J. Kaupužs - Academia.edu (original) (raw)

Papers by J. Kaupužs

Research paper thumbnail of Functional truncations for the solution of the nonperturbative RG equations

Journal of Physics A: Mathematical and Theoretical

We consider the Wetterich exact renormalization group (RG) equation. Approximate closed equations... more We consider the Wetterich exact renormalization group (RG) equation. Approximate closed equations are obtained from it, applying certain truncation schemes for the effective average action. These equations are solved either purely numerically or by certain extra truncations for the potential and related quantities, called the functional truncations. Traditionally, the functional truncations consist of truncated expansions in powers of ρ ˜ − ρ ˜ 0 , where ρ ˜ ∝ ϕ 2 , φ is the averaged order parameter, and ρ ˜ 0 corresponds to the minimum of the dimensionless potential u k ( ρ ˜ ) , depending on the infrared cut-off scale k. We propose a new approach of functional truncations, using the expansion u k ( ρ ˜ ) − u k ( 0 ) = ( 1 − s ) − μ u 1 , k s + u 2 , k s 2 + ⋯ , where s = ρ ˜ / ( ρ ˜ 0 + ρ ˜ ) , ρ ˜ 0 is an optimization parameter and µ is the exponent, describing the ρ ˜ → ∞ asymptotic. The newly developed method provides accurate estimates of the critical exponents η, ν and also ω...

Research paper thumbnail of Ja n 20 02 Tranfer matrix and Monte Carlo tests of critical exponents in lattice models

The corrections to finite-size scaling in the critical two-point correlation function G(r) of 2D ... more The corrections to finite-size scaling in the critical two-point correlation function G(r) of 2D Ising model on a square lattice have been studied numerically by means of exact transfer–matrix algorithms. The systems of square geometry with periodic boundaries oriented either along 〈10〉 or along 〈11〉 direction have been considered, including up to 800 spins. The calculation of G(r) at a distance r equal to the half of the system size L shows the existence of an amplitude correction ∝ L. A nontrivial correction ∝ L of a very small magnitude also has been detected in agreement with predictions of our recently developed GFD (grouping of Feynman diagrams) theory. A refined analysis of the recent MC data for 3D Ising, φ, and XY lattice models has been performed. It includes an analysis of the partition function zeros of 3D Ising model, an estimation of the correction–to–scaling exponent ω from the Binder cumulant data near criticality, as well as a study of the effective critical exponen...

Research paper thumbnail of Corrections to scaling in the 3D Ising model: A comparison between MC and MCRG results

International Journal of Modern Physics C

Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation res... more Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to [Formula: see text]. Our estimated values of the correction-to-scaling exponent [Formula: see text] tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes, i.e. [Formula: see text] with [Formula: see text], are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e. [Formula: see text] and [Formula: see text]. We discuss the possibilities that [Formula: see text] is either really smaller than usually expected or these values of [Formula: see text] describe some transient behavior which, eventually, turns into the correct asymptotic behavior at [Formula: see text]. We propose refining MCRG simulations and analysis to resolve this issue. Our actual MC estimations of the critical exponents [Formula: see...

Research paper thumbnail of Non-perturbative Approaches in Nanoscience and Corrections to Finite-Size Scaling

