Entropy-based measure of structural order in water

We analyze the nature of the structural order established in liquid TIP4P water in the framework provided by the multi-particle correlation expansion of the statistical entropy. Different regimes are mapped onto the phase diagram of the model upon resolving the pair entropy into its translational and orientational components. These parameters are used to quantify the relative amounts of positional and angular order in a given thermodynamic state, thus allowing a structurally unbiased definition of low-density and high-density water. As a result, the structurally anomalous region within which both types of order are simultaneously disrupted by an increase of pressure at constant temperature is clearly identified through extensive molecular-dynamics simulations.Comment: 5 pages, 2 figures, to appear in Phys. Rev. E (Rapid Communication

Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth

We establish global regularity for weak solutions to quasilinear divergence form elliptic and parabolic equations over Lipschitz domains with controlled growth conditions on low order terms. The leading coefficients belong to the class of BMO functions with small mean oscillations with respect to $x$.Comment: 24 pages, to be submitte

Gauge theory of Faddeev-Skyrme functionals

We study geometric variational problems for a class of nonlinear sigma-models in quantum field theory. Mathematically, one needs to minimize an energy functional on homotopy classes of maps from closed 3-manifolds into compact homogeneous spaces G/H. The minimizers are known as Hopfions and exhibit localized knot-like structure. Our main results include proving existence of Hopfions as finite energy Sobolev maps in each (generalized) homotopy class when the target space is a symmetric space. For more general spaces we obtain a weaker result on existence of minimizers in each 2-homotopy class. Our approach is based on representing maps into G/H by equivalence classes of flat connections. The equivalence is given by gauge symmetry on pullbacks of G-->G/H bundles. We work out a gauge calculus for connections under this symmetry, and use it to eliminate non-compactness from the minimization problem by fixing the gauge.Comment: 34 pages, no figure

Twice-daily pain monitoring as standard clinical practice for inpatients at a medical oncology unit: a descriptive study

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