arXiv subjects

Paolo Politi

Publications and source records attributed to Paolo Politi.

At least 55 records · Page 3Linked to original sources

arXiv2012

Coarsening scenarios in unstable crystal growth

Crystal surfaces may undergo thermodynamical as well kinetic, out-of-equilibrium instabilities. We consider the case of mound and pyramid formation, a common phenomenon in crystal growth and a long-standing problem in the field of pattern formation and coarsening dynamics. We are finally able to attack the problem analytically and get rigorous results. Three dynamical scenarios are possible: perpetual coarsening, interrupted coarsening, and no coarsening. In the perpetual coarsening scenario, mound size increases in time as L=t^n, where the coasening exponent is n=1/3 when faceting occurs, otherwise n=1/4.

cond-mat.stat-mech↗

arXiv2012

Disorder strength and field-driven ground state domain formation in artificial spin ice: experiment, simulation and theory

Quenched disorder affects how non-equilibrium systems respond to driving. In the context of artificial spin ice, an athermal system comprised of geometrically frustrated classical Ising spins with a two-fold degenerate ground state, we give experimental and numerical evidence of how such disorder washes out edge effects, and provide an estimate of disorder strength in the experimental system. We prove analytically that a sequence of applied fields with fixed amplitude is unable to drive the system to its ground state from a saturated state. These results should be relevant for other systems where disorder does not change the nature of the ground state.

cond-mat.mes-hall↗

arXiv2012

A network model for field and quenched disorder effects in artificial spin ice

We have performed a systematic study of the effects of field strength and quenched disorder on the driven dynamics of square artificial spin ice. We construct a network representation of the configurational phase space, where nodes represent the microscopic configurations and a directed link between node i and node j means that the field may induce a transition between the corresponding configurations. In this way, we are able to quantitatively describe how the field and the disorder affect the connectedness of states and the reversibility of dynamics. In particular, we have shown that for optimal field strengths, a substantial fraction of all states can be accessed using external driving fields, and this fraction is increased by disorder. We discuss how this relates to control and potential information storage applications for artificial spin ices.

cond-mat.mes-hall↗

arXiv2011

Diversity enabling equilibration: disorder and the ground state in artificial spin ice

We report a novel approach to the question of whether and how the ground state can be achieved in square artificial spin ices where frustration is incomplete. We identify two types of disorder: quenched disorder in the island response to fields and disorder in the sequence of driving fields. Numerical simulations show that quenched disorder can lead to final states with lower energy, and disorder in the driving fields always lowers the final energy attained by the system. We use a network picture to understand these two effects: disorder in island responses creates new dynamical pathways, and disorder in driving fields allows more pathways to be followed.

cond-mat.mes-hall↗

arXiv2011

Disorder regimes and equivalence of disorder types in artificial spin ice

The field-induced dynamics of artificial spin ice are determined in part by interactions between magnetic islands, and the switching characteristics of each island. Disorder in either of these affects the response to applied fields. Numerical simulations are used to show that disorder effects are determined primarily by the strength of disorder relative to inter-island interactions, rather than by the type of disorder. Weak and strong disorder regimes exist and can be defined in a quantitative way.

cond-mat.mes-hall↗

arXiv2011

Fractal characterization of rain-gauge networks and precipitations: an application in Central Italy

The measuring stations of a geophysical network are often spatially distributed in an inhomogeneous manner. The areal inhomogeneity can be well characterized by the fractal dimension D_H of the network, which is usually smaller than the euclidean dimension of the surface, this latter equal to 2. The resulting dimensional deficit, (2-D_H), is a measure of precipitating events which cannot be detected by the network. The aim of the present study is to estimate the fractal dimension of a rain-gauge network in Tuscany (Central Italy) and to relate its dimension to the dimensions of daily rainfall events detected by a mixed satellite/radar methodology. We find that D_H = 1.85, while typical summer precipitations are characterized by a dimension much greater than the dimensional deficit 0.15.

