arXiv subjects

Alberto Rosso

Publications and source records attributed to Alberto Rosso.

At least 91 records · Page 5Linked to original sources

arXiv2016

Pickands' constant at first order in an expansion around Brownian motion

In the theory of extreme values of Gaussian processes, many results are expressed in terms of the Pickands constant $\mathcal{H}_α$. This constant depends on the local self-similarity exponent $α$ of the process, i.e. locally it is a fractional Brownian motion (fBm) of Hurst index $H=α/2$. Despite its importance, only two values of the Pickands constant are known: ${\cal H}_1 =1$ and ${\cal H}_2=1/\sqrtπ$. Here, we extend the recent perturbative approach to fBm to include drift terms. This allows us to investigate the Pickands constant $\mathcal{H}_α$ around standard Brownian motion ($α=1$) and to derive the new exact result $\mathcal{H}_α=1 - (α-1) γ_{\rm E} + \mathcal{O}\!\left( α-1\right)^{2}$.

cond-mat.stat-mech↗

arXiv2016

Scaling Description of Non-Local Rheology

Non-locality is crucial to understand the plastic flow of an amorphous material, and has been successfully described by the fluidity, along with a cooperativity length scale ξ. We demonstrate, by applying the scaling hypothesis to the yielding transition, that non-local effects in non-uniform stress configurations can be explained within the framework of critical phenomena. From the scaling description, scaling relations between different exponents are derived, and collapses of strain rate profiles are made both in shear driven and pressure driven flow. We find that the cooperative length in non-local flow is governed by the same correlation length in finite dimensional homogeneous flow, excluding the mean field exponents. We also show that non-locality also affects the finite size scaling of the yield stress, especially the large finite size effects observed in pressure driven flow. Our theoretical results are nicely verified by the elasto-plastic model, and experimental data.

cond-mat.soft↗

arXiv2016

Occupation time statistics of the random acceleration model

The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation time and related properties are non-trivial and not yet completely understood. In this paper we consider the occupation time $T_+$ of the one-dimensional random acceleration model on the positive half-axis. We calculate the first two moments of $T_+$ analytically and also study the statistics of $T_+$ with Monte Carlo simulations. One goal of our work was to ascertain whether the occupation time $T_+$ and the time $T_m$ at which the maximum of the process is attained are statistically equivalent. For regular Brownian motion the distributions of $T_+$ and $T_m$ coincide and are given by Lévy's arcsine law. We show that for randomly accelerated motion the distributions of $T_+$ and $T_m$ are quite similar but not identical. This conclusion follows from the exact results for the moments of the distributions and is also consistent with our Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2016

Nuclear Magnetic Resonance studies of DNP-ready trehalose obtained by solid state mechanochemical amorphization

$^1$H nuclear spin-lattice relaxation and Dynamic Nuclear Polarization (DNP) have been studied in amorphous samples of trehalose sugar doped with TEMPO radicals by means of mechanical milling, in the 1.6 K $÷$ 4.2 K temperature range. The radical concentration was varied between 0.34 and 0.81 $\%$. The highest polarization of 15 \% at 1.6 K, observed in the sample with concentration $0.50 \%$, is of the same order of magnitude of that reported in standard frozen solutions with TEMPO. The temperature and concentration dependence of the spin-lattice relaxation rate $1/T_{\text{1}}$, dominated by the coupling with the electron spins, were found to follow power laws with an exponent close to $3$ in all samples. The observed proportionality between $1/T_{\text{1}}$ and the polarization rate $1/T_{\text{pol}}$, with a coefficient related to the electron polarization, is consistent with the presence of Thermal Mixing (TM) and a good contact between the nuclear and the electron spins. At high electron concentration additional relaxation channels causing a decrease in the nuclear polarization must be considered. These results provide further support for a more extensive use of amorphous DNP-ready samples, obtained by means of comilling, in dissolution DNP experiments and possibly for $\textit{in vivo}$ metabolic imaging.

cond-mat.soft↗

arXiv2016

Thermalization and many-body localization in systems under dynamic nuclear polarization

