The Escape Problem in a Classical Field Theory With Two Coupled Fields

We introduce and analyze a system of two coupled partial differential equations with external noise. The equations are constructed to model transitions of monovalent metallic nanowires with non-axisymmetric intermediate or end states, but also have more general applicability. They provide a rare example of a system for which an exact solution of nonuniform stationary states can be found. We find a transition in activation behavior as the interval length on which the fields are defined is varied. We discuss several applications to physical problems.Comment: 24 page

The KINDRA project – towards Open Science in Hydrogeology for higher impact

Groundwater knowledge and research in the European Union is often scattered and non-standardised. Therefore, KINDRA is conducting an EU-wide assessment of existing groundwater-related practical and scientific knowledge based on a new Hydrogeological Research Classification System (HRC-SYS). The classification is supported by a web service, the European Inventory of Groundwater Research (EIGR), which acts not only as a knowledge repository but also as a tool to help identify relevant research topics, existing research trends and critical research challenges. These results will be useful for producing synergies, implementing policies and optimising water management in Europe. This article presents the work of the project during the first two years in relation to a common classification system and an activity for data collection and training delivered by the EFG’s National Associations in 20 European countries

Heat kernel estimates and spectral properties of a pseudorelativistic operator with magnetic field

Based on the Mehler heat kernel of the Schroedinger operator for a free electron in a constant magnetic field an estimate for the kernel of E_A is derived, where E_A represents the kinetic energy of a Dirac electron within the pseudorelativistic no-pair Brown-Ravenhall model. This estimate is used to provide the bottom of the essential spectrum for the two-particle Brown-Ravenhall operator, describing the motion of the electrons in a central Coulomb field and a constant magnetic field, if the central charge is restricted to Z below or equal 86

Dynamics of Flux Creep in Underdoped Single Crystals of Y_1-xPr_xBa_2Cu_3O_7-d

Transport as well as magnetic relaxation properties of the mixed state were studied on strongly underdoped Y_1-xPr_xBa_2Cu_3O_7-d crystals. We observed two correlated phenomena - a coupling transition and a transition to quantum creep. The distribution of transport current below the coupling transition is highly nonuniform, which facilitates quantum creep. We speculate that in the mixed state below the coupling transition, where dissipation is nonohmic, the current distribution may be unstable with respect to self-channeling resulting in the formation of very thin current-carrying layers.Comment: 11 pages, 9 figures, Submitted to Phys. Rev.

Quantum Limits of Measurements Induced by Multiplicative Conservation Laws: Extension of the Wigner-Araki-Yanase Theorem

The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws limit the accuracy of measurements. Recently, various quantitative expressions have been found for quantum limits on measurements induced by additive conservation laws, and have been applied to the study of fundamental limits on quantum information processing. Here, we investigate generalizations of the WAY theorem to multiplicative conservation laws. The WAY theorem is extended to show that an observable not commuting with the modulus of, or equivalently the square of, a multiplicatively conserved quantity cannot be precisely measured. We also obtain a lower bound for the mean-square noise of a measurement in the presence of a multiplicatively conserved quantity. To overcome this noise it is necessary to make large the coefficient of variation (the so-called relative fluctuation), instead of the variance as is the case for additive conservation laws, of the conserved quantity in the apparatus.Comment: 8 pages, REVTEX; typo added, to appear in PR

Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses

We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent boundary conditions, such as periodic, at most a pair of flip-related (or the appropriate number of symmetry-related in the non-Ising case) states appear, and the Parisi overlap distribution correspondingly exhibits at most a pair of delta-functions at plus/minus the self-overlap. This rules out the nonstandard SK picture introduced by us earlier, and when combined with our previous elimination of more standard versions of the mean field picture, argues against the possibility of even limited versions of mean field ordering in realistic spin glasses. If broken spin flip symmetry should occur, this leaves open two main possibilities for ordering in the spin glass phase: the droplet/scaling two-state picture, and the chaotic pairs many-state picture introduced by us earlier. We present scaling arguments which provide a possible physical basis for the latter picture, and discuss possible reasons behind numerical observations of more complicated overlap structures in finite volumes.Comment: 22 pages (LaTeX; needs revtex), 1 figure (PostScript); to appear in Physical Review

Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist novel hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.Comment: 4 pages, 4 figure

The Classification of Obsessive–Compulsive and Related Disorders in the ICD-11

Background To present the rationale for the new Obsessive–Compulsive and Related Disorders (OCRD) grouping in the Mental and Behavioural Disorders chapter of the Eleventh Revision of the World Health Organization’s International Classification of Diseases and Related Health Problems (ICD-11), including the conceptualization and essential features of disorders in this grouping. Methods Review of the recommendations of the ICD-11 Working Group on the Classification for OCRD. These sought to maximize clinical utility, global applicability, and scientific validity. Results The rationale for the grouping is based on common clinical features of included disorders including repetitive unwanted thoughts and associated behaviours, and is supported by emerging evidence from imaging, neurochemical, and genetic studies. The proposed grouping includes obsessive–compulsive disorder, body dysmorphic disorder, hypochondriasis, olfactory reference disorder, and hoarding disorder. Body-focused repetitive behaviour disorders, including trichotillomania and excoriation disorder are also included. Tourette disorder, a neurological disorder in ICD-11, and personality disorder with anankastic features, a personality disorder in ICD-11, are recommended for cross-referencing. Limitations Alternative nosological conceptualizations have been described in the literature and have some merit and empirical basis. Further work is needed to determine whether the proposed ICD-11 OCRD grouping and diagnostic guidelines are mostly likely to achieve the goals of maximizing clinical utility and global applicability. Conclusion It is anticipated that creation of an OCRD grouping will contribute to accurate identification and appropriate treatment of affected patients as well as research efforts aimed at improving our understanding of the prevalence, assessment, and management of its constituent disorders

Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics

In this article, we study the effect of small-cut elements on the critical time-step size in an immersogeometric context. We analyze different formulations for second-order (membrane) and fourth-order (shell-type) equations, and derive scaling relations between the critical time-step size and the cut-element size for various types of cuts. In particular, we focus on different approaches for the weak imposition of Dirichlet conditions: by penalty enforcement and with Nitsche's method. The stability requirement for Nitsche's method necessitates either a cut-size dependent penalty parameter, or an additional ghost-penalty stabilization term is necessary. Our findings show that both techniques suffer from cut-size dependent critical time-step sizes, but the addition of a ghost-penalty term to the mass matrix serves to mitigate this issue. We confirm that this form of `mass-scaling' does not adversely affect error and convergence characteristics for a transient membrane example, and has the potential to increase the critical time-step size by orders of magnitude. Finally, for a prototypical simulation of a Kirchhoff-Love shell, our stabilized Nitsche formulation reduces the solution error by well over an order of magnitude compared to a penalty formulation at equal time-step size

Interfaces (and Regional Congruence?) in Spin Glasses

We present a general theorem restricting properties of interfaces between thermodynamic states and apply it to the spin glass excitations observed numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3 and 4. We show that such excitations, with interface dimension smaller than d, cannot yield regionally congruent thermodynamic states. More generally, zero density interfaces of translation-covariant excitations cannot be pinned (by the disorder) in any d but rather must deflect to infinity in the thermodynamic limit. Additional consequences concerning regional congruence in spin glasses and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter