Searcharxiv⌕ Search

arXiv subjects

Alessio Zaccone

Publications and source records attributed to Alessio Zaccone.

At least 19 recordsLinked to original sources
arXiv2026

When will androids outnumber humans?

Humanoid robots are increasingly discussed not only as machines but also as a potential technological population. We develop a nonlinear population-dynamical framework to examine their possible diffusion relative to humans, without assuming that large-scale adoption or numerical crossover is inevitable. The human population $H(t)$ is calibrated to the United Nations World Population Prospects 2024 median trajectory. The android population $A(t)$ is represented through the normalized stock $a=A/A_s$. A conventional, human-organized manufacturing and adoption channel is calibrated to a conditional scenario spanning approximately $10^4$ humanoids in 2025 to $10^9$ in 2050 and follows $\dot a=(q_M+r_Ma)\exp(K_Ma^γ)$. We separately introduce a hypothetical autonomous channel in which installed androids contribute materially to producing additional androids. Under the minimal canonical TZ closure, the corresponding production--feedback number is $\mathcal{P}(a)=(r_A/δ_A)\exp(K_Ra)$, where $r_A$ is the gross robot-mediated production coefficient, $δ_A$ the retirement rate, and $K_R$ the autonomous feedback parameter. This channel is locally self-amplifying if and only if $\mathcal{P}>1$, whereas numerical human--android parity, $A=H$, is a separate cumulative condition. Global uncertainty analysis shows that crossover dates remain strongly scenario-dependent, while the production--feedback threshold is more robust. An extreme early-autonomy stress test can produce parity by 2050, but this represents a conditional dynamical boundary rather than a technological forecast.

physics.soc-ph↗
arXiv2026

Nonlinear visco-elasto-plastic model for the stress-strain and stress-relaxation in metallic glass

We develop a nonlinear visco-elasto-plastic (VEP) model for the stress-strain response of metallic glasses by connecting the deformation dynamics with the material relaxation time obtained from independent stress-relaxation measurements. The material is modeled as a Maxwell-type element, with a nonlinear elastic spring and a stretched-exponential dashpot whose behavior is determined from the separate stress-relaxation data. The model captures the effects of temperature and strain rate on the initial elastic response, stress overshoot, post-yield softening, and steady flow. We independently determine the reference material-time function $X_0(\varepsilon)$ from the stress-relaxation response and the nonlinear material-time variable $X(\varepsilon)$ from the elastic-viscoplastic strain decomposition based on the stress-strain response. We introduce an Eyring-type function or material-time ratio $ϕ(\varepsilon)=X(\varepsilon)/X_0(\varepsilon)$ which quantifies the change of relaxation dynamics during nonlinear deformation. Our model provides a simple connection between structural relaxation and yielding in metallic glasses.

cond-mat.soft↗
arXiv2026

Ginzburg-Landau Theory with Elastic Incompatibility Describes the Liquid-G-phase-Crystal State Diagram

We derive a mechanically consistent Ginzburg-Landau theory for the metastable heterogeneous G state reported in deeply undercooled metallic liquids. The central result is that type-II-like mixed-state physics can emerge structurally with the random internal stress field playing the role of the magnetic field. Frozen eigenstrain due to elastic incompatibility between ordered cores and the amorphous matrix generates incompatible stress, while the non-affine internal strain in the liquid-like matrix in between the ordered cores relaxes that stress over a finite screening length $λ_σ$ (analogous to the London length in the superconducting problem). Structural order heals over a distinct mechanically-dressed length $ξ_G$; their ratio $κ_G=λ_σ/ξ_G$ provides the structural counterpart of the Ginzburg-Landau parameter. Because the matrix is transiently rigid yet locally relaxational only over an intermediate time window, the same mechanism selects crystal for slow protocols, a heterogeneous G state at intermediate rates, and a homogeneous L-like glass under rapid arrest. Residual incompatibility frustrates coarsening, allowing finite ordered cores and screened, orientation-dependent core interactions. The resulting texture is an inverted Abrikosov analogue: structural order resides in the cores, whereas incompatible-stress screening is carried by the surrounding disordered matrix. The theory yields direct simulation and experimental tests through stress-decay, structural-healing, non-affine-susceptibility, and kinetic measurements.