We study the role of dipolar interactions in the standard protocol used to achieve dynamic nuclear polarization (DNP). In the so-called spin-temperature regime, where the interactions establish an effective thermodynamic behavior in the out-of-equilibrium stationary state, we provide numerical predictions for the level of hyperpolarization. We show that nuclear spins equilibrate to the effective spin-temperature established among the electron spins of radicals, as expected from the quantum theory of thermalization. Moreover, we present an analytical technique to estimate the spin temperature, and thus, the nuclear hyperpolarization in the steady state, as a function of interaction strength and quenched disorder. This reproduces both our numerical data and experimental results. Our central finding is that the nuclear hyperpolarization increases steadily upon reducing the interaction strength (by diluting the radical density). Interestingly, the highest polarization is reached at a point where the establishment of a spin temperature is just about to break down due to the incipient many-body localization transition in the electron spin system.

cond-mat.str-el↗

arXiv2015

Extreme value statistics of 2d Gaussian Free Field: effect of finite domains

We study minima statistics of the 2d Gaussian Free Field on circles in the unit disk with Dirichlet boundary condition. Free energy distributions of the associated Random Energy models are exactly calculated in the high temperature phase, and shown to satisfy the duality property, which enables us to predict the minima distribution by assuming the freezing scenario. Numerical tests are provided. Related questions concerning the GFF on a sphere are also considered.

cond-mat.stat-mech↗

arXiv2015

Criticality in the approach to failure in amorphous solids

Failure of amorphous solids is fundamental to various phenomena, including landslides and earthquakes. Recent experiments indicate that highly plastic regions form elongated structures that are especially apparent near the maximal shear stress $Σ_{\max}$ where failure occurs. This observation suggested that $Σ_{\max}$ acts as a critical point where the length scale of those structures diverges, possibly causing macroscopic transient shear bands. Here we argue instead that the entire solid phase ($Σ<Σ_{\max}$) is critical, that plasticity always involves system-spanning events, and that their magnitude diverges at $Σ_{\max}$ independently of the presence of shear bands. We relate the statistics and fractal properties of these rearrangements to an exponent $θ$ that captures the stability of the material, which is observed to vary continuously with stress, and we confirm our predictions in elastoplastic models.

cond-mat.soft↗

arXiv2015

The critical catastrophe revisited

The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to absorption events. When the reactor is operated at the critical point, and fissions are exactly compensated by absorptions, the whole neutron population might in principle go to extinction because of the wild fluctuations induced by births and deaths. This phenomenon, which has been named critical catastrophe, is nonetheless never observed in practice: feedback mechanisms acting on the total population, such as human intervention, have a stabilizing effect. In this work, we revisit the critical catastrophe by investigating the spatial behaviour of the fluctuations in a confined geometry. When the system is free to evolve, the neutrons may display a wild patchiness (clustering). On the contrary, imposing a population control on the total population acts also against the local fluctuations, and may thus inhibit the spatial clustering. The effectiveness of population control in quenching spatial fluctuations will be shown to depend on the competition between the mixing time of the neutrons (i.e., the average time taken for a particle to explore the finite viable space) and the extinction time.

cond-mat.stat-mech↗

arXiv2015

Frictional dynamics of viscoelastic solids driven on a rough surface

We study the effect of viscoelastic dynamics on the frictional properties of a (mean field) spring-block system pulled on a rough surface by an external drive. When the drive moves at constant velocity V, two dynamical regimes are observed: at fast driving, above a critical threshold Vc, the system slides at the drive velocity and displays a friction force with velocity weakening. Below Vc the steady sliding becomes unstable and a stick-slip regime sets in. In the slide-hold-slide driving protocol, a peak of the friction force appears after the hold time and its amplitude increases with the hold duration. These observations are consistent with the frictional force encoded phenomenologically in the rate-and-state equations. Our model gives a microscopical basis for such macroscopic description.