Springer Proceedings in Mathematics & Statistics, 2018

The meeting will take place in the new TransCanada Pipelines Pavilion (TCPL) at the Banff Interna... more The meeting will take place in the new TransCanada Pipelines Pavilion (TCPL) at the Banff International Research Station (BIRS). Open wireless Internet access("wifi", no password required) is available is available in all areas of BIRS, including the TCPL building. Please consult the Technology page for more detail on equipment. The BIRS is physically located on the campus of The Banff Centre. BIRS occupies Corbett Hall and the TransCanada Pipelines Pavilion. TransCanada Pipelines Pavilion is wheelchair accessible, and Corbett Hall is wheelchair accessible through Max Bell. A detailed desription of these facilities can be found here. TCPL 201 is our main lecture room. It features a tiered lecture auditorium, has chalkboards, an LCD projector and screen, and a document camera. We will use other breakout rooms for brainstrorming sessions and discussions located in the TCPL building. Maps are provided on the next page and further details on the meeting facilities can be found here. Participants of BIRS programs are housed in Corbett Hall at the Banff Centre. Our workshop participants are expected to arrive on August 28, Sunday afternoon or evening (check-in is after 4 p.m.) and to depart on September 2, Friday midday (check-out is at noon). Accommodation and meals are provided for all invitees of this workshop (the organizers and participants) for this period. Check-in desk at the Banff Centre is located in the Professional Development Centre (PDC). The desk is open 24 hours* so participants can check in anytime. Here you will be given the key to your room in Corbett Hall as well as any information useful for BIRS participants. During your stay at BIRS, you can be contacted by telephone through The Banff Centre switchboard, which is open 24 hours, at +1-403-762-6100. Registration should be straightforward as the Banff Centre should be expecting your arrival. They will ask you for a Credit Card imprint. This is only to cover your incidental expenses, and to allow you to use the telephone in your bedroom. Without it your phone will not work. After you have registered and received your key, please proceed to Corbett Hall. Corbett Hall is the home of BIRS and there you will be able to find more information about the many facilities available to you at the Banff Centre. Every bedroom at BIRS has a telephone and has an ethernet network port for fast connectivity to the Internet. Wireless is also available. Further information on accommodations can be found here.

Research paper thumbnail of Impact of the Cu Substrate Surface Preparation on the Morphological, Superconductive and RF Properties of the Nb Superconductive Coatings

Nowadays, one of the main issues of the superconducting thin film resonant cavities is the Cu sur... more Nowadays, one of the main issues of the superconducting thin film resonant cavities is the Cu surface preparation. A better understanding of the impact of copper surface preparation on the morphological, superconductive (SC) and RF properties of the coating, is mandatory in order to improve the performances of superconducting cavities by coating techniques. ARIES H₂020 collaboration includes a specific work package (WP15) to study the influence of Cu surface polishing on the SRF performances of Nb coatings that involves a team of 8 research groups from 7 different countries. In the present work, a comparison of 4 different polishing processes for Cu (Tumbling, EP, SUBU, EP+SUBU) is presented through the evaluation of the SC and morphological properties of Nb thin film coated on Cu planar samples and QPR samples, polished with different procedures. Effects of laser annealing on Nb thin films have also been studied. Different surface characterizations have been applied: roughness meas...

Research paper thumbnail of The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application Metastability in the Zero-Range Process

The zero-range process (ZRP) [1] is a simple lattice-based model for driven diffusive systems. Fo... more The zero-range process (ZRP) [1] is a simple lattice-based model for driven diffusive systems. For certain choices of parameters, the model exhibits a condensation transition (analogous to Bose-Einstein condensation) where a macroscopic proportion of particles accumulate on a single site [2]. Condensation is well-known in colloidal and granular

Research paper thumbnail of Jauns viedoklis gaismas emisijai no silīcija nanokristāliem

Research paper thumbnail of Mechanisms of Strong Photoluminescence of Si Nanoparticles

Research paper thumbnail of Si, CdTe Nanocrystals and Surface Structuring for Solar Cell Application

Research paper thumbnail of About Anomalous Redshift of Photoluminescence in Si Nanocrystals

Although the photoluminescence (PL) maximum is shifted to a smaller wavelength if the diameter of... more Although the photoluminescence (PL) maximum is shifted to a smaller wavelength if the diameter of Si nanocrystals (Si-nc) decreases (blueshift), Rama Krishna and Friesner (1992) have shown theoretically that it does not hold for the Γ-point. An anomalous redshift exists there. After 20 years this phenomenon has been verified experimentally by Yassievich a. o. Nonetheless, we have found that the existing microscopic explanation is unsatisfactory, and here we propose a scenario that elucidates this phenomenon

Research paper thumbnail of Origin of n-type conductivity in ZnO crystal and formation of Zn and ZnO nanoparticles by laser radiation

Optics & Laser Technology, 2019

• Zn interstitials as origin of n-type conductivity in ZnO crystal. • Laser-induced thermal gener... more • Zn interstitials as origin of n-type conductivity in ZnO crystal. • Laser-induced thermal generation and redistribution of point defects. • Controlled formation of Zn and ZnO nanoparticles by laser radiation.

