Tracking the time evolution of soft matter systems via topological structural heterogeneity

Persistent homology is an effective topological data analysis tool to quantify the structural and morphological features of soft materials, but so far it has not been used to characterise the dynamical behaviour of complex soft matter systems. Here, we introduce structural heterogeneity, a topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder transition at the microscopic scale. We show that structural heterogeneity tracks structural changes in a liquid crystal nanocomposite, reveals the effect of confined geometry on the nematic-isotropic and isotropic-nematic phase transitions, and uncovers physical differences between these two processes. The system used in this work is representative of a class of composite nanomaterials, partially ordered and with complex structural and physical behaviour, where their precise characterisation poses significant challenges. Our developed analytic framework can provide both a qualitative and quantitative characterisation of the dynamical behaviour of a wide range of semi-ordered soft matter systems.

Time Evolution of Market Efficiency and Multifractality of the Japanese Stock Market

This study investigates the time evolution of market efficiency in the Japanese stock markets, considering three indices: Tokyo Stock Price Index (TOPIX), Tokyo Stock Exchange Second Section Index, and TOPIX-Small. The Hurst exponent reveals that the Japanese markets are inefficient in their early stages and improve gradually. TOPIX and TOPIX-Small showed an anti-persistence around the year 2000, which still persists. The degree of multifractality varies over time and does not show that the Japanese markets are permanently efficient. The multifractal properties of the Japanese markets changed considerably around the year 2000; this may have been caused by the complete migration from the stock trading floor to the Tokyo Stock Exchange’s computer trading system and the financial system reform, also known as the “Japanese Big Bang”.

Stress Accumulation and Earthquake Activity on the Great Sumatran Fault, Indonesia

The seismically active Sumatra subduction zone has generated some of the largest earthquakes in the instrumental record, and both historical accounts and paleogeodetic coral studies indicate such activity has historical recorded megathrust earthquakes and transferred stress to the surrounding, including the Great Sumatran Fault (GSF). Therefore, evaluating the stress transfer from these large subduction earthquakes could delineate the highly stressed area as potential-earthquake region along the GSF. In this study, we investigated eight megathrust earthquakes from 1797 to 2010 and resolved the accumulated Coulomb stress changes onto the 18 segments along the GSF. Additionally, we also estimated the rate of tectonic stress on the GSF segments which experienced large earthquake using the case of: (1) no sliver movement and (2) with sliver movement. Based on the historical stress changes of large earthquakes and the increase in tectonic stress rate, we analysed the historical stress changes time evolution on the GSF. The Coulomb stress accumulation of megathrust earthquakes between 1797-1907 increase the stress changes mainly on the southern part of GSF which followed by four major events between 1890-1943. The estimation of tectonic stress rates using case (1) produces low rate and long recurrence intervals which implies that the megathrust earthquakes plays an important role in allowing the GSF earthquake to occur. When implementing the arc-parallel sliver movement of case (2) to the calculation, the tectonic stress rates is 9 to 58 times higher than case (1) of no sliver movement. The observed slip rate of 15-16 mm/yr at the GSF is consistent with the recurrence interval for full-segment rupture of 100-200 years obtained from case (2). This suggests that the GSF earthquake is more controlled by the rapid arc-parallel forearc sliver motion. Furthermore, the analysis of stress changes time evolution model shows that some segments such as Tripa (North and South), Angkola, Musi and Manna appear to be brought back in their seismic cycles since these segments have experienced full-segment rupture and likely locked, increasing their earthquake hazard potentials.

Late time transition of Universe and the hybrid scale factor

In this study, we propose an interacting model to explain the physical mechanism of the late time transition from matter-dominated era to the dark energy-dominated era of the Universe evolution and to obtain a scale factor a(t) representing two eras together. In the present model, we consider a minimal coupling of two scalar fields which correspond to the dark matter and dark energy interacting through a potential based on the FLRW framework. Analytical solution of this model leads to a new scale factor a(t) in the hybrid form $$a(t)=a_{0} (t/t_{0})^{\alpha } e^{ht/t_{0}}$$ a ( t ) = a 0 ( t / t 0 ) α e h t / t 0 . This peculiar result reveals that the scale factor behaving as $$a (t) \propto (t/t_{0})^{\alpha }$$ a ( t ) ∝ ( t / t 0 ) α in the range $$t/t_{0}\le t_{c}$$ t / t 0 ≤ t c corresponds to the matter-dominated era while $$a(t) \propto \exp (ht/t_{0})$$ a ( t ) ∝ exp ( h t / t 0 ) in the range $$t/t_{0}>t_{c}$$ t / t 0 > t c accounts for the dark energy-dominated era, respectively. Surprisingly, we explore that the transition from the power-law to the exponential expansion appears at the crossover time $$t_{0} \approx 9.8$$ t 0 ≈ 9.8 Gyear. We attain that the presented model leads to precisely correct results so that the crossover time $$t_{0}$$ t 0 and $$\alpha $$ α are completely consistent with the exact solution of the FLRW and re-scaled Hubble parameter $$H_{0}$$ H 0 lies within the observed limits given by Planck, CMB and SNIa data (or other combinations), which lead to consistent cosmological quantities such as the dimensionless Hubble parameter h, deceleration parameter q, jerk parameter j and EoS parameter w. We also discuss time dependent behavior of the dark energy and dark matter to show their roles on the time evolution of the universe. Additionally, we observe that all main results completely depend on the structure of the interaction potential when the parameter values are tuned to satisfy the zero energy condition. Finally, we conclude that interactions in the dark sector may play an important role on the time evolution and provides a mechanism to explain the late time transition of the Universe.

A Modified SIR Model for the COVID-19 Epidemic in China

The analysis of the coronavirus disease 2019 (COVID-19) is of great importance to deeply understand the dynamics of this coronavirus spread. Based on the complexity of it, a modified susceptible-infected-removed (SIR) model is applied to analyse the time dependence of active and hospitalized cases in China. The time evolution of the virus spread in different provinces was adequately modelled. Changeable parameters among them have been obtained and turned to be not naively independent with each other. The non-extensive parameter was found to be strongly connected with the freedom of systems. Taken into the prevention and treatment of disease, more measures by the government lead to higher values of it.