cond-mat.stat-mech↗

arXiv2015

Dynamic nuclear polarization and the paradox of Quantum Thermalization

Dynamic Nuclear Polarization (DNP) is to date the most effective technique to increase the nuclear polarization up to a factor $100,000$ opening disruptive perspectives for medical applications. In DNP, the nuclear spins are driven to an - out of equilibrium - hyperpolarized state by microwave saturation of the electron spins in interaction with them. Here we show that the electron dipolar interactions compete with the local magnetic fields resulting in two distinct dynamical phases: for strong interactions the electron spins equilibrate to an extremely low effective temperature that boosts DNP efficiency. For weak interaction this spin temperature is not defined and the polarization profile has an 'hole burning' shape characteristic of the non interacting case. The study of the many-body eigenstates reveals that these two phases are intimately related to the problem of thermalization in closed quantum systems where breaking of ergodicity is expected varying the strength of the interactions.

cond-mat.str-el↗

arXiv2015

Viscoelastic Effects in Avalanche Dynamics: A Key to Earthquake Statistics

In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the inter-avalanche periods, and thus miss basic features observed in some real systems. We address this issue by studying a model with viscoelastic relaxation, showing how coherent oscillations of the stress field can emerge spontaneously. Remarkably, these oscillations generate avalanche patterns that are similar to those observed in seismic phenomena.

cond-mat.stat-mech↗

arXiv2015

Conformal invariance of loop ensembles under Kardar-Parisi-Zhang dynamics

We study scaling properties of the honeycomb fully packed loop ensemble associated with a lozenge tiling model of rough surface, when the latter is driven out of equilibrium by Kardar-Parisi-Zhang (KPZ) type dynamics. We show numerically that conformal invariance and signatures of critical percolation appear in the stationary KPZ state. In terms of the two-component Coulomb gas description of the Edwards-Wilkinson stationary state, our finding is understood as the invariance of one component under the effect of the non-linear KPZ term. On the other hand, we show a breaking of conformal invariance when the level lines of the other component are considered.

cond-mat.stat-mech↗

arXiv2015

Role of the glassy dynamics and thermal mixing in the dynamic nuclear polarization and relaxation mechanisms of pyruvic acid

The temperature dependence of $^1$H and $^{13}$C nuclear spin-lattice relaxation rate $1/T_1$ has been studied in the 1.6 K - 4.2 K temperature range in pure pyruvic acid and in pyruvic acid containing trityl radicals at a concentration of 15 mM. The temperature dependence of $1/T_1$ is found to follow a quadratic power law for both nuclei in the two samples. Remarkably the same temperature dependence is displayed also by the electron spin-lattice relaxation rate $1/T_{1e}$ in the sample containing radicals. These results are explained by considering the effect of the structural dynamics on the relaxation rates in pyruvic acid. Dynamic nuclear polarization experiments show that below 4 K the $^{13}$C build up rate scales with $1/T_{\text{1e}}$, in analogy to $^{13}$C $1/T_1$ and consistently with a thermal mixing scenario where all the electrons are collectively involved in the dynamic nuclear polarization process and the nuclear spin reservoir is in good thermal contact with the electron spin system.

cond-mat.soft↗

arXiv2014

Scaling description of the yielding transition in soft amorphous solids at zero temperature

Yield stress materials flow if a sufficiently large shear stress is ap- plied. Although such materials are ubiquitous and relevant for indus- try, there is no accepted microscopic description of how they yield, even in the simplest situations where temperature is negligible and where flow inhomogeneities such as shear bands or fractures are ab- sent. Here we propose a scaling description of the yielding transition in amorphous solids made of soft particles at zero temperature. Our description makes a connection between the Herschel-Bulkley expo- nent characterizing the singularity of the flow curve near the yield stress Σc, the extension and duration of the avalanches of plasticity observed at threshold, and the density P(x) of soft spots, or shear transformation zones, as a function of the stress increment x be- yond which they yield. We argue that the critical exponents of the yielding transition can be expressed in terms of three independent exponents θ, df and z, characterizing respectively the density of soft spots, the fractal dimension of the avalanches, and their duration. Our description shares some similarity with the depinning transition that occurs when an elastic manifold is driven through a random potential, but also presents some striking differences. We test our arguments in an elasto-plastic model, an automaton model similar to those used in depinning, but with a different interaction kernel, and find satisfying agreement with our predictions both in two and three dimensions.