Research paper thumbnail of On one approach for calculation of the thermal conductivity coefficients for heat transfer: part II

In present work, we consider some class of homogeneous one-dimensional on spatial variable coeffi... more In present work, we consider some class of homogeneous one-dimensional on spatial variable coefficient inverse problems of thermal conductivity in the bounded domain under some additional information. Authors offer one simple analytical method for determination of required coefficient of thermal conductivity under various type additional conditions. Offered method lets reduce the initial inverse problem to the problem for the solution of the first kind Volterra linear integral equation.

Research paper thumbnail of A Method of Conversion of some Coefficient Inverse Parabolic Problems to a Unified Type of Integral-Differential Equation

Advanced Materials Research, 2011

Coefficient inverse problems are reformulated to a unified integral differential equation. The pr... more Coefficient inverse problems are reformulated to a unified integral differential equation. The presented method of conversion of the considered inverse problems to a unified Volterra integral-differential equation gives an opportunity to distribute the acquired results also to analogous inverse problems for non-linear parabolic equations of different types.

Research paper thumbnail of Modeling of Surface Structure Formation after Laser Irradiation

Advanced Materials Research, 2011

The Stefan problem in a semi-infinite media under laser irradiation is considered. It is related ... more The Stefan problem in a semi-infinite media under laser irradiation is considered. It is related to the melting and solidification processes, resulting in certain surface structure after the solidification. A simple model, as well as a more sophisticated one is proposed to describe this process. The latter model allows us to calculate the surface profile by solving a system of two nonlinear differential equations, if the shape of the solid-liquid interface is known. It has to be found as a solution of two-phases Stefan problem. The results of example calculations by the fourth-order Runge-Kutta method are presented, assuming that the solid-liquid interface has a parabolic shape. The calculated crossection of the surface structure shows a characteristic cone in the center, in agreement with experimental observations.

Research paper thumbnail of Theory and modeling of polarization switching in ferroelectrics

Journal of the European Ceramic Society, 2005

Thermodynamic approach of ferroelectrics is reconsidered in recourse to thermal activated nature ... more Thermodynamic approach of ferroelectrics is reconsidered in recourse to thermal activated nature of polarization switching under arbitrary driving voltage. This analysis heavy relies on transformation of the problem to imaginary time Schrödinger equation and its integration by means adopted from pure quantum problems. It turns out that this nonadiabatic treatment reveals non-equilibrium properties directly relevant to essential application-grade performance specifications like hysteresis and spatial inhomogeneity.

Research paper thumbnail of Application of thermodynamics to driven systems

The European Physical Journal B, 2007

Application of thermodynamics to driven systems is discussed. As particular examples, simple traf... more Application of thermodynamics to driven systems is discussed. As particular examples, simple traffic flow models are considered. On a microscopic level, traffic flow is described by Bando's optimal velocity model in terms of accelerating and decelerating forces. It allows to introduce kinetic, potential, as well as total energy, which is the internal energy of the car system in view of thermodynamics. The latter is not conserved, although it has certain value in any of two possible stationary states corresponding either to fixed point or to limit cycle in the space of headways and velocities. On a mesoscopic level of description, the size n of car cluster is considered as a stochastic variable in master equation. Here n = 0 corresponds to the fixed-point solution of the microscopic model, whereas the limit cycle is represented by coexistence of a car cluster with n > 0 and free flow phase. The detailed balance holds in a stationary state just like in equilibrium liquid-gas system. It allows to define free energy of the car system and chemical potentials of the coexisting phases, as well as a relaxation to a local or global free energy minimum. In this sense the behaviour of traffic flow can be described by equilibrium thermodynamics. We find, however, that the chemical potential of the cluster phase of traffic flow depends on an outer parameter-the density of cars in the free-flow phase. It allows to distinguish between the traffic flow as a driven system and purely equilibrium systems.

Research paper thumbnail of Critical exponents predicted by grouping of Feynman diagrams in 4 model

Annalen der Physik, 2001

Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discus... more Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The usual perturbation theory is reorganized by appropriate grouping of Feynman diagrams of ϕ 4 model with O(n) symmetry. As a result, equations for calculation of the two-point correlation function are obtained which allow to predict possible exact values of critical exponents in two and three dimensions by proving relevant scaling properties of the asymptotic solution at (and near) the criticality. The new values of critical exponents are discussed and compared to the results of numerical simulations and experiments.