cond-mat.mtrl-sci↗
arXiv2026

Generalized Constraint-Controlled Rheological Model: Two Constitutive Pathways under Sinusoidal Periodic Shear Deformation

We formulate the Generalized Constraint-Controlled Rheological Model (GCCRM) for entangled linear and long-arm-branched polymer melts under sinusoidal periodic shear deformation (SPSD), spanning the linear and strongly nonlinear regimes. Molecular architecture, conformation, chain stretch, flow-active constraints, convective constraint release, dynamic tube dilation, and activated arm retraction define a common upstream molecular state. This state feeds two time-domain constitutive pathways (a configurational stress and a dissipative internal-variable stress) which are recombined before Fourier analysis. For branched polymers, the architecture is described by an entire backbone of molecular weight $M_{bb}$ and $N_a$ long arms of molecular weight $M_a$, with a compliance-weighted representative-constitutive-cell partition. The linear limit is normalized so that the configurational moduli sum to the entanglement modulus, while dynamic tube dilation and stretch drive distinct contributions to dissipative activation. Under reduced closures, GCCRM generates a smooth nonlinear elastic response with an onset of nonlinearity, an approximately logarithmic growth regime, an architecture-dependent maximum, and distinct high-deformation asymptotes. Fourier harmonics, ELR, VLR, and Lissajous curves are treated as post-processing observables of the total stress. The framework establishes a consistent constitutive architecture whose quantitative validation requires one parameter set per material across SPSD and, prospectively, transient shear histories.

cond-mat.soft↗
arXiv2026

Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields

The Generalized Langevin Equation (GLE) can be derived from a particle-bath Hamiltonian, in both classical and quantum dynamics, and provides a route to the (both Markovian and non-Markovian) fluctuation-dissipation theorem (FDT). All previous studies have focused either on particle-bath systems with time-independent external forces only, or on the simplified case where only the tagged particle is subject to the external time-dependent oscillatory field. Here we extend the GLE and the corresponding FDT for the more general case where both the tagged particle and the bath oscillators respond to an external oscillatory field. This is the example of a charged or polarisable particle immersed in a bath of other particles that are also charged or polarizable, under an external AC electric field. For this Hamiltonian, we find that the ensemble average of the stochastic force is not zero, but proportional to the AC field. The associated FDT reads as $\langle F_P(t)F_P(t')\rangle=mk_BTν(t-t')+(γe)^2E(t)E(t')$, where $F_{p}$ is the random force, $ν(t-t')$ is the friction memory function, and $γ$ is a numerical prefactor.

cond-mat.stat-mech↗
arXiv2026

Microscopic origin of the Baumgärtel-Schausberger-Winter Relaxation Spectrum in Polymer Melts and Particle Rafts

Entangled polymer melts exhibit the robust two-branch Baumgärtel-Schausberger-Winter (BSW) relaxation spectrum, while related spectra occur in nonpolymeric monodisperse disordered systems. In spite of the successful application of BSW to many different materials, a molecular derivation of these spectra is lacking. We construct a molecular theory in which a chain segment moves relative to a screened, dynamically responding multichain environment. Gaussian-chain preaveraging gives $M_{\rm seg}(Δm)\sim(Δm)^{-1/2}$, hence $λ_p\sim p^{3/2}$ and, after stress projection, $H(τ)\simτ^{-2/3}$. Independently, longitudinal primitive-path diffusion gives contour-length fluctuations with $H(τ)\simτ^{1/4}$. A molecular-weight-constrained implementation is tested simultaneously against experimental $G'(ω)$ and $G''(ω)$ data for four monodisperse polybutadiene (PBD) melts, without fitting spectral exponents or individual modal weights. The resulting BSW spectrum exhibits a continuous transfer from the fast cooperative to the slow constraint-renewal cascade before a finite-chain terminal edge. A common two-sector caged dynamics then connects polymers to particle rafts without assuming identical microscopic mechanisms.

