arXiv subjects

Paolo Biscari

Publications and source records attributed to Paolo Biscari.

At least 19 recordsLinked to original sources

arXiv2026

Rejection-free Glauber Monte Carlo for the 2D Random Field Ising Model via Hierarchical Probabilistic Counters

We present an efficient Monte Carlo algorithm for the simulation of the two-dimensional Random Field Ising Model (RFIM). The method combines the event-driven, rejection-free character of the Bortz Kalos-Lebowitz (BKL) algorithm with Glauber transition probabilities, introducing hierarchical probabilistic counters to perform spin selection in O(log N) operations. This enables efficient sampling of the system's dynamics, especially in the low-temperature and low-disorder regime, where traditional Metropolis updates suffer from critical slowing down. Furthermore, this approach allows a proper dynamical simulation of the Ising system's behavior even in the presence of a Random Field (RF), unlike the BKL method. RFIM simulations with Gaussian field distributions reproduce the expected reduction of the pseudo-critical temperature with increasing disorder. Benchmarking shows speedups exceeding two orders of magnitude compared to the Metropolis algorithm in the low-temperature regime. The proposed method provides an efficient and dynamically faithful tool for studying both equilibrium and non-equilibrium phenomena in disordered spin systems.

cond-mat.stat-mech↗

arXiv2025

Reconstructive martensitic phase transitions: intermittency, anti-trasformation, plasticity, irreversibility

We study the mechanics of temperature-driven reconstructive martensitic transformations in crystalline materials, within the framework of nonlinear elasticity theory. We focus on the prototypical case of the square-hexagonal transition in 2D crystals, using a modular Ericksen-Landau-type strain energy whose infinite and discrete invariance group originates from the full symmetry of the underlying lattice. In the simulation of quasi-static thermally-driven transitions we confirm the role of the valley-floor network in establishing the strain-field transition-pathways on the symmetry-moulded strain energy landscape of the crystal. We also observe the phase change to progress through abrupt microstructure reorganization via strain avalanching under the slow driving. We reveal at the same time the presence of assisting anti-transformation activity, which locally goes against the overall transition course. Both transformation and anti-transformation avalanches exhibit Gutenberg-Richter like heavy-tailed size statistics. A parallel analysis shows agreement of these numerical results with their counterparts in empirical observations on temperature-induced martensitic transformations. The simulation furthermore shows that, in the present case of a reconstructive transformation, strain avalanching mostly involves lattice-invariant shears (LIS). As a consequence, microstructure evolution is accompanied by slip-induced defect nucleation and movement in the lattice. LIS activity also leads to the development of polycrystal grain-like lattice-homogeneity domains exhibiting high boundary segmentation in the body. All these effects ultimately lead to transformation irreversibility.

cond-mat.mtrl-sci↗

arXiv2024

Inter-Event Time Power Laws in Heterogeneous Systems

We investigate the dynamic behavior of spin reversal events in the dilute Ising model, focusing on the influence of static disorder introduced by pinned spins. Our Monte Carlo simulations reveal that in a homogeneous, defect-free system, the inter-event time (IET) between local spin flips follows an exponential distribution, characteristic of Poissonian processes. However, in heterogeneous systems where defects are present, we observe a significant departure from this behavior. At high temperatures, the IET exhibits a power-law distribution resulting from the interplay of spins located in varying potential environments, where defect density influences reversal probabilities. At low temperatures, all site classes converge to a unique power-law distribution, regardless of their potential, leading to distinct critical exponents for the high- and low-temperature regimes. This transition from exponential to power-law behavior underscores the critical response features of magnetic systems with defects, suggesting analogies to glassy dynamics. Our findings highlight the complex mechanisms governing spin dynamics in disordered systems, with implications for understanding the universal aspects of relaxation in glassy materials.