Research paper thumbnail of Spatio-Temporal Correlations of Local Polarization in Ferroelectrics

Ferroelectrics, 2003

ABSTRACT

Research paper thumbnail of Critical Phenomena and Phase Transitions in Large Lattices within Monte-Carlo Based Non-perturbative Approaches

Ukrainian Journal of Physics, 2022

Critical phenomena and Goldstone mode effects in spin models with the O(n) rotational symmetry ar... more Critical phenomena and Goldstone mode effects in spin models with the O(n) rotational symmetry are considered. Starting with Goldstone mode singularities in the XY and O(4) models, we briefly review various theoretical concepts, as well as state-of-the-art Monte Carlo simulation results. They support recent results of the GFD (grouping of Feynman diagrams) theory, stating that these singularities are described by certain nontrivial exponents, which differ from those predicted earlier by perturbative treatments. Furthermore, we present the recent Monte Carlo simulation results of the three-dimensional Ising model for lattices with linear sizes up to L = 1536, which are very large as compared to L ≤ 128 usually used in the finite-size scaling analysis. These results are obtained, using a parallel OpenMP implementation of the Wolff single-cluster algorithm. The finite-size scaling analysis of the critical exponent η, assuming the usually accepted correction-to-scaling exponent ω ≈ 0.8,...

Research paper thumbnail of Metastability in the Zero-Range Process

1. Introduction The zero-range process (ZRP) [1] is a simple lattice-based model for driven diffu... more 1. Introduction The zero-range process (ZRP) [1] is a simple lattice-based model for driven diffusive systems. For certain choices of parameters, the model exhibits a condensation transition (analogous to Bose-Einstein condensation) where a macroscopic proportion of particles accumulate on a single site [2]. Condensation is well-known in colloidal and granular systems [3] and also occurs in a variety of other contexts [4], including socio-economics, biology, and networks. Furthermore, the ZRP can be mapped to well-studied exclusion processes which describe the single-file diffusion of interacting particles. Condensation in the ZRP corresponds to phase separation in the exclusion process [5].

Research paper thumbnail of Functional truncations for the solution of the nonperturbative RG equations

Journal of Physics A: Mathematical and Theoretical

We consider the Wetterich exact renormalization group (RG) equation. Approximate closed equations... more We consider the Wetterich exact renormalization group (RG) equation. Approximate closed equations are obtained from it, applying certain truncation schemes for the effective average action. These equations are solved either purely numerically or by certain extra truncations for the potential and related quantities, called the functional truncations. Traditionally, the functional truncations consist of truncated expansions in powers of ρ ˜ − ρ ˜ 0 , where ρ ˜ ∝ ϕ 2 , φ is the averaged order parameter, and ρ ˜ 0 corresponds to the minimum of the dimensionless potential u k ( ρ ˜ ) , depending on the infrared cut-off scale k. We propose a new approach of functional truncations, using the expansion u k ( ρ ˜ ) − u k ( 0 ) = ( 1 − s ) − μ u 1 , k s + u 2 , k s 2 + ⋯ , where s = ρ ˜ / ( ρ ˜ 0 + ρ ˜ ) , ρ ˜ 0 is an optimization parameter and µ is the exponent, describing the ρ ˜ → ∞ asymptotic. The newly developed method provides accurate estimates of the critical exponents η, ν and also ω...

Research paper thumbnail of Ja n 20 02 Tranfer matrix and Monte Carlo tests of critical exponents in lattice models

The corrections to finite-size scaling in the critical two-point correlation function G(r) of 2D ... more The corrections to finite-size scaling in the critical two-point correlation function G(r) of 2D Ising model on a square lattice have been studied numerically by means of exact transfer–matrix algorithms. The systems of square geometry with periodic boundaries oriented either along 〈10〉 or along 〈11〉 direction have been considered, including up to 800 spins. The calculation of G(r) at a distance r equal to the half of the system size L shows the existence of an amplitude correction ∝ L. A nontrivial correction ∝ L of a very small magnitude also has been detected in agreement with predictions of our recently developed GFD (grouping of Feynman diagrams) theory. A refined analysis of the recent MC data for 3D Ising, φ, and XY lattice models has been performed. It includes an analysis of the partition function zeros of 3D Ising model, an estimation of the correction–to–scaling exponent ω from the Binder cumulant data near criticality, as well as a study of the effective critical exponen...

