Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media

In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler time-discrete scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal $L^2$ error estimates hold without any time-step (convergence) condition, while all previous works require certain time-step condition. Our theoretical results provide a new understanding on commonly-used linearized schemes for nonlinear parabolic equations. The proof is based on a splitting of the error function into two parts: the error from the time discretization of the PDEs and the error from the finite element discretization of corresponding time-discrete PDEs. The approach used in this paper is applicable for more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations

Interdisciplinary Development of a Transdiagnostic Mobile App to Enhance Children’s Emotion Regulation: Sharing Insights and Lessons Learned

Background: Digital interventions, including mobile apps represent promising means to provide effective mental health support to young people. Despite the increased availability of mental health apps, there is a significant gap for this age group, especially for younger children. Research investigating the effectiveness and development process of child mental health apps is limited, and the field faces persistent issues in relation to low user up-take and engagement, which is assumed to be a result of lacking interdisciplinary approaches. // Objective: We present the development and design process of a new mental health app for children that targets their emotion regulation abilities. We describe the creation of a new interdisciplinary development framework, to guide the design process, and explain how each activity informed different app features. // Methods: The first two stages of the framework employed a variety of methods, including: 1) classroom observations, 2) public-engagement events with the target group (N=21), 3) synthesis of the existing evidence as part of a meta-analysis, 4) a series of co-design and participatory workshops with young users (N=33), clinicians (N=7), researchers (N=12), app developers (N=1) , designers (N=2), and lastly 5) testing of the first high-tech prototype (N=15). // Results: For the interdisciplinary framework we drew on methods derived from the medical research council framework for complex interventions, the patient-clinician-framework and Druin’s cooperative inquiry. The classroom observations, public-engagement events, and synthesis of the existing evidence informed the first key pillars of the app and wireframes. Subsequently, a series of workshops shaped and reshaped the content and app features, including games, psychoeducational films, and practice modules. Based on the prototype testing sessions we made further adjustments to improve the app. // Conclusions: Although mobile apps could be highly suitable to support young people’s mental health on a wider scale, there is little guidance on how these interventions could be designed. The involvement of the different methods and especially the young users was very valuable. We hope that the interdisciplinary framework and multiple methods that we applied will be helpful to others who are also aiming to develop suitable apps for young peopl

Relationship Between Exercise Motivation, Exercise Enjoyment, and Daily Cognition of Collegiate Student-Athletes

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Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data, and the structural stability for the equation are established.Comment: 33 page

Spontaneous symmetry breaking in gauge theories via Bose-Einstein condensation

We propose a mechanism naturally leading to the spontaneous symmetry breaking in a gauge theory. The Higgs field is assumed to have global and gauged internal symmetries. We associate a non zero chemical potential to one of the globally conserved charges commuting with all of the gauge transformations. This induces a negative mass squared for the Higgs field triggering the spontaneous symmetry breaking of the global and local symmetries. The mechanism is general and we test the idea for the electroweak theory in which the Higgs sector is extended to possess an extra global Abelian symmetry. To this symmetry we associate a non zero chemical potential. The Bose-Einstein condensation of the Higgs leads, at tree level, to modified dispersion relations for the Higgs field while the dispersion relations of the gauge bosons and fermions remain undisturbed. The latter are modified through higher order corrections. We have computed some corrections to the vacuum polarizations of the gauge bosons and fermions. To quantify the corrections to the gauge boson vacuum polarizations with respect to the Standard Model we considered the effects on the T parameter. We finally derive the one loop modified fermion dispersion relations.Comment: RevTeX 4, 13 pages. Added references and corrected typo

Spreading of a density front in the K\"untz-Lavall\'ee model of porous media

We analyze spreading of a density front in the K\"untz-Lavall\'ee model of porous media. In contrast to previous studies, where unusual properties of the front were attributed to anomalous diffusion, we find that the front evolution is controlled by normal diffusion and hydrodynamic flow, the latter being responsible for apparent enhancement of the front propagation speed. Our finding suggests that results of several recent experiments on porous media, where anomalous diffusion was reported based on the density front propagation analysis, should be reconsidered to verify the role of a fluid flow

Bidirectional synaptic mechanisms of ocular dominance plasticity in visual cortex

As in other mammals with binocular vision, monocular lid suture in mice induces bidirectional plasticity: rapid weakening of responses evoked through the deprived eye followed by delayed strengthening of responses through the open eye. It has been proposed that these bidirectional changes occur through three distinct processes: first, deprived-eye responses rapidly weaken through homosynaptic long-term depression (LTD); second, as the period of deprivation progresses, the modification threshold determining the boundary between synaptic depression and synaptic potentiation becomes lower, favouring potentiation; and third, facilitated by the decreased modification threshold, open-eye responses are strengthened via homosynaptic long-term potentiation (LTP). Of these processes, deprived-eye depression has received the greatest attention, and although several alternative hypotheses are also supported by current research, evidence suggests that α-amino-3- hydroxy-5-methyl-4-isoxazolepropionate (AMPA) receptor endocytosis through LTD is a key mechanism. The change in modification threshold appears to occur partly through changes in N-methyl-d-aspartate (NMDA) receptor subunit composition, with decreases in the ratio of NR2A to NR2B facilitating potentiation. Although limited research has directly addressed the question of open-eye potentiation, several studies suggest that LTP could account for observed changes in vivo. This review will discuss evidence supporting this three-stage model, along with outstanding issues in the field

Stability of Relativistic Matter with Magnetic Fields for Nuclear Charges up to the Critical Value

We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge $Z\alpha=2/\pi$.Comment: LaTeX2e, 12 page

Lack of uniqueness for weak solutions of the incompressible porous media equation

In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove non-uniqueness for solutions in $L^\infty$ in space and time.Comment: 23 pages, 2 fugure

Robotic milking technologies and renegotiating situated ethical relationships on UK dairy farms

Robotic or automatic milking systems (AMS) are novel technologies that take over the labor of dairy farming and reduce the need for human-animal interactions. Because robotic milking involves the replacement of 'conventional' twice-a-day milking managed by people with a system that supposedly allows cows the freedom to be milked automatically whenever they choose, some claim robotic milking has health and welfare benefits for cows, increases productivity, and has lifestyle advantages for dairy farmers. This paper examines how established ethical relations on dairy farms are unsettled by the intervention of a radically different technology such as AMS. The renegotiation of ethical relationships is thus an important dimension of how the actors involved are re-assembled around a new technology. The paper draws on in-depth research on UK dairy farms comparing those using conventional milking technologies with those using AMS. We explore the situated ethical relations that are negotiated in practice, focusing on the contingent and complex nature of human-animal-technology interactions. We show that ethical relations are situated and emergent, and that as the identities, roles, and subjectivities of humans and animals are unsettled through the intervention of a new technology, the ethical relations also shift. © 2013 Springer Science+Business Media Dordrecht