arXiv subjects

Kostya Trachenko

Publications and source records attributed to Kostya Trachenko.

At least 19 recordsLinked to original sources

arXiv2025

Global population crisis scenarios predicted by a general nonlinear dynamical model

We show that a simple nonlinear differential equation (originally studied in the physics of disordered systems) is able to mathematically describe the global population growth over the past 12000 years. Different regimes of population growth since the early Neolithic until today are shown to be all solutions to the same nonlinear differential equation in its various limits. These also include the well-known Malthus (exponential) and Verhulst (logistic) growth regimes, as well as von Foerster's ``doomsday'' formula. All these limits correspond to neglecting higher-order terms in a more general nonlinear dynamic model described by the proposed nonlinear differential equation. While the older models may provide valid fittings to limited time intervals in the global population growth curve in time, their clearly approximate nature prevents them from being predictive over longer periods of time. The proposed comprehensive solution of the proposed model is instead well suited to provide predictions for future scenarios. These include a scenario where the global population could halve as early as 2064 under a deliberately conservative, worst-case assumption that carrying-capacity constraints become abruptly active today.

q-bio.PE↗

arXiv2024

Thermodynamics and transport in molten chloride salts and their mixtures

Molten salts are important in a number of energy applications, but the fundamental mechanisms operating in ionic liquids are poorly understood, particularly at higher temperatures. This is despite their candidacy for deployment in solar cells, next-generation nuclear reactors, and nuclear pyroprocessing. We perform extensive molecular dynamics simulations over a variety of molten chloride salt compositions at varying temperature and pressures to calculate the thermodynamic and transport properties of these liquids. Using recent developments in the theory of liquid thermophysical properties, we interpret our results on the basis of collective atomistic dynamics (phonons). We find that the properties of ionic liquids well explained by their collective dynamics, as in simple liquids. In particular, we relate the decrease of heat capacity, viscosity, and thermal conductivity to the loss of transverse phonons from the liquid spectrum. We observe the singular dependence of the isochoric heat capacity on the mean free path of phonons, and the obeyance of the Stokes-Einstein equation relating the viscosity to the mass diffusion. The transport properties of mixtures are more complicated compared to simple liquids, however viscosity and thermal conductivity are well guided by fundamental bounds proposed recently. The kinematic viscosity and thermal diffusivity lie very close to one another and obey the theoretical fundamental bounds determined solely by fundamental physical constants. Our results show that recent advances in the theoretical physics of liquids are applicable to molten salts mixtures, and therefore that the evolution and interplay of properties common to all liquids may act as a guide to a deeper understanding of these mixtures.

physics.chem-ph↗

arXiv2024

Performance of the MACE-MP-0 potential for calculating viscosity in LiF molten salt

We perform molecular dynamics simulations of molten Lithium Fluoride using the MACE-MP-0 (small) machine learnt interatomic potential and the classical Buckingham and Born-Huggins-Mayer potentials. We find that the MACE-MP-0, out-of-the-box, is able to accurately reproduce the experimental viscosity across the liquid state. Whilst the previous predicted viscosities from classical potentials are under-predicted, which has previously been attributed to a suppressed melting temperature. We find that the melting temperature simulated by MACE-MP-0, simply by heating a crystal structure, is significantly closer to the experimental melting temperature of LiF.

cond-mat.mtrl-sci↗

arXiv2024

Thermodynamic modeling of the LiCl-KCl-LaCl$_3$ system with Bayesian model selection and uncertainty quantification

Chloride molten salts are increasingly used in pyroprocessing techniques for the separation of lanthanides. Understanding thermodynamic properties of these salts is essential to predict their critical characteristics and optimize the separation process. Several thermodynamic models, including the associate model, the two-sublattice ionic model, and the modified quasichemical model with quadruplet approximation (MQMQA), have been utilized in the literature to capture the complexity of molten salts. In the present work, the Bayes factor is used to guide the model selection process for thermodynamic modeling of the KCl-LaCl3 system and provide statistical comparison of various models. The results indicate that the MQMQA model is the most favorable one based on available data. The LiCl-KCl-LaCl3 system has been further modelled with uncertainty quantification (UQ) using MQMQA with the thermodynamic properties of compounds in KCl-LaCl3 predicted by the quasiharmonic approach in terms of first-principles phonon calculations as a function of temperature. The calculated phase stability shows excellent agreement with experimental data, indicating that an appropriate thermodynamic model is important for accurately predicting critical characteristics of complex molten salts.