Research paper thumbnail of Corrections to scaling in the 3D Ising model: A comparison between MC and MCRG results

International Journal of Modern Physics C

Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation res... more Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to [Formula: see text]. Our estimated values of the correction-to-scaling exponent [Formula: see text] tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes, i.e. [Formula: see text] with [Formula: see text], are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e. [Formula: see text] and [Formula: see text]. We discuss the possibilities that [Formula: see text] is either really smaller than usually expected or these values of [Formula: see text] describe some transient behavior which, eventually, turns into the correct asymptotic behavior at [Formula: see text]. We propose refining MCRG simulations and analysis to resolve this issue. Our actual MC estimations of the critical exponents [Formula: see...

Research paper thumbnail of Non-perturbative Approaches in Nanoscience and Corrections to Finite-Size Scaling

Springer Proceedings in Mathematics & Statistics, 2018

The meeting will take place in the new TransCanada Pipelines Pavilion (TCPL) at the Banff Interna... more The meeting will take place in the new TransCanada Pipelines Pavilion (TCPL) at the Banff International Research Station (BIRS). Open wireless Internet access("wifi", no password required) is available is available in all areas of BIRS, including the TCPL building. Please consult the Technology page for more detail on equipment. The BIRS is physically located on the campus of The Banff Centre. BIRS occupies Corbett Hall and the TransCanada Pipelines Pavilion. TransCanada Pipelines Pavilion is wheelchair accessible, and Corbett Hall is wheelchair accessible through Max Bell. A detailed desription of these facilities can be found here. TCPL 201 is our main lecture room. It features a tiered lecture auditorium, has chalkboards, an LCD projector and screen, and a document camera. We will use other breakout rooms for brainstrorming sessions and discussions located in the TCPL building. Maps are provided on the next page and further details on the meeting facilities can be found here. Participants of BIRS programs are housed in Corbett Hall at the Banff Centre. Our workshop participants are expected to arrive on August 28, Sunday afternoon or evening (check-in is after 4 p.m.) and to depart on September 2, Friday midday (check-out is at noon). Accommodation and meals are provided for all invitees of this workshop (the organizers and participants) for this period. Check-in desk at the Banff Centre is located in the Professional Development Centre (PDC). The desk is open 24 hours* so participants can check in anytime. Here you will be given the key to your room in Corbett Hall as well as any information useful for BIRS participants. During your stay at BIRS, you can be contacted by telephone through The Banff Centre switchboard, which is open 24 hours, at +1-403-762-6100. Registration should be straightforward as the Banff Centre should be expecting your arrival. They will ask you for a Credit Card imprint. This is only to cover your incidental expenses, and to allow you to use the telephone in your bedroom. Without it your phone will not work. After you have registered and received your key, please proceed to Corbett Hall. Corbett Hall is the home of BIRS and there you will be able to find more information about the many facilities available to you at the Banff Centre. Every bedroom at BIRS has a telephone and has an ethernet network port for fast connectivity to the Internet. Wireless is also available. Further information on accommodations can be found here.

Research paper thumbnail of Impact of the Cu Substrate Surface Preparation on the Morphological, Superconductive and RF Properties of the Nb Superconductive Coatings

Nowadays, one of the main issues of the superconducting thin film resonant cavities is the Cu sur... more Nowadays, one of the main issues of the superconducting thin film resonant cavities is the Cu surface preparation. A better understanding of the impact of copper surface preparation on the morphological, superconductive (SC) and RF properties of the coating, is mandatory in order to improve the performances of superconducting cavities by coating techniques. ARIES H₂020 collaboration includes a specific work package (WP15) to study the influence of Cu surface polishing on the SRF performances of Nb coatings that involves a team of 8 research groups from 7 different countries. In the present work, a comparison of 4 different polishing processes for Cu (Tumbling, EP, SUBU, EP+SUBU) is presented through the evaluation of the SC and morphological properties of Nb thin film coated on Cu planar samples and QPR samples, polished with different procedures. Effects of laser annealing on Nb thin films have also been studied. Different surface characterizations have been applied: roughness meas...