cond-mat.soft↗
arXiv2026

Giant second-harmonic generation in few-atomic layer metals

Quantum confinement restructures the electronic phase space of ultrathin metals, but the resulting density-of-states (DOS) change is not generically large. We show that, within a three-dimensional confinement theory based on the suppression of long-wavelength electronic states, the Fermi-level DOS enhancement on the weak-confinement branch is bounded by $(4/3)^{1/3}-1\simeq10.1\%$. Instead, confinement-induced redistribution of electronic phase space can be strongly amplified by resonant denominators in the second-order susceptibility. A minimal double-resonance closure predicts giant amplification when the film thickness approaches $L_c=(2π/n)^{1/3}$, where $n$ is the carrier density, and a dominant optical pathway lies within a dephasing linewidth of resonance. Applied to recent Ag(111) measurements, the theory gives an effective phase-space carrier density parameter $n_{\rm eff}\simeq3.6\times10^{20}\,\mathrm{cm}^{-3}$, a tenfold enhancement of $|χ^{(2)}|$, and hence the observed $\sim100$-fold increase of thickness-normalized second-harmonic-generation efficiency, together with the observed non-oscillatory thickness dependence.

cond-mat.mes-hall↗
arXiv2026

Ginzburg-Landau Theory for Confined Thin-Film Superconductors

We develop a Ginzburg-Landau theory for superconducting thin films under quantum confinement. Starting from the Ginzburg-Landau theory and the recently developed confinement theory of metallic thin films, explicit analytical expressions are derived for the coherence length, penetration depth, electronic mean free path, and Ginzburg-Landau parameter in confined geometries. The central result is that quantum confinement directly renormalizes the intrinsic superconducting coherence length through confinement-induced modifications of the electronic density of states and Fermi energy. This effect is absent in conventional thin-film transport theories based solely on surface scattering. As a consequence, confinement simultaneously suppresses the coherence length and enhances the penetration depth, thereby driving superconductors toward stronger type-II behavior over a broad thickness range. The interplay between quantum confinement and disorder can also produce reentrant type-I/type-II crossovers. The theory predicts a crossover regime in which confinement-induced renormalization of superconducting length scales and transport scattering become strongly intertwined. Comparison with recent penetration-depth measurements in Al thin films shows that the observed enhancement of the penetration depth originates from the interplay between confinement-induced renormalization of the coherence length and suppression of the effective mean free path by surface and disorder scattering. The results establish a direct connection between quantum confinement and superconducting electrodynamics in confined metallic films.

cond-mat.supr-con↗
arXiv2026

The Trachenko-Zaccone equation: nonlinear relaxation from glasses to complex systems

The Trachenko-Zaccone equation provides a compact nonlinear dynamical framework for describing non-Debye relaxation in disordered condensed matter. Originally developed to rationalize stretched- and compressed-exponential relaxation in liquids and glasses from the dynamics of interacting local relaxation events, the same equation has subsequently appeared in broader contexts, including polymer relaxation and nonlinear models of global population dynamics. This review retraces the conceptual development of the equation, with particular emphasis on its physical origin in Kostya Trachenko's feed-forward interaction mechanism, its mathematical structure, and its possible generalizations. We also include personal recollections of the work with Kostya Trachenko at Queen Mary University of London in August 2019, during which the equation emerged in essentially its present form. After reviewing applications to stress relaxation, glassy materials, polymer relaxation and population dynamics, we discuss future directions including time-dependent feedback parameters, coupled order parameters, heterogeneous and spatially resolved formulations, flux terms, network versions and stochastic extensions. The central theme of the review is that the Trachenko-Zaccone equation should be viewed not only as a model of glassy relaxation, but as a general nonlinear feedback equation with potential applications across complex systems.

cond-mat.dis-nn↗
arXiv2026

Modeling the Fatigue Behavior of Amorphous Polymers

Prediction of material durability is both very important and very difficult. In many cases, material durability is measured by subjecting a sample to repeating oscillatory cycles (in shear or tension-compression) until it fails in either ductile or brittle fashion. Typically, the stress amplitude is denoted S, and the number of cycles N, so the resulting dependence is known as the SN-curve. For many materials, SN curve has been shown to obey the empirical Basquin's law, N = AS^(-m), where the prefactor A was a function of the temperature, load frequency, and sample history, and the power law m was a real number, usually between 3 and 12. Here, we derive the Basquin's law using a linearized version of the Long's plasticity model and demonstrate that within this framework, m = 3. We also derive the expression for the prefactor A. Finally, we show that our theory successfully describes experimental data for three amorphous polymers, PS, PMMA, and PVC.

