Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions

We prove existence and uniqueness of solutions to a nonlinear stochastic evolution equation on the $d$-dimensional torus with singular $p$-Laplace-type or total variation flow-type drift with general sublinear doubling nonlinearities and Gaussian gradient Stratonovich noise with divergence-free coefficients. Assuming a weak defective commutator bound and a curvature-dimension condition, the well-posedness result is obtained in a stochastic variational inequality setup by using resolvent and Dirichlet form methods and an approximative It\^{o}-formula.Comment: 26 pages, 58 references. Essential changes to Version 4: Examples revised. Accepted for publication in Stochastic Processes and their Application

Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts

In this paper, a new decay estimate for a class of stochastic evolution equations with weakly dissipative drifts is established, which directly implies the uniqueness of invariant measures for the corresponding transition semigroups. Moreover, the existence of invariant measures and the convergence rate of corresponding transition semigroup to the invariant measure are also investigated. As applications, the main results are applied to singular stochastic $p$-Laplace equations and stochastic fast diffusion equations, which solves an open problem raised by Barbu and Da Prato in [Stoc. Proc. Appl. 120(2010), 1247-1266].Comment: http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=2308&layout=abstrac

Room temperature spin thermoelectrics in metallic films

Considering metallic films at room temperature, we present the first theoretical study of the spin Nernst and thermal Edelstein effects which takes into account dynamical spin-orbit coupling, i.e., direct spin-orbit coupling with the vibrating lattice (phonons) and impurities. This gives rise to two novel processes, namely a dynamical Elliott-Yafet spin relaxation and a dynamical side-jump mechanism. Both are the high-temperature counterparts of the well-known $T = 0$ Elliott-Yafet and side-jump, central to the current understanding of the spin Hall, spin Nernst and Edelstein effects at low $T$. We consider the experimentally relevant regime $T > T_D$, with $T_D$ the Debye temperature, as the latter is lower than room temperature in transition metals such as Pt, Au and Ta typically employed in spin injection/extraction experiments. We show that the interplay between intrinsic (Bychkov-Rashba type) and extrinsic (dynamical) spin-orbit coupling yields a nonlinear $T$- dependence of the spin Nernst and spin Hall conductivities.Comment: 9 pages, 4 figure

Universal few-body physics in a harmonic trap

Few-body systems with resonant short-range interactions display universal properties that do not depend on the details of their structure or their interactions at short distances. In the three-body system, these properties include the existence of a geometric spectrum of three-body Efimov states and a discrete scaling symmetry. Similar universal properties appear in 4-body and possibly higher-body systems as well. We set up an effective theory for few-body systems in a harmonic trap and study the modification of universal physics for 3- and 4-particle systems in external confinement. In particular, we focus on systems where the Efimov effect can occur and investigate the dependence of the 4-body spectrum on the experimental tuning parameters.Comment: 20 pages, 10 figures, final version, new references adde

Założenia i możliwości współpracy transnarodowej między metropoliami na przykładzie Poznania i Berlina

Today’s inevitability to create transnational networks between regions is a result of the progressing European integration process as well as of the globalisation of socioeconomic and cultural relations. Managing the development process of a European metropolis requires increasinglycooperation structures with other metropolises in the field of best practice exchange, lobbying, project implementation and regional specialisation, in order to cope with the ever faster changing development challenges. International experience shows that there are also action fields on which cooperation between neighbouring metropolitan regions maycontribute to solve specific problems. From this perspective a set-up analyses of the cooperation potentials between the metropolitan regions of Poznań and Berlin –against the background of both metropolitan regions being members in the transnational macro-cooperation space of the Oder Partnership – highlights the existence of numerous joint interests that maycontribute to the creation of transnational networks.Konieczność tworzenia transnarodowych sieci powiązań między regionami jest skutkiem postępującej integracji europejskiej oraz globalizacji stosunków społeczno- gospodarczych. W ramach zarządzania rozwojem metropolii europejskich strategie z dziedzin wymiany doświadczeń, lobbingu, realizacji projektów i specjalizacji razem z innymi metropoliami odgrywają coraz ważniejszą rolę w reagowaniu na zmieniające się wyzwania. Istnieją także pola działania, na których współpraca między sąsiadującymi ze sobą regionami metropolitalnymi może ułatwić rozwiązania pewnych problemów. Z tej perspektywy wstępna analiza możliwości współpracy między regionami metropolitalnymi Poznania i Berlina – na tle członkostwa obu regionów w Partnerstwie-Odra – ukazuje istnienie wspólnych interesów, które mogą się przyczyniać do powstawania transnarodowych sieci powiązań

