Let $\sigma$ be a simple involution of an algebraic semisimple group $G$ and let $H$ be the subgroup of $G$ of points fixed by $\sigma$. If the restricted root system is of type $A$, $C$ or $BC$ and $G$ is simply connected or if the restricted root system is of type $B$ and $G$ is adjoint, then we describe a standard monomial theory and the equations for the coordinate ring $k[G/H]$ using the standard monomial theory and the Pl\"ucker relations of an appropriate (maybe infinite dimensional) Grassmann variety.

Rocco Chiriví Peter Littelmann Andrea Maffei

We study the propagation of a ``pulled'' front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a separation of time scales for sufficiently large $t$ creates a diffusive wandering of the front position about its mean, we predict that for so-called pulled fronts, the fluctuations are subdiffusive with root mean square wandering $\Delta(t) \sim t^{1/4}$, {\em not} $t^{1/2}$. The subdiffusive behavior is confirmed by numerical simulations: For $t \le 600$, these yield an effective exponent slightly larger than 1/4.

Andrea Rocco Ute Ebert Wim van Saarloos

It has recently been proposed that fluctuating ``pulled'' fronts propagating into an unstable state should not be in the standard KPZ universality class for rough interface growth. We introduce an effective field equation for this class of problems, and show on the basis of it that noisy pulled fronts in {\em d+1} bulk dimensions should be in the universality class of the {\em (d+1)+1}D KPZ equation rather than of the {\em d+1}D KPZ equation. Our scenario ties together a number of heretofore unexplained observations in the literature, and is supported by previous numerical results.

Goutam Tripathy Andrea Rocco Jaume Casademunt Wim van Saarloos

Recent studies have shown that in the presence of noise both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper we derive an expression for the effective diffusion coefficient of such fronts, which was motivated before on the basis of a multiple scale ansatz. Our systematic derivation is based on the decomposition of the fluctuating front into a suitably positioned average profile plus fluctuating eigenmodes of the stability operator. While the fluctuations of the front position in this particular decomposition are a Wiener process on all time scales, the fluctuations about the time averaged front profile relax exponentially.

Andrea Rocco Jaume Casademunt Ute Ebert Wim van Saarloos

We generalize the method of Van Hove so as to deal with the case of non-ordinary statistical mechanics, that being phenomena with no time-scale separation. We show that in the case of ordinary statistical mechanics, even if the adoption of the Van Hove method imposes randomness upon Hamiltonian dynamics, the resulting statistical process is described using normal calculus techniques. On the other hand, in the case where there is no time-scale separation, this generalized version of Van Hove's method not only imposes randomness upon the microscopic dynamics, but it also transmits randomness to the macroscopic level. As a result, the correct description of macroscopic dynamics has to be expressed in terms of the fractional calculus.

P. Grigolini A. Rocco B. J. West

Atom interferometers are promising tools for precision measurement with applications ranging from geophysical exploration to tests of the equivalence principle of general relativity, or the detection of gravitational waves. Their optimal sensitivity is ultimately limited by their detection noise. We review resonant and near-resonant methods to detect the atom number of the interferometer outputs and we theoretically analyze the relative influence of various scheme dependent noise sources and the technical challenges affecting the detection. We show that for the typical conditions under which an atom interferometer operates, simultaneous fluorescence detection with a CCD sensor is the optimal imaging scheme. We extract the laser beam parameters such as detuning, intensity, and duration, required for reaching the atom shot noise limit.

Emanuele Rocco Rebecca Palmer Tristan Valenzuela Vincent Boyer Andreas Freise Kai Bongs

The Cosserat continuum is used in this paper to regularize the ill-posed governing equations of the Cauchy/Maxwell continuum. Most available constitutive models adopt yield and plastic potential surfaces with a circular deviatoric section. This is a too crude an approximation which hinders the application of the Cosserat continuum into practice, particularly in the geotechnical domain. An elasto-plastic constitutive model for the linear formulation of the Cosserat continuum is here presented, which features non-associated flow and hardening/softening behaviour, whilst linear hyper-elasticity is adopted to reproduce the recoverable response. For the formulation of the yield and plastic potential functions, a definition of the \textit{equivalent von Mises stress} is used which is based on Hencky's interpretation of the von Mises criterion and also on the theory of representations. The dependency on the Lode's angle of both the yield and plastic potential functions is introduced through the adoption of a recently proposed \textit{Generalized classical} criterion, which rigorously defines most of the classical yield and failure criteria.

Andrea Panteghini Rocco Lagioia

We present a method for fast 3D reconstruction and real-time rendering of dynamic humans from monocular videos with accompanying parametric body fits. Our method can reconstruct a dynamic human in less than 3h using a single GPU, compared to recent state-of-the-art alternatives that take up to 72h. These speedups are obtained by using a lightweight deformation model solely based on linear blend skinning, and an efficient factorized volumetric representation for modeling the shape and color of the person in canonical pose. Moreover, we propose a novel local ray marching rendering which, by exploiting standard GPU hardware and without any baking or conversion of the radiance field, allows visualizing the neural human on a mobile VR device at 40 frames per second with minimal loss of visual quality. Our experimental evaluation shows superior or competitive results with state-of-the art methods while obtaining large training speedup, using a simple model, and achieving real-time rendering.

Ignacio Rocco Iurii Makarov Filippos Kokkinos David Novotny Benjamin Graham Natalia Neverova Andrea Vedaldi

A general setting for a standard monomial theory on a multiset is introduced and applied to the Cox ring of a wonderful variety. This gives a degeneration result of the Cox ring to a multicone over a partial flag variety. Further, we deduce that the Cox ring has rational singularities.

Paolo Bravi Rocco Chirivì Jacopo Gandini Andrea Maffei

We study the front propagation in Reaction-Diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on the wandering of the front around its average position. Assuming that the reaction term acts periodically in an impulsive way, the dynamical evolution of the system can be written as the convolution between a spatial propagator and a discrete-time map acting locally. This approach allows us to perform accurate numerical analysis. They reveal that in the pulled regime the front speed is basically determined by the shape of the map around the unstable fixed point, while its chaotic or noisy features play a marginal role. In contrast, in the pushed regime the presence of chaos or noise is more relevant. In particular the front speed decreases when the degree of chaoticity is increased, but it is not straightforward to derive a direct connection between the chaotic properties (e.g. the Lyapunov exponent) and the behaviour of the front. As for the fluctuations of the front position, we observe for the noisy maps that the associated mean square displacement grows in time as $t^{1/2}$ in the pushed case and as $t^{1/4}$ in the pulled one, in agreement with recent findings obtained for continuous models with multiplicative noise. Moreover we show that the same quantity saturates when a chaotic deterministic dynamics is considered for both pushed and pulled regimes.

Alessandro Torcini Angelo Vulpiani Andrea Rocco