cond-mat.mtrl-sci↗

arXiv2023

How heat propagates in liquid $^3$He

In Landau's Fermi liquid picture, transport is governed by scattering between quasi-particles. The normal liquid $^3$He conforms to this picture but only at very low temperature. Here, we show that the deviation from the standard behavior is concomitant with the fermion-fermion scattering time falling below the Planckian time, $\frac{\hbar}{k_{\rm B}T}$ and the thermal diffusivity of this quantum liquid is bounded by a minimum set by fundamental physical constants and observed in classical liquids. This points to collective excitations (a sound mode) as carriers of heat. We propose that this mode has a wavevector of 2$k_F$ and a mean free path equal to the de Broglie thermal length. This would provide an additional conducting channel with a $T^{1/2}$ temperature dependence, matching what is observed by experiments. The experimental data from 0.007 K to 3 K can be accounted for, with a margin of 10\%, if thermal conductivity is the sum of two contributions: one by quasi-particles (varying as the inverse of temperature) and and another by sound (following the square root of temperature).

cond-mat.stat-mech↗

arXiv2023

Fast dynamics and high effective dimensionality of liquid fluidity

Fluidity, the ability of liquids to flow, is the key property distinguishing liquids from solids. This fluidity is set by the mobile transit atoms moving from one quasi-equilibrium point to the next. The nature of this transit motion is unknown. Here, we show that flow-enabling transits form a dynamically distinct sub-ensemble where atoms move on average faster than the overall system, with a manifestly non-Maxwellian velocity distribution. This is in contrast to solids and gases where no distinction of different ensembles can be made and where the distribution is always Maxwellian. The non-Maxwellian distribution is described by an exponent $\alpha$ corresponding to high dimensionality of space. This is generally similar to extra synthetic dimensions in topological quantum matter, albeit higher dimensionality in liquids is not integer but is fractional. The dimensionality is close to 4 at melting and exceeds 4 at high temperature. $\alpha$ has a maximum as a function of temperature and pressure in liquid and supercritical states, returning to its Maxwell value in the solid and gas states.

cond-mat.stat-mech↗

arXiv2022

Double universality of the transition in the supercritical state

Universality aids consistent understanding of physical properties. This includes understanding the states of matter where a theory predicts how a property of a phase (solid, liquid, gas) changes with temperature or pressure. Here, we show that the matter above the critical point has a remarkable double universality not limited by pressure and temperature. The first universality is the transition between the liquidlike and gaslike states seen in the crossover of the specific heat on the dynamical length scale in deeply supercritical state and characterised by a fixed inversion point. The second universality is the operation of this effect in many supercritical fluids, including N$_2$, CO$_2$, Pb, H$_2$0 and Ar. Despite the differences in structure and chemical bonding in these fluids, the transition has the same fixed inversion point deep in the supercritical state. This provides new understanding of the supercritical state previously considered to be a featureless area on the phase diagram and a theoretical guide for improved and more efficient deployment of supercritical fluids in green and environmental applications.

cond-mat.stat-mech↗

arXiv2021

Dynamical indistinguishability and statistics in quantum fluids

For a system to qualify as a quantum fluid, quantum-statistical effects should operate in addition to quantum-mechanical ones. Here, we address the hitherto unexplored dynamical condition for the quantum-statistical effects to be manifested, and consider particle exchange events in the gaslike regime of fluid dynamics as a dynamical process with an intrinsic time scale. We subsequently propose a quantitative criterion of particle indistinguishability and associated quantum statistics to be inoperative at short time and emerge at long time. Verifiable experimentally, our predictions enable a systematic search for a transition between statistics-active and statistics-inactive regimes in quantum fluids.

quant-ph↗

arXiv2021

Radiation damage effects on helium diffusion in zircon

We report the effects of radiation damage on helium diffusion in zircon using data from molecular dynamics simulations. We observe an increase in activation energy for helium diffusion as a result of radiation damage and increasing structural disorder. The activation energy in a heavily damaged region is smaller than in a completely amorphous system which is correlated with remaining order in the cation sublattices of the damaged structure not present in the fully amorphized system. The reduction of activation energy is related to the disappearance of fast diffusion pathways that present in the crystal. Consistent with the change in activation energy, we observe the accumulation of helium atoms in the damaged structure and discuss the implications of this effect for the formation of helium bubbles and zircon's performance as an encapsulation material for nuclear waste.