Rozrastanie się miasta w krajobrazie. Dawne i współczesne utopijne koncepcje

Owing to globalisation, the present process of deep socio-economic and spatial changes undermines the traditional ways of thinking and acting concerning the organisation of urban-rural relations in the face of parallel developments, like suburbanisation and urban sprawl as well as de-urbanisation and degradation of urban areas. The article seeks to elucidate the contemporary discourse on the mutual penetration of landscapes and urban forms in terms of the formation of congruous, balanced urban structures in a historical perspective. In this way it will describe a curve from the urban utopias of the 19th and early 20th centuries through the conceptions of the garden city and the modernist city to those of cities without cities, right to the city, and energy self-sufficient city. As it turns out, the modern ‘utopian’ projects follow the historical line of traditional ideas for the organisation of democratic, consistent and healthy forms of coexistence.Wskutek globalizacji obecny proces głębokich przemian społeczno-ekonomicznych i przestrzennych kwestionuje zwyczajowe formy myślenia i działania w zakresie organizacji stosunków miejsko-wiejskich wobec równoległych zjawisk, takich jak suburbanizacja i rozprzestrzenianie się miast oraz dezurbanizacja i degradacja obszarów miejskich. Niniejszy artykuł ma na celu przybliżenie współczesnego dyskursu z zakresu regionalizacji miasta i umiastowienia krajobrazu w kontekście tworzenia spójnych i zrównoważonych struktur miejskich z perspektywy historycznej. W ten sposób zostanie zatoczony łuk od miejskich utopii z XIX i początku XX w. poprzez koncepcję miasta-ogrodu i miasta modernizmu aż do ukształtowania się miasta pomiędzy oraz koncepcji prawa do miasta i miast samowystarczalnych energetycznie. Okazuje się, że nowoczesne formy „utopijnych” projektów nawiązują do historycznej linii tradycyjnych idei zmierzających do organizacji demokratycznych, spójnych i zdrowych form współżycia

Proton Transport in Additives to the Polymer Electrolyte Membrane for Fuel Cell Application

The enhancement of proton transport in polymer electrolyte membranes is an important issue for the development of fuel cell technology. The objective is a material providing proton transport at a temperature range of 350 K to 450 K independent from a purely water based mechanism. To enhance the PEM properties of standard polymer materials, a class of additives is studied by means of atomistic simulations consisting of functionalised mesoporous silicon dioxide particles. The functional molecules are imidazole or sulphonic acid, covalently bound to the surface via a carbon chain with a surface density of about 1.0 nm−2 groups. At first, the proton transport mechanism is explored in a system of functional molecules in vacuum. The molecules are constrained by the terminal carbon groups according to the geometric arrangement in the porous silicon dioxide. The proton transport mechanism is characterised by structural properties obtained from classical molecular dynamics simulations and consists of the aggregation of two or more functional groups, a barrier free proton transport between these groups followed by the separation of the groups and formation of new aggregates due to fluctuations in the hydrogen bond network and movement of the carbon chain. For the different proton conducting groups, i.e. methyl imidazole, methyl sulphonic acid and water, the barrier free proton transport and the formation of protonated bimolecular complexes were addressed by potential energy calculations of the density functional based tight binding method (DFTB). For sulphonic acid even at a temperature of 450 K, relatively stable aggregates are formed, while most imidazole groups are isolated and the hydrogen bond fluctuations are high. However, high density of groups and elevated temperatures enhance the proton transport in both systems. Besides the anchorage and the density of the groups, the influence of the chemical environment on the proton transport was studied. Therefore, the uptake and distribution of water molecules was estimated from classical molecular dynamic simulations and the local chemical environment was determined for different functional groups. The sulphonic acid functionalised silicon dioxide pores are more hydrophilic than the unfunctionalised and the imidazole functionalised systems. At lower hydration, the distribution of water is inhomogeneous and the surface of the pore is covered by a water layer for all systems. In addition to the interaction with water, an interaction of functional groups with the surface is observed which is shielded under hydration. Due to these interactions, the number of isolated groups and their stability is increased under the influence of the environment that reduces the proton transport mechanism which has been described before. Apart from the proton transport mechanism known from the vacuum system, two additional mechanisms occur under the chemical environment. These mechanism directly involve water molecules. One possibility is the complete deprotonation of the functional group, followed by water based proton transport as expected for acidic system, e.g. sulphonic acid. Another possibility is a water based proton transport over short distances from one proton conducting group to another. The three competing mechanisms are studied by free energy calculations and their occurance is evaluated according to the local environment conditions. The proton transport mechanisms involving water are more favourable in sulphonic acid functionalised particles, while the dominating mechanism is comparable to the mechanism in vacuum for imidazole system

Transnational metropolitan development strategies and governance in a post-socialist setting: The case of Szczecin

The integration of cities and their regions into transnational networks has become a key municipal strategy, with the creation of a metropolitan governance structure being seen in this context as a fundamental element. The Szczecin Metropolitan Area constitutes an example of meagre results in intercommunal cooperation in post-socialist East-Central Europe. This has its repercussions on the task of creating cross-border metropolitan governance structures including adjacent German counties, a task which, in turn, may help to overcome development barriers. This becomes apparent particularly in the process of defining joint development objectives as well as an image for the cross-border metropolitan region