cond-mat.mtrl-sci↗
arXiv2026

Microscopic constitutive theory of stress overshoot, yielding, and strain hardening in amorphous materials

We develop a microscopic constitutive theory for the nonlinear deformation of metallic and polymer glasses based on nonaffine elasticity coupled to irreversible many-body relaxation. The theory predicts the full stress--strain response, from linear elasticity through stress overshoot and yielding to steady plastic flow. We show that stress overshoot originates from the competition between a nonaffine elastic instability induced by strain-driven loss of mechanical connectivity at the atomic/molecular level, and viscous dissipation associated with structural relaxation. For polymer glasses, finite chain extensibility naturally accounts for strain hardening at large deformation. The stretched-exponential relaxation exponent is obtained independently from stress or modulus relaxation measurements and provides the primary dynamical input to the theory. Using a small set of physically meaningful parameters, the model quantitatively reproduces experimental stress--strain curves for metallic glasses, polycarbonate, PMMA, and epoxy resins over a broad range of strain rates. These results establish a unified microscopic framework linking relaxation dynamics, yielding, plastic flow, and strain hardening in amorphous solids.

cond-mat.soft↗
arXiv2026

Delayed Arm Retraction Controls the Nonlinear Oscillatory Response of Long-Chain-Branched Polymer Melts

Long-chain branching profoundly modifies the nonlinear oscillatory response of entangled polymer melts by introducing arm-retraction pathways absent in linear polymers. We present a molecular tube theory that explains the characteristic maximum of the Nonlinearity Index (NLI) observed experimentally in long-chain-branched polymers. The theory extends the recently developed nonlinear tube-orientation description of linear polymers by incorporating branch-point force transmission and delayed arm retraction. The backbone initially develops nonlinear orientation as in the corresponding linear polymer, whereas long-arm retraction subsequently relaxes the stored branch-point tension and progressively erases backbone orientational memory. This competition produces a characteristic NLI maximum followed by a post-peak decay. The theory predicts two distinct nonlinear regimes corresponding to sparse and dense long-chain branching and introduces an architecture parameter governing the height and width of the nonlinear peak. The resulting framework provides a molecular interpretation of nonlinear Fourier rheology and directly links the nonlinear harmonic response to polymer architecture.

cond-mat.soft↗
arXiv2026

The Physics of Topological Defects in Glasses

Topological defects play a central role in the mechanical behavior of crystalline materials, yet their relevance to amorphous solids has only recently begun to emerge. Over the last few years, theoretical, computational, and experimental studies have revealed the presence of well-defined topological invariants in vibrational eigenmodes, non-affine displacement fields, and deformation-induced vector fields of glasses. These defects have been shown to correlate strongly with soft spots, localized plastic rearrangements, yielding, and shear-band formation, suggesting a new perspective on the microscopic origins of plasticity in disordered materials. In this review, we provide a comprehensive overview of recent developments in the rapidly growing field of topological defects in glasses. We discuss the underlying theoretical concepts, including Burgers vectors, non-affine plasticity, vibrational modes, and topological invariants, and review recent numerical and experimental advances. Finally, we assess the current achievements, limitations, and open questions, and discuss future directions toward a unified topological description of plasticity and mechanical failure in amorphous solids.

cond-mat.dis-nn↗
arXiv2026

Electrical transport in ultra-thin films: from Fuchs-Sondheimer to quantum-confinement

Ultra-thin films are fundamental components of modern nanoelectronics, where reducing thickness to the few-nanometer scale leads to a dramatic increase in electrical resistivity. For decades, this behavior has been interpreted in terms of classical size effects, primarily surface scattering within the Fuchs--Sondheimer theory and grain-boundary scattering in the Mayadas--Shatzkes model. While these approaches successfully describe transport when the film thickness is comparable to the electronic mean free path, growing experimental evidence indicates that they become insufficient under extreme confinement. This review discusses the crossover from classical scattering to a quantum-confinement regime in which the electronic states available for transport are fundamentally restructured by finite size. We review the recently proposed reciprocal-space confinement theory, which predicts an exponential increase of resistivity with decreasing thickness at the nanoscale, and discuss how it can be combined with classical surface-scattering models to provide a unified description of ultra-thin metallic and semiconducting films. Finally, we summarize recent experimental evidence supporting this picture and discuss its implications for future nanoelectronic devices, nanoscale interconnects, and quantum transport under extreme spatial confinement.

