Characterizing groundwater heat-transport in a complex lowland aquifer using paleo-temperature reconstruction, satellite data, temperature-depth profiles, and numerical models

Heat is a naturally occurring widespread groundwater tracer that can be used to identify flow patterns in groundwater systems. Temperature measurements, being relatively inexpensive and effortless to gather, represent a valuable source of information which can be exploited to reduce uncertainties on groundwater flow, and e.g. support performance assessment studies on waste disposal sites. In a lowland setting, however, hydraulic gradients are typically small, and whether temperature measurements can be used to inform us about catchment-scale groundwater flow remains an open question. For the Neogene aquifer in Flanders, groundwater flow and solute transport models have been developed in the framework of safety and feasibility studies for the underlying Boom Clay Formation as potential host rock for geological disposal of radioactive waste. However, the simulated fluxes by these models are still subject to large uncertainties, as they are typically constrained by hydraulic heads only. In the current study we use a state-of-the-art 3D steady-state groundwater flow model, calibrated against hydraulic head measurements, to build a 3D transient heat-transport model, for assessing the use of heat as an additional state variable, in a lowland setting, at the catchment scale. We therefore use temperature-depth (TD) profiles as additional state variable observations for inverse conditioning. Furthermore, a Holocene paleo-temperature time curve was constructed based on paleo-temperature reconstructions in Europe from several sources in combination with land-surface temperature (LST) imagery remote sensing monthly data from 2001 to 2019 (retrieved from NASA’s MODIS). The aim of the research is to understand the mechanisms of heat transport and to characterize the temperature distribution and dynamics in the Neogene aquifer. The simulation results clearly underline advection/convection and conduction as the major heat transport mechanisms, with a reduced role of advection/convection in zones where flux magnitudes are low, which suggests temperature is a useful indicator also in a lowland setting. Furthermore, performed scenarios highlight the important roles of i) surface hydrological features and withdrawals driving local groundwater flow systems, and ii) the inclusion of subsurface features like faults in the conceptualization and development of hydrogeological investigations. These findings serve as a proxy of the influence of advective transport and barrier/conduit role of faults, particularly the Rauw Fault in this case, and suggest that solutes released from the Boom Clay might be affected in similar ways.

Modeling student engagement using optimal control theory

<p style='text-indent:20px;'>Student engagement in learning a prescribed body of knowledge can be modeled using optimal control theory, with a scalar state variable representing mastery, or self-perceived mastery, of the material and control representing the instantaneous cognitive effort devoted to the learning task. The relevant costs include emotional and external penalties for incomplete mastery, reduced availability of cognitive resources for other activities, and psychological stresses related to engagement with the learning task. Application of Pontryagin's maximum principle to some simple models of engagement yields solutions of the synthesis problem mimicking familiar behaviors including avoidance, procrastination, and increasing commitment in response to increasing mastery.</p>

Solvability of Some Nonlocal Fractional Boundary Value Problems at Resonance in Rn

In this paper, the solvability of a system of nonlinear Caputo fractional differential equations at resonance is considered. The interesting point is that the state variable x∈Rn and the effect of the coefficient matrices matrices B and C of boundary value conditions on the solvability of the problem are systematically discussed. By using Mawhin coincidence degree theory, some sufficient conditions for the solvability of the problem are obtained.

Mesoscale Simulation-based Parametric Study of Damage Potential in Brain Tissue Using Hyperelastic and Internal State Variable Models

Two-dimensional mesoscale finite element analysis (FEA) of a multi-layered brain tissue was performed to calculate the damage related average stress triaxiality and local maximum von Mises strain in the brain. The FEA was integrated with rate dependent hyperelastic and internal state variable (ISV) models respectively describing the behaviors of wet and dry brain tissues. Using the finite element results, a statistical method of design of experiments (DOE) was utilized to independently screen the relative influences of seven parameters related to brain morphology (sulcal width/depth, gray matter (GM) thickness, cerebrospinal fluid (CSF) thickness and brain lobe) and loading/environment conditions (strain rate and humidity) with respect to the potential damage growth/coalescence in the brain tissue. The results of the parametric study illustrated that the GM thickness and humidity were the two most crucial parameters affecting average stress triaxiality. For the local maximum von Mises strain at the depth of brain sulci, the brain lobe/region was the most influential factor. The conclusion of this investigation gives insight for the future development and refinement of a macroscale brain damage model incorporating information from lower length scale

Local-Activity and Simultaneous Zero-Hopf Bifurcations Leading to Multistability in a Memristive Circuit

In this paper, we consider a memristive circuit consisting of three elements: a passive linear inductor, a passive linear capacitor and an active memristive device. The circuit is described by a four-parameter system of ordinary differential equations. We study in detail the role of parameters in the dynamics of the system. Using the existence of first integrals, we show that the circuit may present a continuum of stable periodic orbits, which arise due to the occurrence of infinitely many simultaneous zero-Hopf bifurcations on a line of equilibria located in the region where the memristance is negative and, consequently, the memristive device is locally-active. These bifurcations lead to multistability, which is a difficult and interesting problem in applied models, since the final state of a solution depends crucially on its initial condition. We also study the control of multistability by varying a parameter related to the state variable of the memristive device. All analytical results obtained were corroborated by numerical simulations.

Slow periodic oscillation without radiation damping: New evolution laws for rate and state friction

Summary The dynamics of sliding friction is mainly governed by the frictional force. Previous studies have shown that the laboratory-scale friction is well described by an empirical law stated in terms of the slip velocity and the state variable. The state variable represents the detailed physicochemical state of the sliding interface. Despite some theoretical attempts to derive this friction law, there has been no unique equation for time evolution of the state variable. Major equations known to date have their own merits and drawbacks. To shed light on this problem from a new aspect, here we investigate the feasibility of periodic motion without the help of radiation damping. Assuming a patch on which the slip velocity is perturbed from the rest of the sliding interface, we prove analytically that three major evolution laws fail to reproduce stable periodic motion without radiation damping. Furthermore, we propose two new evolution equations that can produce stable periodic motion without radiation damping. These two equations are scrutinized from the viewpoint of experimental validity and the relevance to slow earthquakes.

DESAIN KONTROL PENGOBATAN PADA MODEL SIRD UNTUK PENYEBARAN VIRUS COVID-19 MENGGUNAKAN BACKSTEPPING

In this article, we present a control design on a SIRD model with treatment in infected individuals. The SIRD model with treatment is obtained from literature study and the parameter model is obtained from covid-19 daily case in the Riau province using the Particle Swarm Optimization method. The control design is carried out based on the backstepping method combined with feedback linearization based on input and output (IOFL). The SIRD model which is a nonlinear system will be transformed into a normal form using IOFL. Each variable is then stabilized Lyapunov using virtual control which at the same time generates a new state variable. This stage will be carried out iteratively until the last state variable is stabilized using a real control function. This control function is then applied to the SIRD model using the inverse of IOFL transformation. The simulation results compared with the Pontryagin Minimum Principle (PMP) method show that by selecting the appropriate control parameters, backstepping obtains better control performance which is a smaller number of infected populations.