cond-mat.stat-mech↗

arXiv2023

Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects

We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter. By doing so, we demonstrate that the inclusion of quenched defects lowers the dynamic critical temperature as well, with a linear trend across the range of defect fractions considered. We also explore if and how it is possible to predict the dynamic behavior of specific magnetic systems with quenched randomness. Various geometric quantities, such as a defect potential index, the defect dipole moment, and the properties of the defect Delaunay triangulation, prove useful for this purpose.

cond-mat.stat-mech↗

arXiv2022

Finite-temperature avalanches in 2D disordered Ising models

We study the qualitative and quantitative properties of the Barkhausen noise emerging at finite temperatures in random Ising models. The random-bond Ising Model is studied with a Wolff cluster Monte-Carlo algorithm to monitor the avalanches generated by an external driving magnetic field. Satisfactory power-law distributions are found which expand over five decades, with a temperature-dependent critical exponent which matches the existing experimental measurements. We also focus on a Ising system in which a finite fraction of defects is quenched. Also the presence of defects proves able to induce a critical response to a slowly oscillating magnetic field, though in this case the critical exponent associated with the distributions obtained with different defect fractions and temperatures seems to belong to the same universality class, with a critical exponent equal to 1.

cond-mat.stat-mech↗

arXiv2022

Ericksen-Landau Modular Strain Energies for Reconstructive Phase Transformations in 2D crystals

By using modular functions on the upper complex half-plane, we study a class of strain energies for crystalline materials whose global invariance originates from the full symmetry group of the underlying lattice. This follows Ericksen's suggestion which aimed at extending the Landau-type theories to encompass the behavior of crystals undergoing structural phase transformation, with twinning, microstructure formation, and possibly associated plasticity effects. Here we investigate such Ericksen-Landau strain energies for the modelling of reconstructive transformations, focusing on the prototypical case of the square-hexagonal phase change in 2D crystals. We study the bifurcation and valley-floor network of these potentials, and use one in the simulation of a quasi-static shearing test. We observe typical effects associated with the micro-mechanics of phase transformation in crystals, in particular, the bursty progression of the structural phase change, characterized by intermittent stress-relaxation through microstructure formation, mediated, in this reconstructive case, by defect nucleation and movement in the lattice.

cond-mat.mtrl-sci↗

arXiv2022

The Effect of Defects on Magnetic Droplet Nucleation

Defects and impurities strongly affect the timing and the character of the (re)ordering or disordering transitions of thermodynamic systems captured in metastable states. In this paper we analyze the case of two-dimensional magnetic systems. We adapt the classical JMAK theory to account for the effects of defects on the free energy barriers, the critical droplet area and the associated metastable time. The resulting predictions are successfully tested against the Monte-Carlo simulations performed by adopting Glauber dynamics, to obtain reliable time-dependent results during the out-of-equilibrium transformations. We also focus on finite-size effects, and study how the spinodal line (separating the singledroplet from the multi-droplet regime) depends on the system size, the defect fraction, and the external field.

cond-mat.stat-mech↗

arXiv2021

Temperature-dependent criticality in random 2D Ising models

We consider 2D random Ising ferromagnetic models, where quenched disorder is represented either by random local magnetic fields (Random Field Ising Model) or by a random distribution of interaction couplings (Random Bond Ising Model). In both cases we first perform zero- and finite-temperature Monte-Carlo simulations to determine how the critical temperature depends on the disorder parameter. We then focus on the reversal transition triggered by an external field, and study the associated Barkhausen noise. Our main result is that the critical exponents characterizing the power-law associated with the Barkhausen noise exhibit a temperature dependence in line with existing experimental observations.

cond-mat.dis-nn↗

arXiv2020

Crystal elasto-plasticity on the Poincaré half-plane

We explore the nonlinear variational modelling of two-dimensional (2D) crystal plasticity based on strain energies which are invariant under the full symmetry group of 2D lattices. We use a natural parameterization of strain space via the upper complex Poincaré half-plane. This transparently displays the constraints imposed by lattice symmetry on the energy landscape. Quasi-static energy minimization naturally induces bursty plastic flow and shape change in the crystal due to the underlying coordinated basin-hopping local strain activity. This is mediated by the nucleation, interaction, and annihilation of lattice defects occurring with no need for auxiliary hypotheses. Numerical simulations highlight the marked effect of symmetry on all these processes. The kinematical atlas induced by symmetry on strain space elucidates how the arrangement of the energy extremals and the possible bifurcations of the strain-jump paths affect the plastification mechanisms and defect-pattern complexity in the lattice.

