Fractional uncertain differential equations with general memory effects: Existences and alpha-path solutions

General fractional calculus is popular recently. Fractional uncertain differential equations (FUDEs) with general memory effects are proposed in this paper. Firstly, existence and uniqueness theorems of solution for general fractional uncertain differential equations (GFUDEs) is presented, and the analytic solution of a linear one is given. Then the concept of α-path is introduced, and relationship between solution of GFUDE and corresponding α-path is also discussed. In addition, a theorem is proved to obtain the expected value of a monotonic function related to solutions of GFUDEs. Finally, a numerical example is given to better understand the significance of general memory effects. This paper provides more types of FUDEs to better describe some phenomena in uncertain environments

High-resolution simulations of fluid flow in active hydrothermal systems : applications to the Tjornes Fracture Zone and Askja Volcanic complex in Iceland

This study provides new insights into the transient uid ow dynamics that characterise high temperature hydrothermal systems. So far, these kind of studies have used process models that tend to over-simplify the geology and focus instead on the physical processes, hence not revealing the hidden behaviour that depends on the complex geological structures often encountered in hydrothermal systems. This study is one of the rst examples where high resolution numerical simulations in two and three dimensions have been applied to hydrothermal systems in order to preserve geological detail in the models explicitly. Two prime examples in Iceland for seismicity-induced uid ow and groundwater ow during volcanic eruptions, respectively, have been selected for this purpose. The rst example is the Tjörnes Fracture Zone, a heavily faulted transform zone o shore in North Iceland where most of the Icelandic earthquakes occur. The work demonstrated that a moderate permeability contrast between the shallow sedimentary basins and deep crustal basement causes two distinct uid ow regimes which are only connected during a seismic event. When such an event occurs, faults in the Tjörnes Fracture Zone in ate and connect the two uid ow systems, causing hot uids migrating from the basement into the basins at extreme ow rates. This explains key geochemical observations made in the Tjörnes Fracture Zone before and after a seismic event. The second study investigated the 1874 to 1875 volcano-tectonic episode at the Askja volcano, which is the third largest silicic eruption since settlement in Iceland. Here it was demonstrated how syn-eruptive groundwater ow inside the Askja caldera changed the eruptive style of the March 1875 eruption, causing a well-documented change from a wet to dry eruptive style. The results of this work provide some fundamental new insights into the transient dynamics of uid ow in active high temperature hydrothermal systems and suggest that these kind of simulations may be used to complement studies assessing the risk and hazard of future volcanic eruptions and seismic events

Impact of the crises on the efficiency of the financial market: evidence from the SDM

A thesis submitted to the University of Bedfordshire in partial fulfilment of the requirements for the degree of Doctor of PhilosophyThe efficient market hypothesis has been around since 1962, the theory based on a simple rule that states the price of any asset must fully reflect all available information. Yet there is empirical evidence suggesting that markets are too volatile to be efficient. In essence, this evidence seems to suggest that the reaction of the market participants to the information or events that is the crucial factor, rather than the actual information. This highlights the need to include the behavioural finance theory in the pricing of assets. Essentially, the research aims to analyse the efficiency of six key sovereign debt markets during a period of changing volatility including the recent global financial and sovereign debt crises. We analyse the markets in the pre-crisis period and during the financial and sovereign debt crises to determine the impact of the crises on the efficiency of these financial markets. We use two GARCH-based variance bound tests to test the null hypothesis of the market being too volatile to be efficient. Proposing a GJR-GARCH variant of the variance bound test to account for variation in the asymmetrical effect. This leads to an analysis of the changing behaviour of price volatility to identify what makes the market efficient or inefficient. In general, our EMH tests resulted in mixed results, hinting at the acceptance of the null hypothesis of the market being too volatile to be efficient. However, interestingly a number of 2017 observations under both models seem to be hinting at the rejection of the null hypothesis. Furthermore, our proposed GJR-GARCH variant of the variance bound test seems to be more likely to accept the EMH than the GARCH variant of the test. Key words: Efficient Market Hypothesis, Behavioural Finance Theory, Volatility Tests, GJR, GARCH, EGARCH-M, SWARCH, Sovereign Debt Market, Cris

Three Risky Decades: A Time for Econophysics?

Our Special Issue we publish at a turning point, which we have not dealt with since World War II. The interconnected long-term global shocks such as the coronavirus pandemic, the war in Ukraine, and catastrophic climate change have imposed significant humanitary, socio-economic, political, and environmental restrictions on the globalization process and all aspects of economic and social life including the existence of individual people. The planet is trapped—the current situation seems to be the prelude to an apocalypse whose long-term effects we will have for decades. Therefore, it urgently requires a concept of the planet's survival to be built—only on this basis can the conditions for its development be created. The Special Issue gives evidence of the state of econophysics before the current situation. Therefore, it can provide excellent econophysics or an inter-and cross-disciplinary starting point of a rational approach to a new era

Rate And State Friction Laws For Interfacial Chemical Bond-Induced Friction At The Nanoscale

Rate and state friction (RSF) laws are widely-used empirical relationships that describe macroscale frictional behavior of a broad range of materials, including rocks. Conventional RSF laws entail a linear combination of the direct effect (friction increasing with sliding velocity) and evolution effect (evolution of the state of the contact). One manifestation of evolution effect is ageing , where static friction increases logarithmically with contact time. In order to understand the physical origins of RSF laws, we use atomic force microscope (AFM) to study nanoscale friction of silica, which is one important component of rocks. Overall, we observe RSF behavior, due to interfacial chemical bond-induced (ICBI) friction, which is manifested in several ways. The first aspect is the load and time dependence of ageing, whereby ageing magnitude increases approximately linearly with the product of the normal load and the log of the hold time. The second aspect is a physically-based RSF law we establish for single asperity contact, which we call the Prandtl-Tomlinson with temperature and evolution effect (PTTE) model. In PTTE model, the velocity for the direct effect is loading point velocity rather than tip velocity. Also, the combination of direct effect and evolution effect is nonlinear. The third aspect is the velocity dependence of kinetic friction, which reflects the competition of direct effect and evolution effect. Kinetic friction first decreases and then increases logarithmically with sliding velocity (the increase corroborates PTTE model). We explain the logarithmic decreasing by assuming that during low-velocity sliding, after an interfacial bond breaks, the resulting dangling bond can easily bond with other dangling bonds on the opposing surface. The fourth aspect is stick-slip, which could be better understood with PTTE model. We observe quasi-periodic stick-slip at lower velocities and uncover the velocity dependence of stick-slip. We also observe partial dropping of lateral force in some slip events in the transition regime between quasi-periodic stick-slip and smooth sliding, which corroborates the physical picture of dangling bonds forming interfacial bonds. In conclusion, these four aspects together demonstrate the nature of RSF behavior for nanoscale single-asperity contacts, and establish new, physically-based frictional laws for nanoscale contacts

Acoustic and Elastic Waves: Recent Trends in Science and Engineering

The present Special Issue intends to explore new directions in the field of acoustics and ultrasonics. The interest includes, but is not limited to, the use of acoustic technology for condition monitoring of materials and structures. Topics of interest (among others): • Acoustic emission in materials and structures (without material limitation) • Innovative cases of ultrasonic inspection • Wave dispersion and waveguides • Monitoring of innovative materials • Seismic waves • Vibrations, damping and noise control • Combination of mechanical wave techniques with other types for structural health monitoring purposes. Experimental and numerical studies are welcome