Recursion relations for Double Ramification Hierarchies

In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in [Bur15] using intersection theory of the double ramification cycle in the moduli space of stable curves. In particular, we prove a recursion formula that recovers the full hierarchy starting from just one of the Hamiltonians, the one associated to the first descendant of the unit of a cohomological field theory. Moreover, we introduce analogues of the topological recursion relations and the divisor equation both for the hamiltonian densities and for the string solution of the double ramification hierarchy. This machinery is very efficient and we apply it to various computations for the trivial and Hodge cohomological field theories, and for the $r$-spin Witten's classes. Moreover we prove the Miura equivalence between the double ramification hierarchy and the Dubrovin-Zhang hierarchy for the Gromov-Witten theory of the complex projective line (extended Toda hierarchy).Comment: Revised version, to be published in Communications in Mathematical Physics, 27 page

Mean-field expansion for spin models with medium-range interactions

We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections. In particular we show that, in three dimensions, the leading correction scales as $R^{-3}, R$ being the range of the interactions. We compare our results with the existing numerical ones obtained by Monte Carlo simulations and present a critical discussion of other approaches.Comment: 49 pages, 8 figure

Performance Analysis and Design of Maximum Ratio Combining in Channel-Aware MIMO Decision Fusion

In this paper we present a theoretical performance analysis of the maximum ratio combining (MRC) rule for channel-aware decision fusion over multiple-input multiple-output (MIMO) channels for (conditionally) dependent and independent local decisions. The system probabilities of false alarm and detection conditioned on the channel realization are derived in closed form and an approximated threshold choice is given. Furthermore, the channel-averaged (CA) performances are evaluated in terms of the CA system probabilities of false alarm and detection and the area under the receiver operating characteristic (ROC) through the closed form of the conditional moment generating function (MGF) of the MRC statistic, along with Gauss-Chebyshev (GC) quadrature rules. Furthermore, we derive the deflection coefficients in closed form, which are used for sensor threshold design. Finally, all the results are confirmed through Monte Carlo simulations.Comment: To appear in IEEE Transactions on Wireless Communication

Quantized vortices in two dimensional solid 4He

Diagonal and off-diagonal properties of 2D solid 4He systems doped with a quantized vortex have been investigated via the Shadow Path Integral Ground State method using the fixed-phase approach. The chosen approximate phase induces the standard Onsager-Feynman flow field. In this approximation the vortex acts as a static external potential and the resulting Hamiltonian can be treated exactly with Quantum Monte Carlo methods. The vortex core is found to sit in an interstitial site and a very weak relaxation of the lattice positions away from the vortex core position has been observed. Also other properties like Bragg peaks in the static structure factor or the behavior of vacancies are very little affected by the presence of the vortex. We have computed also the one-body density matrix in perfect and defected 4He crystals finding that the vortex has no sensible effect on the off-diagonal long range tail of the density matrix. Within the assumed Onsager Feynman phase, we find that a quantized vortex cannot auto-sustain itself unless a condensate is already present like when dislocations are present. It remains to be investigated if backflow can change this conclusion.Comment: 4 pages, 3 figures, LT26 proceedings, accepted for publication in Journal of Physics: Conference Serie

Linear stability analysis of magnetized relativistic jets: the nonrotating case

We perform a linear analysis of the stability of a magnetized relativistic non-rotating cylindrical flow in the aproximation of zero thermal pressure, considering only the m = 1 mode. We find that there are two modes of instability: Kelvin-Helmholtz and current driven. The Kelvin-Helmholtz mode is found at low magnetizations and its growth rate depends very weakly on the pitch parameter. The current driven modes are found at high magnetizations and the value of the growth rate and the wavenumber of the maximum increase as we decrease the pitch parameter. In the relativistic regime the current driven mode is splitted in two branches, the branch at high wavenumbers is characterized by the eigenfunction concentrated in the jet core, the branch at low wavenumbers is instead characterized by the eigenfunction that extends outside the jet velocity shear region.Comment: 22 pages, 13 figures, MNRAS in pres

Fully Convective Magnetorotational Turbulence in Stratified Shearing Boxes

We present a numerical study of turbulence and dynamo action in stratified shearing boxes with zero magnetic flux. We assume that the fluid obeys the perfect gas law and has finite (constant) thermal diffusivity. We choose radiative boundary conditions at the vertical boundaries in which the heat flux is propor- tional to the fourth power of the temperature. We compare the results with the corresponding cases in which fixed temperature boundary conditions are applied. The most notable result is that the formation of a fully convective state in which the density is nearly constant as a function of height and the heat is transported to the upper and lower boundaries by overturning motions is robust and persists even in cases with radiative boundary conditions. Interestingly, in the convective regime, although the diffusive transport is negligible the mean stratification does not relax to an adiabatic state.Comment: 11 pages, 4 figures, accepted for publication in ApJ Letter

Deformed W_N algebras from elliptic sl(N) algebras

We extend to the sl(N) case the results that we previously obtained on the construction of W_{q,p} algebras from the elliptic algebra A_{q,p}(\hat{sl}(2)_c). The elliptic algebra A_{q,p}(\hat{sl}(N)_c) at the critical level c=-N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(N-1)/2 integers, defining q-deformations of the W_N algebra, are constructed. The operators t(z) also close an exchange algebra when (-p^1/2)^{NM} = q^{-c-N} for M in Z. It becomes Abelian when in addition p=q^{Nh} where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W_N algebras depending on the parity of h, characterizing the exchange structures at p \ne q^{Nh} as new W_{q,p}(sl(N)) algebras.Comment: LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 page

On the convergence of Magnetorotational turbulence in stratified isothermal shearing boxes

We consider the problem of convergence in stratified isothermal shearing boxes with zero net magnetic flux. We present results with the highest resolution to-date--up to 200 grid-point per pressure scale height--that show no clear evidence of convergence. Rather, the Maxwell stresses continue to decrease with increasing resolution. We propose some possible scenarios to explain the lack of convergence based on multi-layer dynamo systems.Comment: 10 pages, 4 figures, accepted for publication in ApJ Letter