cond-mat.mtrl-sci↗

arXiv2016

Liquid relaxation: A new Parodi-like relation for nematic liquid crystals

We put forward a hydrodynamic theory of nematic liquid crystals that includes both anisotropic elasticity and dynamic relaxation. Liquid remodeling is encompassed through a continuous update of the shear-stress free configuration. The low-frequency limit of the dynamical theory reproduces the classical Ericksen-Leslie theory, but it predicts two independent identities between the six Leslie viscosity coefficients. One replicates Parodi's relation, while the other-which involves five Leslie viscosities in a nonlinear way-is new. We discuss its significance, and we test its validity against evidence from physical experiments, independent theoretical predictions, and molecular-dynamics simulations.

cond-mat.soft↗

arXiv2015

Intermittency in crystal plasticity informed by lattice symmetry

We develop a nonlinear, three-dimensional phase field model for crystal plasticity which accounts for the infinite and discrete symmetry group G of the underlying periodic lattice. This generates a complex energy landscape with countably-many G-related wells in strain space, whereon the material evolves by energy minimization under the loading through spontaneous slip processes inducing the creation and motion of dislocations without the need of auxiliary hypotheses. Multiple slips may be activated simultaneously, in domains separated by a priori unknown free boundaries. The wells visited by the strain at each position and time, are tracked by the evolution of a G-valued discrete plastic map, whose non-compatible discontinuities identify lattice dislocations. The main effects in the plasticity of crystalline materials at microscopic scales emerge in this framework, including the long-range elastic fields of possibly interacting dislocations, lattice friction, hardening, band-like vs. complex spatial distributions of dislocations. The main results concern the scale-free intermittency of the flow, with power-law exponents for the slip avalanche statistics which are significantly affected by the symmetry and the compatibility properties of the activated fundamental shears.

cond-mat.mtrl-sci↗

arXiv2015

Strain intermittency in shape-memory alloys

We study experimentally the intermittent progress of the mechanically induced martensitic transformation in a Cu-Al-Be single crystal through a full-field measurement technique: the grid method. We utilize an in- house, specially designed gravity-based device, wherein a system controlled by water pumps applies a perfectly monotonic uniaxial load through very small force increments. The sample exhibits hysteretic superelastic behavior during the forward and reverse cubic-monoclinic transformation, produced by the evolution of the strain field of the phase microstructures. The in-plane linear strain components are measured on the sample surface during the loading cycle, and we characterize the strain intermittency in a number of ways, showing the emergence of power-law behavior for the strain avalanching over almost six decades of magnitude. We also describe the nonstationarity and the asymmetry observed in the forward versus reverse transformation. The present experimental approach, which allows for the monitoring of the reversible martensitic transformation both locally and globally in the crystal, proves useful and enhances our capabilities in the analysis and possible control of transition-related phenomena in shape-memory alloys.

cond-mat.mtrl-sci↗

arXiv2015

Encasement as a morphogenetic mechanism: The case of bending

We study how the encasement of a growing elastic bulk within a possibly differently growing elastic coat may induce mechanical instabilities in the equilibrium shape of the combined body. The inhomogeneities induced in an incompressible bulk during growth are also discussed. These effects are illustrated through a simple example in which a growing elastic cylinder may undergo a shape transition towards a bent configuration.

