frobenius-Perron and from Kantz-Grassberger equationsKaotični tranzijenti i predslike istražuju se za novu mapu koja ima rupu unutar jediničnog intervala logističke mape za r 4. Ovu mapu karakteriziraju odstupanja od Frobenius-Perronove jednadžbe za vrijeme poluraspada u ovisnosti o položaju rupe, u obliku skokova u vremenu poluraspada. Primjenom vremenske mape istražuje se kako ti skokovi nastaju kao posljedica nedostajućih predslika rupnog intervala. Izvodi se približan izraz za omjer vremena poluraspada dobivenog pomoću Frobenius-Perronove i Kantz-Grassbergerove jednadžbe