cond-mat.mtrl-sci↗

arXiv2021

Transition in the supercritical state of matter: experimental evidence

A large and mostly unexplored part of the phase diagram lies above the critical point. The supercritical matter was traditionally believed to be physically homogeneous with no discernible differences between liquidlike and gaslike states. More recently, several proposals have been put forward challenging this view, and here we review the history of this research. Close to the critical point, persisting critical anomalies enable the separation of the supercritical state into two different states. About a decade ago, it was proposed that the Frenkel line (FL), corresponding to the dynamical transition of particle motion and related thermodynamic and structural transitions, gives a unique and path-independent way to separate the supercritical states into two qualitatively different states and extends to arbitrarily high pressure and temperature on the phase diagram. Here, we review several lines of enquiry that followed. We focus on the experimental evidence of transitions in deeply supercritical Ne, N$_2$, CH$_4$, C$_2$H$_6$, CO$_2$ and H$_2$O at the FL detected by a number of techniques including X-ray, neutron and Raman scattering experiments. %Except for H$_2$O, these experiments were stimulated by the FL and followed the state points of the FL mapped in preceding calculations. We subsequently summarise other developments in the field, including recent extensions of analysis of dynamics at the FL, quantum simulations, topological and geometrical approaches as well as universality of properties at the FL. Finally, we review current theoretical understanding of the supercritical state and list open problems in the field.

cond-mat.soft↗

arXiv2021

Universal interrelation between dynamics and thermodynamics of fluids: dynamically-driven "c"-transition

Our first very wide survey of the supercritical phase diagram and its key properties reveals a universal interrelation between dynamics and thermodynamics and an unambiguous transition between liquidlike and gaslike states. This is seen in the master plot showing a collapse of the data representing the dependence of specific heat on key dynamical parameters in the system for many different paths on the phase diagram. As a result, the observed transition is path-independent. We call it a "c"-transition due to the "c"-shaped curve parameterizing the dependence of the specific heat on key dynamical parameters. The "c"-transition has a fixed inversion point and provides a new structure to the phase diagram, operating deep in the supercritical state (up to at least 2000 times the critical pressure and 50 times the critical temperature). The data collapse and path independence as well as the existence of a special inversion point on the phase diagram are indicative of either of a sharp crossover or a new phase transition in the deeply supercritical state.

cond-mat.stat-mech↗

arXiv2020

Radiation damage effects in amorphous zirconolite

We report the results of a large-scale modelling study of radiation damage effects in the nuclear waste form zirconolite. We particularly focus on the effects of radiation damage in amorphous zirconolite and have developed a new way to analyse the damaged structure in terms of local coordination statistics. On the basis of this analysis, we find that the amorphous structure responds to radiation damage differently from the crystal. Amorphous zirconolite is found to be "softer" than crystalline zirconolite with a much larger number of atoms becoming displaced and changing coordination during a 70 keV cascade. The local coordination and connectivity analysis shows that the amorphous structure continues to evolve as a result of repeated radiation damage, changes which cannot be identified from globally averaged properties such as pair distribution functions. We also find large density inhomogeneities at the local level which we suggest may play an important role for future developments in nuclear waste storage. Finally, we find a correlation between the changes in enthalpy and local coordination, suggesting that measurements of enthalpy change can be linked quantitatively to structural radiation damage. Our results raise an interesting possibility of whether an evolution of the amorphous structure due to radiation damage can converge to a new equilibrium amorphous regime, posing the fundamental question of what that structure may be.

cond-mat.mtrl-sci↗

arXiv2020

Explaining the low-frequency shear elasticity of confined liquids

Experimental observations of unexpected shear rigidity in confined liquids, on very low frequency scales on the order of 0.01-0.1 Hz, call into question our basic understanding of the elasticity of liquids and have posed a challenge to theoretical models of the liquid state ever since. Here we combine the nonaffine theory of lattice dynamics valid for disordered condensed matter systems with the Frenkel theory of the liquid state. The emerging framework shows that applying confinement to a liquid can effectively suppress the low frequency modes that are responsible for nonaffine soft mechanical response, thus leading to an effective increase of the liquid shear rigidity. The new theory successfully predicts the scaling law $G'\sim L^{-3}$ for the low-frequency shear modulus of liquids as a function of the confinement length $L$, in agreement with experimental results, and provides the basis for a more general description of the elasticity of liquids across different time and length scales.

cond-mat.soft↗

arXiv2020

Collective modes and gapped momentum states in liquid Ga: experiment, theory and simulation