cond-mat.soft↗

arXiv2014

Anisotropic wave propagation in nematic liquid crystals

Despite the fact that quantitative experimental data have been available for more than forty years now, nematoacoustics still poses intriguing theoretical and experimental problems. In this paper, we prove that the main observed features of acoustic wave propagation through a nematic liquid crystal cell -- namely, the anisotropy of sound velocity and its frequency dependence -- may be plausibly explained by a first-gradient continuum theory characterized by a hyperelastic anisotropic response from an evolving relaxed configuration. We compare and contrast our proposal with a competing theory where the liquid crystal is modeled as an isotropically compressible, anisotropic second-gradient fluid.

cond-mat.soft↗

arXiv2006

Bulk and surface biaxiality in nematic liquid crystals

Nematic liquid crystals possess three different phases: isotropic, uniaxial, and biaxial. The ground state of most nematics is either isotropic or uniaxial, depending on the external temperature. Nevertheless, biaxial domains have been frequently identified, especially close to defects or external surfaces. In this paper we show that any spatially-varying director pattern may be a source of biaxiality. We prove that biaxiality arises naturally whenever the symmetric tensor $\Sb=(\grad \nn)(\grad \nn)^T$ possesses two distinct nonzero eigenvalues. The eigenvalue difference may be used as a measure of the expected biaxiality. Furthermore, the corresponding eigenvectors indicate the directions in which the order tensor \QQ is induced to break the uniaxial symmetry about the director \nn. We apply our general considerations to some examples. In particular we show that, when we enforce homeotropic anchoring on a curved surface, the order tensor become biaxial along the principal directions of the surface. The effect is triggered by the difference in surface principal curvatures.

cond-mat.soft↗

arXiv2006

Boundary-roughness effects in nematic liquid crystals

We study the equilibrium configuration of a nematic liquid crystal bounded by a rough surface. The wrinkling of the surface induces a partial melting in the degree of orientation. This softened region penetrates the bulk up to a length scale which turns out to coincide with the characteristic wave length of the corrugation. Within the boundary layer where the nematic degree of orientation decreases, the tilt angle steepens and gives rise to a nontrivial structure, that may be interpreted in terms of an effective weak anchoring potential. We determine how the effective surface extrapolation length is related to the microscopic anchoring parameters. We also analyze the crucial role played by the boundary conditions assumed on the degree of orientation. Quite different features emerge depending on whether they are Neumann- or Dirichlet-like. These features may be useful to ascertain experimentally how the degree of orientation interacts with an external boundary.

cond-mat.soft↗

arXiv2004

Field-induced motion of nematic disclinations

An individual defect in a nematic liquid crystal moves not only in response to its interaction with other defects but also in response to an external field. We analyze the motion of a wedge disclination in the presence of an applied field of strength $H$. We neglect backflow and seek steadily travelling patterns. The stationary picture yields a semi-infinite wall of strength $π$, bounded by the defect line. We find that the disclination advances into the region containing the wall at velocity $v(H)$, where $v$ scales as $H/|\log H|$ as long as the magnetic coherence length is greater than the core radius. When the external field is applied in the presence of a pair of disclinations, their dynamics is strongly influenced. We compute the expected relative velocity of the disclinations as a function of distance and field. The natural tendency for the disclinations to annihilate each other can be overcome by a sufficiently strong field suitably directed.

cond-mat.soft↗

arXiv2004

Telephone-cord instabilities in thin smectic capillaries

Telephone-cord patterns have been recently observed in smectic liquid crystal capillaries. In this paper we analyse the effects that may induce them. As long as the capillary keeps its linear shape, we show that a nonzero chiral cholesteric pitch favors the SmA*-SmC* transition. However, neither the cholesteric pitch nor the presence of an intrinsic bending stress are able to give rise to a curved capillary shape. The key ingredient for the telephone-cord instability is spontaneous polarization. The free energy minimizer of a spontaneously polarized SmA* is attained on a planar capillary, characterized by a nonzero curvature. More interestingly, in the SmC* phase the combined effect of the molecular tilt and the spontaneous polarization pushes towards a helicoidal capillary shape, with nonzero curvature and torsion.

cond-mat.soft↗