physics.ao-ph↗

arXiv2010

Small-scale behaviour in deterministic reaction models

In a recent paper published in this journal [J. Phys. A: Math. Theor. 42 (2009) 495004] we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power αof their distance and coalesce upon encounter. Numerics yielded a distribution function h(z) for the gap between neighbouring particles, with h(z)=z^{β(α)} for small z and β(α)>α. We can now prove analytically that in the strict limit of z\to 0, β=αfor α>0, corresponding to the mean-field result, and we compute the length scale where mean-field breaks down. More generally, in that same limit correlations are negligible for any similar reaction model where attractive forces diverge with vanishing distance. The actual meaning of the measured exponent β(α) remains an open question.

cond-mat.stat-mech↗

arXiv2010

Vertex dynamics in finite two dimensional square spin ices

Local magnetic ordering in artificial spin ices is discussed from the point of view of how geometrical frustration controls dynamics and the approach to steady state. We discuss the possibility of using a particle picture based on vertex configurations to interpret time evolution of magnetic configurations. Analysis of possible vertex processes allows us to anticipate different behaviors for open and closed edges and the existence of different field regimes. Numerical simulations confirm these results and also demonstrate the importance of correlations and long range interactions in understanding particle population evolution. We also show that a mean field model of vertex dynamics gives important insights into finite size effects.

cond-mat.stat-mech↗

arXiv2009

Deterministic reaction models with power-law forces

We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution function for the gap between neighbouring particles serves to discriminate between different laws of attraction. We develop an exact Fokker-Planck approach for the infinite hierarchy of distribution functions for multiple adjacent gaps and solve it exactly, at the mean-field level, where correlations are ignored. The crucial role of correlations and their effect on the gap distribution function is explored both numerically and analytically. Finally, we analyse a random input of particles, which results in a stationary state where the effect of correlations is largely diminished.

cond-mat.stat-mech↗

arXiv2009

Phase instability and coarsening in two dimensions

Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one dynamics prevails over the other is a longstanding problem, particularly beyond one dimension. It is shown that the challenge can be defied in two dimensions, using the concept of phase diffusion equation. We find that coarsening is related to the λ-dependence of a suitable phase diffusion coefficient, D_{11}(λ), depending on lattice symmetry and conservation laws. These results are exemplified analytically on prototypical nonlinear equations.

cond-mat.stat-mech↗

arXiv2008

Even-odd effects in finite Heisenberg spin chains

Magnetic superlattices and nanowires may be described as Heisenberg spin chains of finite length N, where N is the number of magnetic units (films or atoms, respectively). We study antiferromagnetically coupled spins which are also coupled to an external field H (superlattices) or to a ferromagnetic substrate (nanowires). The model is analyzed through a two-dimensional map which allows fast and reliable numerical calculations. Both open and closed chains have different properties for even and odd N (parity effect). Open chains with odd N are known [S.Lounis et al., Phys. Rev. Lett. 101, 107204 (2008)] to have a ferrimagnetic state for small N and a noncollinear state for large N. In the present paper, the transition length N_c is found analytically. Finally, we show that closed chains arrange themselves in the uniform bulk spin-flop state for even N and in nonuniform states for odd N.

cond-mat.mtrl-sci↗

arXiv2008

Comment on "Magnetism of Nanowires Driven by Novel Even-Odd Effects"

In a recent Letter, S. Lounis et al. find that the ground state of finite antiferromagnetic nanowires deposited on ferromagnets depends on the parity of the number N of atoms and that a collinear-noncollinear transition exists for odd N. Authors use ab initio results and a Heisenberg model, which is studied numerically with an iterative scheme. In this Comment we argue that the Heisenberg model can much easier be investigated in terms of a two-dimensional map, which allows to find an analytic expression for the transition length, a central result of Lounis et al. (see their Fig.3).

cond-mat.mtrl-sci↗

arXiv2008

From the conserved Kuramoto-Sivashinsky equation to a coalescing particles model

The conserved Kuramoto-Sivashinsky (CKS) equation, u_t = -(u+u_xx+u_x^2)_xx, has recently been derived in the context of crystal growth, and it is also strictly related to a similar equation appearing, e.g., in sand-ripple dynamics. We show that this equation can be mapped into the motion of a system of particles with attractive interactions, decaying as the inverse of their distance. Particles represent vanishing regions of diverging curvature, joined by arcs of a single parabola, and coalesce upon encounter. The coalescing particles model is easier to simulate than the original CKS equation. The growing interparticle distance \ell represents coarsening of the system, and we are able to establish firmly the scaling \ell(t) \sim \sqrt{t}. We obtain its probability distribution function, g(\ell), numerically, and study it analytically within the hypothesis of uncorrelated intervals, finding an overestimate at large distances. Finally, we introduce a method based on coalescence waves which might be useful to gain better analytical insights into the model.