Research paper thumbnail of The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application Metastability in the Zero-Range Process

The zero-range process (ZRP) [1] is a simple lattice-based model for driven diffusive systems. Fo... more The zero-range process (ZRP) [1] is a simple lattice-based model for driven diffusive systems. For certain choices of parameters, the model exhibits a condensation transition (analogous to Bose-Einstein condensation) where a macroscopic proportion of particles accumulate on a single site [2]. Condensation is well-known in colloidal and granular

Research paper thumbnail of Jauns viedoklis gaismas emisijai no silīcija nanokristāliem

Research paper thumbnail of Mechanisms of Strong Photoluminescence of Si Nanoparticles

Research paper thumbnail of Si, CdTe Nanocrystals and Surface Structuring for Solar Cell Application

Research paper thumbnail of About Anomalous Redshift of Photoluminescence in Si Nanocrystals

Although the photoluminescence (PL) maximum is shifted to a smaller wavelength if the diameter of... more Although the photoluminescence (PL) maximum is shifted to a smaller wavelength if the diameter of Si nanocrystals (Si-nc) decreases (blueshift), Rama Krishna and Friesner (1992) have shown theoretically that it does not hold for the Γ-point. An anomalous redshift exists there. After 20 years this phenomenon has been verified experimentally by Yassievich a. o. Nonetheless, we have found that the existing microscopic explanation is unsatisfactory, and here we propose a scenario that elucidates this phenomenon

Research paper thumbnail of Origin of n-type conductivity in ZnO crystal and formation of Zn and ZnO nanoparticles by laser radiation

Optics & Laser Technology, 2019

• Zn interstitials as origin of n-type conductivity in ZnO crystal. • Laser-induced thermal gener... more • Zn interstitials as origin of n-type conductivity in ZnO crystal. • Laser-induced thermal generation and redistribution of point defects. • Controlled formation of Zn and ZnO nanoparticles by laser radiation.

Research paper thumbnail of On one approach for calculation of the thermal conductivity coefficients for heat transfer: part II

In present work, we consider some class of homogeneous one-dimensional on spatial variable coeffi... more In present work, we consider some class of homogeneous one-dimensional on spatial variable coefficient inverse problems of thermal conductivity in the bounded domain under some additional information. Authors offer one simple analytical method for determination of required coefficient of thermal conductivity under various type additional conditions. Offered method lets reduce the initial inverse problem to the problem for the solution of the first kind Volterra linear integral equation.

Research paper thumbnail of A Method of Conversion of some Coefficient Inverse Parabolic Problems to a Unified Type of Integral-Differential Equation

Advanced Materials Research, 2011

Coefficient inverse problems are reformulated to a unified integral differential equation. The pr... more Coefficient inverse problems are reformulated to a unified integral differential equation. The presented method of conversion of the considered inverse problems to a unified Volterra integral-differential equation gives an opportunity to distribute the acquired results also to analogous inverse problems for non-linear parabolic equations of different types.

Research paper thumbnail of Modeling of Surface Structure Formation after Laser Irradiation

Advanced Materials Research, 2011

The Stefan problem in a semi-infinite media under laser irradiation is considered. It is related ... more The Stefan problem in a semi-infinite media under laser irradiation is considered. It is related to the melting and solidification processes, resulting in certain surface structure after the solidification. A simple model, as well as a more sophisticated one is proposed to describe this process. The latter model allows us to calculate the surface profile by solving a system of two nonlinear differential equations, if the shape of the solid-liquid interface is known. It has to be found as a solution of two-phases Stefan problem. The results of example calculations by the fourth-order Runge-Kutta method are presented, assuming that the solid-liquid interface has a parabolic shape. The calculated crossection of the surface structure shows a characteristic cone in the center, in agreement with experimental observations.

Research paper thumbnail of Theory and modeling of polarization switching in ferroelectrics

Journal of the European Ceramic Society, 2005

Thermodynamic approach of ferroelectrics is reconsidered in recourse to thermal activated nature ... more Thermodynamic approach of ferroelectrics is reconsidered in recourse to thermal activated nature of polarization switching under arbitrary driving voltage. This analysis heavy relies on transformation of the problem to imaginary time Schrödinger equation and its integration by means adopted from pure quantum problems. It turns out that this nonadiabatic treatment reveals non-equilibrium properties directly relevant to essential application-grade performance specifications like hysteresis and spatial inhomogeneity.