cond-mat.mes-hall↗
arXiv2026

Thermal rectification due to phonon confinement in nanoparticles

We demonstrate that thermal rectification can arise at the contact between two spherical nanoparticles of identical material but different size due to the geometric confinement of phonons. This confinement suppresses long-wavelength phonons differently in differently sized particles and creates a size-dependent gap in the phonon density of states. This gives rise to direction-dependent heat transport even in perfectly homogeneous materials. We develop an analytical model based on phonon confinement and phonon ray-tracing in the Casimir regime and derive expressions for heat fluxes and rectification efficiency as functions of particle sizes and temperatures. The model predicts measurable rectification efficiencies for nanoparticles with radii of a few tens of nanometers, reaching fraction of percent at room temperature and much larger values at low temperatures. The proposed mechanism provides a straightforward and scalable route to thermal rectification in granular nanomaterials without requiring material heterogeneity or strong nonlinearities.

cond-mat.mes-hall↗
arXiv2026

Thermal Rectification from Size-Dependent Phonon Confinement in Nanoparticle Assemblies

Thermal insulation remains an important technological challenge across the vast number of applications, from living quarters to quantum technology. Here, we exploit the size-dependent modification of the phonon density of states arising from phonon confinement in nanoparticles to fabricate a simple phonon rectifier. The smaller of the two connected nanoparticles imposes stronger phonon confinement leading to rectifying phonon transport. This concept is extended to the macroscale by constructing two overlapping layers of differently sized nanoparticles, thereby realizing a macroscopic phonon diode. Following the localized heat deposition by laser light, the temperature profiles across a phonon-diode were measured by infrared imaging. Although the rectifying strength is moderate, the abundance of optimization possibilities makes this method promising for ultra-low volume thermal insulation at both the nano- and macroscale

cond-mat.mtrl-sci↗
arXiv2026

Constraint-Limited Tube Orientation of Entangled Polymers in Oscillatory Shear Deformation

We develop a molecularly motivated description of the nonlinear index (NLI) in oscillatory shear deformation of entangled polymers. The central assumption is that the shear component of the tube-orientation tensor cannot grow without bound. Convective constraint release (CCR), chain stretch, and tube dilation progressively reduce the number and lifetime of orientational constraints, but the maximum shear alignment of a tube segment is geometrically limited by $S_{xy}\leq 1/2$. This motivates a constraint-limited orientation closure in which the NLI first grows approximately with strain amplitude and then approaches the limiting value $\mathrm{NLI}_{\max}=3$ asymptotically rather than through an artificial cutoff. The same framework yields a molecular expression for the characteristic half-saturation strain $γ_s$, defined by $\mathrm{NLI}(γ_s)=3/2$, in terms of the entanglement number, oscillation frequency, and a critical number of remaining orientational constraints. We further derive architecture-dependent expressions for the nonlinear onset strain $γ_c$ for linear, sparsely long-chain-branched, and more regularly branched polymers. The resulting framework provides a compact bridge between Fourier harmonic analysis, CCR-based tube dynamics, and the progressive loss of orientational memory in highly deformed entangled polymer liquids.

cond-mat.soft↗
arXiv2026

Theory of distribution skewness effect on polydisperse random close packing

We investigate the random close packing density, $ϕ_\textrm{RCP}$, of polydisperse hard sphere systems using a theoretical framework based on the equilibrium model of crowding. We derive a closed-form solution for $ϕ_\textrm{RCP}$ in terms of the moments of the diameter distribution, enabling an analytical exploration of the effects of polydispersity ($δ$) and skewness ($S$) on packing density. For a binary mixture, it is possible to explore a broader range of dependence of $ϕ_\textrm{RCP}$ on $δ$ for a given $S$ or on $S$ for a given $δ$. We show that the dependencies of $ϕ_\textrm{RCP}$ on skewness for a variety of continuous distributions collapse onto a theoretical master curve obtained for the binary mixture case. By correcting the theory so that it obeys known exact limiting behaviours for extreme size asymmetry, our analytical predictions not only agree with previously obtained numerical results, but also predict previously unexplored regions of the $ϕ_\textrm{RCP}$ parameter space.

cond-mat.soft↗