cond-mat.stat-mech↗

arXiv2008

Stripe width and non-local domain walls in the two-dimensional Dipolar Frustrated Ising Ferromagnet

We describe a novel type of magnetic domain wall which, in contrast to Bloch or Neel walls, is non-localized and, in a certain temperature range, non-monotonic. The wall appears as the mean-field solution of the two-dimensional ferromagnetic Ising model frustrated by the long-ranged dipolar interaction. We provide experimental evidence of this wall delocalization in the stripe-domain phase of perpendicularly magnetized ultrathin magnetic films. In agreement with experimental results, we find that the stripe width decreases with increasing temperature and approaches a finite value at the Curie-temperature following a power law. The same kind of wall and a similar temperature dependence of the stripe width is expected in the mean-field approximation of the two-dimensional Coulomb frustrated Ising ferromagnet.

cond-mat.stat-mech↗

arXiv2006

Modified Kuramoto-Sivashinsky equation: stability of stationary solutions and the consequent dynamics

We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: \partial_x \tilde G(H_x). We find that the stability of steady states depends on dv/dq, the derivative of the interface velocity on the wavevector q of the steady state. If the standard nonlinearity vanishes, coarsening is possible, in principle, only if \tilde G is an odd function of H_x. In this case, the equation falls in the category of the generalized Cahn-Hilliard equation, whose dynamical behavior was recently studied by the same authors. Instead, if \tilde G is an even function of H_x, we show that steady-state solutions are not permissible.

cond-mat.stat-mech↗

arXiv2006

Single-domain versus two-domain configuration in thin ferromagnetic prisms

Thin ferromagnetic elements in the form of rectangular prisms are theoretically investigated in order to study the transition from single-domain to two-domain state, with changing the in-plane aspect ratio p. We address two main questions: first, how general is the transition; second, how the critical value p_c depends on the physical parameters. We use two complementary methods: discrete-lattice calculations and a micromagnetic continuum approach. Ultrathin films do not appear to split in two domains. Instead, thicker films may undergo the above transition. We have used the continuum approach to analyze recent Magnetic Force Microscopy observations in 30 nm-thick patterned Permalloy elements, finding a good agreement for p_c.

cond-mat.mtrl-sci↗

arXiv2006

Steady states of the conserved Kuramoto-Sivashinsky equation

Recent work on the dynamics of a crystal surface [T.Frisch and A.Verga, Phys. Rev. Lett. 96, 166104 (2006)] has focused the attention on the conserved Kuramoto-Sivashinsky (CKS) equation: \partial_t u = -\partial_{xx}(u+u_{xx}+u_x^2), which displays coarsening. For a quantitative and qualitative understanding of the dynamics, the analysis of steady states is particularly relevant. In this paper we provide a detailed study of the stationary solutions and their explicit form is given. Periodic configurations form an increasing branch in the space wavelength-amplitude (lambda-A), with d(lambda)/dA>0. For large wavelength, lambda=4\sqrt{A} and the orbits in phase space tend to a separatrix, which is a parabola. Steady states are found up to an additive constant a, which is set by the dynamics through the conservation law \partial_t =0: a(lambda(t))=lambda^2(t)/48.

cond-mat.stat-mech↗

arXiv2006

Asymptotic and effective coarsening exponents in surface growth models

We consider a class of unstable surface growth models, z_t = -\partial_x J, developing a mound structure of size lambda and displaying a perpetual coarsening process, i.e. an endless increase in time of lambda. The coarsening exponents n, defined by the growth law of the mound size lambda with time, lambda=t^n, were previously found by numerical integration of the growth equations [A. Torcini and P. Politi, Eur. Phys. J. B 25, 519 (2002)]. Recent analytical work now allows to interpret such findings as finite time effective exponents. The asymptotic exponents are shown to appear at so large time that cannot be reached by direct integration of the growth equations. The reason for the appearance of effective exponents is clearly identified.

cond-mat.stat-mech↗