Research paper thumbnail of Application of thermodynamics to driven systems

The European Physical Journal B, 2007

Application of thermodynamics to driven systems is discussed. As particular examples, simple traf... more Application of thermodynamics to driven systems is discussed. As particular examples, simple traffic flow models are considered. On a microscopic level, traffic flow is described by Bando's optimal velocity model in terms of accelerating and decelerating forces. It allows to introduce kinetic, potential, as well as total energy, which is the internal energy of the car system in view of thermodynamics. The latter is not conserved, although it has certain value in any of two possible stationary states corresponding either to fixed point or to limit cycle in the space of headways and velocities. On a mesoscopic level of description, the size n of car cluster is considered as a stochastic variable in master equation. Here n = 0 corresponds to the fixed-point solution of the microscopic model, whereas the limit cycle is represented by coexistence of a car cluster with n > 0 and free flow phase. The detailed balance holds in a stationary state just like in equilibrium liquid-gas system. It allows to define free energy of the car system and chemical potentials of the coexisting phases, as well as a relaxation to a local or global free energy minimum. In this sense the behaviour of traffic flow can be described by equilibrium thermodynamics. We find, however, that the chemical potential of the cluster phase of traffic flow depends on an outer parameter-the density of cars in the free-flow phase. It allows to distinguish between the traffic flow as a driven system and purely equilibrium systems.

Research paper thumbnail of Critical exponents predicted by grouping of Feynman diagrams in 4 model

Annalen der Physik, 2001

Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discus... more Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The usual perturbation theory is reorganized by appropriate grouping of Feynman diagrams of ϕ 4 model with O(n) symmetry. As a result, equations for calculation of the two-point correlation function are obtained which allow to predict possible exact values of critical exponents in two and three dimensions by proving relevant scaling properties of the asymptotic solution at (and near) the criticality. The new values of critical exponents are discussed and compared to the results of numerical simulations and experiments.

Research paper thumbnail of Spatio-Temporal Correlations of Local Polarization in Ferroelectrics

Ferroelectrics, 2003

ABSTRACT

Research paper thumbnail of Critical Phenomena and Phase Transitions in Large Lattices within Monte-Carlo Based Non-perturbative Approaches

Ukrainian Journal of Physics, 2022

Critical phenomena and Goldstone mode effects in spin models with the O(n) rotational symmetry ar... more Critical phenomena and Goldstone mode effects in spin models with the O(n) rotational symmetry are considered. Starting with Goldstone mode singularities in the XY and O(4) models, we briefly review various theoretical concepts, as well as state-of-the-art Monte Carlo simulation results. They support recent results of the GFD (grouping of Feynman diagrams) theory, stating that these singularities are described by certain nontrivial exponents, which differ from those predicted earlier by perturbative treatments. Furthermore, we present the recent Monte Carlo simulation results of the three-dimensional Ising model for lattices with linear sizes up to L = 1536, which are very large as compared to L ≤ 128 usually used in the finite-size scaling analysis. These results are obtained, using a parallel OpenMP implementation of the Wolff single-cluster algorithm. The finite-size scaling analysis of the critical exponent η, assuming the usually accepted correction-to-scaling exponent ω ≈ 0.8,...

Research paper thumbnail of Metastability in the Zero-Range Process

1. Introduction The zero-range process (ZRP) [1] is a simple lattice-based model for driven diffu... more 1. Introduction The zero-range process (ZRP) [1] is a simple lattice-based model for driven diffusive systems. For certain choices of parameters, the model exhibits a condensation transition (analogous to Bose-Einstein condensation) where a macroscopic proportion of particles accumulate on a single site [2]. Condensation is well-known in colloidal and granular systems [3] and also occurs in a variety of other contexts [4], including socio-economics, biology, and networks. Furthermore, the ZRP can be mapped to well-studied exclusion processes which describe the single-file diffusion of interacting particles. Condensation in the ZRP corresponds to phase separation in the exclusion process [5].