Collective excitations in liquids are important for understanding liquid dynamical and thermodynamic properties. Gapped momentum states (GMS) are a notable feature of liquid dynamics predicted to operate in the transverse sector of collective excitations. Here, we combine inelastic neutron scattering experiments, theory and molecular dynamics modelling to study collective excitations and GMS in liquid Ga in a wide range of temperature and $k$-points. We find that all three lines of enquiry agree for the longitudinal sector of liquid dynamics. In the transverse sector, the experiments agree with theory, modelling as well as earlier X-ray experiments at larger $k$, whereas theory and modelling agree in a wide range of temperature and $k$-points. We observe the emergence and development of the $k$-gap in the transverse sector which increases with temperature and inverse of relaxation time as predicted theoretically.

cond-mat.soft↗

arXiv2020

Experimental and modelling evidence for structural crossover in supercritical CO$_2$

Physics of supercritical state is understood to a much lesser degree compared to subcritical liquids. Carbon dioxide in particular has been intensely studied, yet little is known about the supercritical part of its phase diagram. Here, we combine neutron scattering experiments and molecular dynamics simulations and demonstrate the structural crossover at the Frenkel line. The crossover is seen at pressures as high as 14 times the critical pressure and is evidenced by changes of the main features of the structure factor and pair distribution functions.

cond-mat.other↗

arXiv2020

Field Theory of Dissipative Systems with Gapped Momentum States

We develop a field theory with dissipation based on a finite range of wave propagation and associated gapped momentum states in the wave spectrum. We analyze the properties of the Lagrangian and the Hamiltonian with two scalar fields in different representations and show how the new properties of the two-field Lagrangian are related to Keldysh-Schwinger formalism. The proposed theory is non-Hermitian, and we discuss its properties related to $\mathcal{PT}$ symmetry. The calculated correlation functions show a decaying oscillatory behavior related to gapped momentum states. We corroborate this result using path integration. The interaction potential becomes short-ranged due to dissipation. Finally, we observe that the proposed field theory represents a departure from the harmonic paradigm and discuss the implications of our theory for the Lagrangian formulation of hydrodynamics.

hep-th↗

arXiv2020

Gapped momentum states

Important properties of a particle, wave or a statistical system depend on the form of a dispersion relation (DR). Two commonly-discussed dispersion relations are the gapless phonon-like DR and the DR with the energy or frequency gap. More recently, the third and intriguing type of DR has been emerging in different areas of physics: the DR with the gap in momentum, or $k$-space. It has been increasingly appreciated that gapped momentum states (GMS) have important implications for dynamical and thermodynamic properties of the system. Here, we review the origin of this phenomenon in a range of physical systems, starting from ordinary liquids to holographic models. We observe how GMS emerge in the Maxwell-Frenkel approach to liquid viscoelasticity, relate the $k$-gap to dissipation and observe how the gaps in DR can continuously change from the energy to momentum space and vice versa. We subsequently discuss how GMS emerge in the two-field description which is analogous to the quantum formulation of dissipation in the Keldysh-Schwinger approach. We discuss experimental evidence for GMS, including the direct evidence of gapped DR coming from strongly-coupled plasma. We also discuss GMS in electromagnetic waves and non-linear Sine-Gordon model. We then move on to discuss the recently developed quasihydrodynamic framework which relates the $k$-gap with the presence of a softly broken global symmetry and its applications. Finally, we review recent discussions of GMS in relativistic hydrodynamics and holographic models. Throughout the review, we point out essential physical ingredients required by GMS to emerge and make links between different areas of physics, with the view that new and deeper understanding will benefit from studying the GMS in seemingly disparate fields and from clarifying the origin of potentially similar underlying physical ideas and equations.

cond-mat.stat-mech↗

arXiv2020

Similarity between the kinematic viscosity of quark-gluon plasma and liquids at the viscosity minimum

Recently, it has been found that the kinematic viscosity of liquids at the minimum, $\nu_m$, can be expressed in terms of fundamental physical constants, giving $\nu_m$ on the order of $10^{-7}~{\rm m^2/s}$. Here, we show that the kinematic viscosity of quark-gluon plasma (QGP) has a similar value and support this finding by experimental data and theoretical estimations. The similarity is striking, given that the dynamic viscosity and the density of QGP are about 16 orders of magnitude larger than in liquids and that the two systems have disparate interactions and fundamental theories. We discuss the implications of this result for understanding the QGP including the similarity of flow and particle dynamics at the viscosity minimum, the associated dynamical crossover and universality of shear diffusivity.

hep-th↗