Inverse melting and inverse freezing: a spin model

Systems of highly degenerate ordered or frozen state may exhibit inverse melting (reversible crystallization upon heating) or inverse freezing (reversible glass transition upon heating). This phenomena is reviewed, and a list of experimental demonstrations and theoretical models is presented. A simple spin model for inverse melting is introduced and solved analytically for infinite range, constant paramagnetic exchange interaction. The random exchange analogue of this model yields inverse freezing, as implied by the analytic solution based on the replica trick. The qualitative features of this system (generalized Blume-Capel spin model) are shown to resemble a large class of inverse melting phenomena. The appearance of inverse melting is related to an exact rescaling of one of the interaction parameters that measures the entropy of the system. For the case of almost degenerate spin states perturbative expansion is presented, and the first three terms correspond to the empiric formula for the Flory-Huggins $\chi$ parameter in the theory of polymer melts. Possible microscopic origin of this $\chi$ parameter and the limitations of the Flory-Huggins theory where the state degeneracy is associated with the different conformations of a single polymer or with the spatial structures of two interacting molecules are discussed

Generalized inverse patchy colloid model

We generalize the inverse patchy colloid model that was originally developed for heterogeneously charged particles with two identical polar patches and an oppositely charged equator to a model that can have a considerably richer surface pattern. Based on a Debye-Hueckel framework, we propose a coarse-grained description of the effective pair interactions that is applicable to particles with an arbitrary patch decoration. We demonstrate the versatility of this approach by applying it to models with (i) two differently charged and/or sized patches, and (ii) three, possibly different patches

Combinatorial Gelfand models for some semigroups and q-rook monoid algebras

Inspired by the results of [R. Adin, A. Postnikov, Y. Roichman, Combinatorial Gelfand model, preprint math.RT arXiv:0709.3962], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebras of the symmetric inverse semigroup to a Gelfand model for the $q$-rook monoid algebra.Comment: 14 page

Spin-Glass Model for Inverse Freezing

We analyze the Blume-Emery-Griffiths model with disordered magnetic interaction displaying the inverse freezing phenomenon. The behaviour of this spin-1 model in crystal field is studied throughout the phase diagram and the transition and spinodal lines for the model are computed using the Full Replica Symmetry Breaking Ansatz that always yelds a thermodynamically stable phase. We compare the results both with the quenched disordered model with Ising spins on lattice gas - where no reentrance takes place - and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. 93, 037202 (2004)]. The simplest version of all these models, known as Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase, including the right thermodynamic behavior.Comment: 6 pages, 4 figures, to appear in the Proceeding for the X International Workshop on Disordered Systems (2006), Molveno, Ital

Stochastic modeling error reduction using Bayesian approach coupled with an adaptive kriging based model

Magnetic material properties of an electromagnetic device can be recovered by solving an inverse problem where measurements are adequately interpreted by a mathematical forward model. The accuracy of the material properties recovered by the inverse problem is highly dependent on the accuracy of these forward models. In order to ensure the highest possible accuracy of the inverse problem solution, all physics of the electromagnetic device need to be perfectly modeled using for example a complex numerical model. However, the more accurate ‘fine’ models demand a high computational time and memory storage. Alternatively, less accurate ‘coarse’ models can be used with a demerit of the high expected recovery errors. Therefore, the Bayesian approximation error approach has been used for reducing the modeling error originating from using a coarse model instead of a fine model in the inverse problem procedure. However, the Bayesian approximation error approach may fail to compensate the modeling error completely when the used model in the inverse problem is too coarse. Therefore, there is a definitely need to use a quite accurate coarse model. In this paper, the electromagnetic device is simulated using an adaptive Kriging based model. The accuracy of this ‘coarse’ model is a priori assessed using the cross-validation technique. Moreover, the Bayesian approximation error approach is utilized for improving the inverse problem results by compensating the modeling errors. The proposed methodology is validated on both purely numerical and real experimental results. The results show a significant reduction in the recovery error within an acceptable computational time

Applications of inverse simulation to a nonlinear model of an underwater vehicle

Inverse simulation provides an important alternative to conventional simulation and to more formal mathematical techniques of model inversion. The application of inverse simulation methods to a nonlinear dynamic model of an unmanned underwater vehicle with actuator limits is found to give rise to a number of challenging problems. It is shown that this particular problem requires, in common with other applications that include hard nonlinearities in the model or discontinuities in the required trajectory, can best be approached using a search-based optimization algorithm for inverse simulation in place of the more conventional Newton- Raphson approach. Results show that meaningful inverse simulation results can be obtained but that multi-solution responses exist. Although the inverse solutions are not unique they are shown to generate the required trajectories when tested using conventional forward simulation methods

A supersymmetric electroweak scale seesaw model

In this paper we propose a novel supersymmetric inverse seesaw model which has only one additional $Z_6$ symmetry. The field content is minimal to get a viable neutrino spectrum at tree-level. Interestingly, the inverse seesaw scale in our model is related to the scale of electroweak symmetry breaking. Due to that origin we are less biased about hierarchies and discuss three different types of the inverse seesaw mechanism with different phenomenologies. We can successfully reproduce neutrino masses and mixing and our model is consistent with current bounds on neutrinoless double beta decay, non-unitarity of the PMNS matrix and charged lepton flavor violation.Comment: 20 pages, 1 figure; version published in JHE

Soft leptogenesis in the inverse seesaw model

We consider leptogenesis induced by soft supersymmetry breaking terms ("soft leptogenesis"), in the context of the inverse seesaw mechanism. In this model there are lepton number (L) conserving and L-violating soft supersymmetry-breaking B-terms involving the singlet sneutrinos which, together with the -- generically small-- L-violating parameter responsible of the neutrino mass, give a small mass splitting between the four singlet sneutrino states of a single generation. In combination with the trilinear soft supersymmetry breaking terms they also provide new CP violating phases needed to generate a lepton asymmetry in the singlet sneutrino decays. We obtain that in this scenario the lepton asymmetry is proportional to the L-conserving soft supersymmetry-breaking B-term, and it is not suppressed by the L-violating parameters. Consequently we find that, as in the standard see-saw case, this mechanism can lead to sucessful leptogenesis only for relatively small value of the relevant soft bilinear coupling. The right-handed neutrino masses can be sufficiently low to elude the gravitino problem. Also the corresponding Yukawa couplings involving the lightest of the right-handed neutrinos are constrained to be \sum |Y_{1k}|^2\lesssim 10^{-7} which generically implies that the neutrino mass spectrum has to be strongly hierarchical.Comment: 28 pages, 1 figure; some references added; final version to appear in JHE