Active fluids at circular boundaries: Swim pressure and anomalous droplet ripening

We investigate the swim pressure exerted by non-chiral and chiral active particles on convex or concave circular boundaries. Active particles are modeled as non-interacting and non-aligning self-propelled Brownian particles. The convex and concave circular boundaries are used as models representing a fixed inclusion immersed in an active bath and a cavity (or container) enclosing the active particles, respectively. We first present a detailed analysis of the role of convex versus concave boundary curvature and of the chirality of active particles on their spatial distribution, chirality-induced currents, and the swim pressure they exert on the bounding surfaces. The results will then be used to predict the mechanical equilibria of suspended fluid enclosures (generically referred to as 'droplets') in a bulk with active particles being present either inside the bulk fluid or within the suspended droplets. We show that, while droplets containing active particles and suspended in a normal bulk behave in accordance with standard capillary paradigms, those containing a normal fluid exhibit anomalous behaviors when suspended in an active bulk. In the latter case, the excess swim pressure results in non-monotonic dependence of the inside droplet pressure on the droplet radius. As a result, we find a regime of anomalous capillarity for a single droplet, where the inside droplet pressure increases upon increasing the droplet size. In the case of two interconnected droplets, we show that mechanical equilibrium can occur also when they have different sizes. We further identify a regime of anomalous ripening, where two unequal-sized droplets can reach a final state of equal sizes upon interconnection, in stark contrast with the standard Ostwald ripening phenomenon, implying shrinkage of the smaller droplet in favor of the larger one.Comment: 15 pages, 7 figure

How visas shape and make visible the geopolitical architecture of the planet

The aim of the present study is to provide a picture for geopolitical globalization: the role of all world countries together with their contribution towards globalization is highlighted. In the context of the present study, every country owes its efficiency and therefore its contribution towards structuring the world by the position it holds in a complex global network. The location in which a country is positioned on the network is shown to provide a measure of its "contribution" and "importance". As a matter of fact, the visa status conditions between countries reflect their contribution towards geopolitical globalization. Based on the visa status of all countries, community detection reveals the existence of 4+1 main communities. The community constituted by the developed countries has the highest clustering coefficient equal to 0.9. In contrast, the community constituted by the old eastern European blocks, the middle eastern countries, and the old Soviet Union has the lowest clustering coefficient approximately equal to 0.65. PR China is the exceptional case. Thus, the picture of the globe issued in this study contributes towards understanding "how the world works"

Surface coupling effects on the capacitance of thin insulating films

A general form for the surface roughness effects on the capacitance of a capacitor is proposed. We state that a capacitor with two uncoupled rough surfaces could be treated as two capacitors in series which have been divided from the mother capacitor by a slit. This is in contrast to the case where the two rough surfaces are coupled. When the rough surfaces are coupled, the type of coupling decides the modification of the capacitance in comparison to the uncoupled case. It is shown that if the coupling between the two surfaces of the capacitor is positive (negative), the capacitance is less (higher) than the case of two uncoupled rough plates. Also, we state that when the correlation length and the roughness exponent are small, the coupling effect is not negligible

Chapman-Kolmogorov test for estimating memory length of two coupled process

Real-world processes often display a prolonged memory, which extends beyond the single-step dependency characteristic of Markov processes. In addition, the current state of an empirical process is often not only influenced by its own past but also by the past states of other dependent processes. This study introduces the generalized version of the Chapman-Kolmogorov equation (CKE) to estimate the memory size in such scenarios. To assess the applicability of our approach, we generate coupled time series with predetermined memory lengths using the autoregressive model. The results show a high degree of accuracy in measuring memory lengths. Subsequently, we employ the generalized CKE to analyze cryptocurrency data as a real-world case study. Our results indicate that the past dynamics of cryptocurrencies significantly impact their current states, thereby highlighting interdependencies among them. The method proposed in this study can be also utilized in forecasting coupled time series

Quantum Bohmian-inspired potential to model non–Gaussian time series and Its application in financial markets

We have implemented quantum modeling mainly based on Bohmian mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study was to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ, which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying the quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case

Spectra of empirical autocorrelation matrices: A random-matrix-theory–inspired perspective

We construct an autocorrelation matrix of a time series and analyze it based on the random-matrix theory (RMT) approach. The autocorrelation matrix is capable of extracting information which is not easily accessible by the direct analysis of the autocorrelation function. In order to provide a precise conclusion based on the information extracted from the autocorrelation matrix, the results must be first evaluated. In other words they need to be compared with some sort of criterion to provide a basis for the most suitable and applicable conclusions. In the context of the present study, the criterion is selected to be the well-known fractional Gaussian noise (fGn). We illustrate the applicability of our method in the context of stock markets. For the former, despite the non-Gaussianity in returns of the stock markets, a remarkable agreement with the fGn is achieved