cond-mat.soft↗

arXiv2014

Revisiting Directed Polymers with heavy-tailed disorder

In this mostly numerical study, we revisit the statistical properties of the ground state of a directed polymer in a $d=1+1$ "hilly" disorder landscape, i.e. when the quenched disorder has power-law tails. When disorder is Gaussian, the polymer minimizes its total energy through a collective optimization, where the energy of each visited site only weakly contributes to the total. Conversely, a hilly landscape forces the polymer to distort and explore a larger portion of space to reach some particularly deep energy sites. As soon as the fifth moment of the disorder diverges, this mechanism radically changes the standard "KPZ" scaling behaviour of the directed polymer, and new exponents prevail. After confirming again that the Flory argument accurately predicts these exponent in the tail-dominated phase, we investigate several other statistical features of the ground state that shed light on this unusual transition and on the accuracy of the Flory argument. We underline the theoretical challenge posed by this situation, which paradoxically becomes even more acute above the upper critical dimension.

cond-mat.dis-nn↗

arXiv2014

Diffusion in periodic, correlated random forcing landscapes

We study the dynamics of a Brownian particle in a strongly correlated quenched random potential defined as a periodically-extended (with period $L$) finite trajectory of a fractional Brownian motion with arbitrary Hurst exponent $H \in (0,1)$. While the periodicity ensures that the ultimate long-time behavior is diffusive, the generalised Sinai potential considered here leads to a strong logarithmic confinement of particle trajectories at intermediate times. These two competing trends lead to dynamical frustration and result in a rich statistical behavior of the diffusion coefficient $D_L$: Although one has the typical value $D^{\rm typ}_L \sim \exp(-βL^H)$, we show via an exact analytical approach that the positive moments ($k>0$) scale like $\langle D^k_L \rangle \sim \exp{[-c' (k βL^{H})^{1/(1+H)}]}$, and the negative ones as $\langle D^{-k}_L \rangle \sim \exp(a' (k βL^{H})^2)$, $c'$ and $a'$ being numerical constants and $β$ the inverse temperature. These results demonstrate that $D_L$ is strongly non-self-averaging. We further show that the probability distribution of $D_L$ has a log-normal left tail and a highly singular, one-sided log-stable right tail reminiscent of a Lifshitz singularity.

cond-mat.stat-mech↗

arXiv2014

Clustering of branching Brownian motions in confined geometries

We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry. Such systems are widespread in physics and biology and apply for instance to the study of neutron populations in nuclear reactors and the dynamics of bacterial colonies, only to name a few. The fluctuations affecting the number of individuals in space and time may lead to a strong patchiness, with particles clustered together. We show that the analysis of this peculiar behaviour can be rather easily carried out by resorting to a backward formalism based on the Green's function, which allows the key physical observables, namely, the particle concentration and the pair correlation function, to be explicitly derived.

cond-mat.stat-mech↗

arXiv2014

Relevance of electron spin dissipative processes to dynamic nuclear polarization via thermal mixing

The available theoretical approaches aiming at describing Dynamic Nuclear spin Polarization (DNP) in solutions containing molecules of biomedical interest and paramagnetic centers are not able to model the behaviour observed upon varying the concentration of trityl radicals or the polarization enhancement caused by moderate addition of gadolinium complexes. In this manuscript, we first show experimentally that the nuclear steady state polarization reached in solutions of pyruvic acid with 15 mM trityl radicals is substantially independent from the average internuclear distance. This evidences a leading role of electron (over nuclear) spin relaxation processes in determining the ultimate performances of DNP. Accordingly, we have devised a variant of the Thermal Mixing model for inhomogenously broadened electron resonance lines which includes a relaxation term describing the exchange of magnetic anisotropy energy of the electron spin system with the lattice. Thanks to this additional term, the dependence of the nuclear polarization on the electron concentration can be properly accounted for. Moreover, the model predicts a strong increase of the final polarization on shortening the electron spin-lattice relaxation time, providing a possible explanation for the effect of gadolinium doping.

cond-mat.stat-mech↗