A Novel True Random Number Generator in Near Field Communication as Memristive Wireless Power Transmission

The security of powering systems has been a major problem over the last decade, leading to an increased interest in wireless power and data transfer. In this research paper, a new inductive Wireless Power Transfer (WPT) circuit topology has been used. In traditional WPT circuits, the inverters are used to produce an oscillation for the transmitter coils. The classic WPT system includes intrinsic energy dissipation sources due to the use of switches, necessitating the need of an extra control circuit to ensure proper switching time. Furthermore, they have limited data encryption capabilities. As a result, an unique WPT system based on memristors has been developed, eliminating the need for switches. Furthermore, because this novel topology communicates a synchronised chaotic behaviour, it becomes highly beneficial. This circuit may be used in Near Field Communication (NFC), where chaotic true random numbers (TRNG) can be generated to increase security. The results of simulations indicate the functioning of the Memristor-based WPT (M-WPT) and its ability to generate random numbers. We experimentally proved the chaotic behaviour of the circuit and statistically demonstrated the development of the TRNG, using an Arduino board and the Chua circuit to build the M-WPT circuit.

Chaos in small microbial communities

Predictability is a fundamental requirement in biological engineering. As we move to building coordinated multicellular systems, the potential for such systems to display chaotic behaviour becomes a concern. Therefore understanding which systems show chaos is an important design consideration. We developed a methodology to explore the potential for chaotic dynamics in small microbial communities governed by resource competition, intercellular communication and competitive bacteriocin interactions. We show that we can expect to find chaotic states in relatively small synthetic microbial systems, understand the governing dynamics and provide insights into how to control such systems. This work is the first to query the existence of chaotic behaviour in synthetic microbial communities and has important ramifications for the fields of biotechnology, bioprocessing and synthetic biology.

Weak integrability breaking and level spacing distribution

Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics {which marks the onset of quantum chaotic behaviour, is markedly different for weak vs. strong breaking of integrability. In particular}, for the gapless case we find that the crossover coupling as a function of the volume LL scales with a 1/L^{2}1/L2 law for weak breaking as opposed to the 1/L^{3}1/L3 law previously found for the strong case.

Eastern and North Eastern sub-divisions of India : An analysis of trend and chaotic behaviour of rainfall in different seasons

The aim of the study is to understand trend or non-linearity along with a chaotic behaviour, if any, of Eastern and North Eastern sub-divisional rainfall, namely Orissa, Gangetic West Bengal, Sub Himalayan West Bengal, Assam and Meghalaya and also Nagaland, Manipur, Mizoram and Tripura based on rainfall data of 143 years (1871-2013). The analysis is performed for examining behaviour of rainfall in each of the seasons, namely, Pre monsoon, South West monsoon, North East monsoon and also Annual rainfall extracted from the monthly data. For that purpose, a trend analysis with Hurst Exponent and non-linearity analysis with Lyapunov Exponent are employed. The analysis revealed that rainfall of Orissa is persistent for all the seasons whilst the rainfall is persistent in Gangetic West Bengal in Pre monsoon and North East monsoon and Assam and Meghalaya along with Nagaland, Manipur, Mizoram and Tripura exhibit persistent behaviour in South West Monsoon and annually. Sub Himalayan West Bengal exhibit persistence in annual rainfall only. Chaotic tendency in low magnitude is located in many cases whilst non-chaotic situation has occurred when the persistence is found, mainly in pre-monsoon season. Moreover, the analysis of Hurst and Lyapunov Exponent revealed to identify two groups of sub-divisions with exactly similar region of every respect. Those two groups contain (i) sub-divisions Orissa and Assam and Meghalaya and also (ii) sub-divisions Sub Himalayan West Bengal and Nagaland, Mizoram, Manipur and Tripura although those are at distances of hundreds of kilometers away. The behaviour of those subdivisions in a group has similar behaviour in all respects.

Chaotic correlation functions with complex fermions

We study correlation functions in the complex fermion SYK model. We focus, specifically, on the h=2 mode which explicitly breaks conformal invariance and exhibits the chaotic behaviour. We numerically explore a fermion six-point OTOC, with two and three real-time folds, respectively. While our approach is expected to yield an early-time chaotic growth, we nevertheless observe a near-maximal value. Following the program of Gross-Rosenhaus, we estimate the triple short time limit of the six point function. Unlike the conformal modes with high values of h, the h=2 mode has contact interaction dominating over the planar in the large q limit.

Light rings of five-dimensional geometries

We study massless geodesics near the photon-spheres of a large family of solutions of Einstein-Maxwell theory in five dimensions, including BHs, naked singularities and smooth horizon-less JMaRT geometries obtained as six-dimensional uplifts of the five-dimensional solution. We find that a light ring of unstable photon orbits surrounding the mass center is always present, independently of the existence of a horizon or singularity. We compute the Lyapunov exponent, characterizing the chaotic behaviour of geodesics near the ‘photon-sphere’ and the time decay of ring-down modes dominating the response of the geometry to perturbations at late times. We show that, for geometries free of naked singularities, the Lyapunov exponent is always bounded by its value for a Schwarzschild BH of the same mass.