Research interests, expertise, focus field,
main contribution, key results, and goals
My research
interests are in: Theoretical and Applied Physics – dynamics of plasmas,
fluids, materials; Applied Mathematics – applied analysis, partial differential
equations, boundary value problems, dynamical systems; in Scientific Computing;
in Data Science.
My research expertise
is in theoretical analysis of complex processes and their – far from equilibrium,
nonlinear, non-local, multi-scale, multi-phase, statistically unsteady – dynamics.
The focus is on instabilities, interfaces, mixing.
My contribution to
the field is in the development of physics based mathematically rigorous
theoretical approaches for instabilities, interfaces, and mixing.
My key results are:
the new fluid instabilities; the inertial mechanisms of interface
stabilization; the special self-similarity class in interfacial mixing; the
order in Rayleigh-Taylor mixing; the theory of interface dynamics; the
fundamentals of Rayleigh-Taylor instabilities.
My goals in research are to: explore symmetries
of unstable processes; discover concepts cutting through complexity of the
problem; develop methods of predicting far from equilibrium dynamics; and,
ultimately, ensure progress of science, technology and society.
Interface dynamics: the mechanisms of
stabilization and destabilization
Relevant papers: Abarzhi
et al (in processing); Abarzhi 2024a; Abarzhi 2023b; Ilyin & Abarzhi
2022a,b; Ilyin & Abarzhi 2021; Ilyin et al 2021a,b; Abarzhi et al 2019a; Ilyin
et al 2020; Ilyin et al 2019; Ilyin et al 2018; Abarzhi et al 2015.
Relevant video recordings: Abarzhi 2024; Abarzhi 2023b,c.
Interfacial
transport and mixing are far from equilibrium processes coupling kinetic to
macroscopic scales. They are common to occur in plasmas, fluids, and materials,
over celestial events to atoms. Their understanding has crucial importance for
science, mathematics and engineering, and for technology, energy and
environment. We focus on the long-standing problem of stability of a phase
boundary, i.e., an interface. The phases of matter (plasma, fluid, material) are
broadly defined: These can be the distinct kinds of matter and the same kind of
matter with distinct thermodynamic and electrodynamic properties. The matter may
also experience phase transition, change in chemical composition, be out of thermodynamic
equilibrium, and have a non-diffusive interfacial transports.
We
developed
the general theoretical framework to systematically study the interface
stability and the flow fields’ structure, discovered the new mechanisms
of
stabilization and destabilization of the inertial and accelerated
dynamics, elaborated the new diagnostics that directly link microscopic
transport at
the interface to macroscopic fields in the bulk, and charted
perspectives
for future research.
Particularly,
by
direct linking of the interface stability to the flow fields’
structure, we found that the interfacial inertial dynamics is stable
when it conserves
the fluxes of mass, momentum and energy; the stabilization is due to
the
inertial effect, leading to small oscillations of the velocity of the
interface
as a whole. This mechanism is absent in the classic Landau’s dynamics,
which
postulates the constancy of the interface velocity and the Landau-
Darrieus
instability. An energy imbalance can destabilize the inertial dynamics,
which
is fully consistent with the classic results. In reactive fluids, the
energy
imbalance can be due to chemical reactions. For accelerated dynamics,
the
interface stability is determined by the interplay of the effects of
inertia
and buoyancy. A new hydrodynamic instability is found that develops
when the
gravity value exceeds a threshold. The unstable dynamics conserves the
fluxes
of mass, momentum and energy, has potential velocity fields in the bulk
and is
shear-free at the interface. The qualitative, quantitative and formal
properties of this new instability differ dramatically from those of
the
accelerated Landau-Darrieus instability (LDI) and the Rayleigh-Taylor
instability (RTI). Its potential applications include inertial
confinement
fusion, type-Ia supernova, flames, environmental flows, and fossil fuel
industry.
Dynamics of plasmas, fluids, materials: fluid
instabilities and interfacial mixing
Relevant papers: Abarzhi
2024b; Abarzhi 2023a,c; Abarzhi et al. 2023; Abarzhi et al 2022a,b; Abarzhi
& Williams 2020; Abarzhi et al 2019b; Anisimov et al 2013; Abarzhi 2010a;
Abarzhi 2008.
Rayleigh-Taylor (RT)
instability develops when fluids of different densities are accelerated against
the density gradient. We observe it when watching water flowing out from an
overturned cup. Extensive interfacial mixing of the fluids ensues with time.
This non-equilibrium process governs a broad variety of natural phenomena and
technological applications, at astrophysical and at atomistic scales and in
high- to low- energy-density regimes. Examples include inertial confinement and
magnetic fusion, light-matter interaction and material transformation under
impact, supernovae and accretion discs, stellar and planetary convection,
premixed and non-premixed combustion, supersonic flows and non-canonical
boundary layers, atmosphere and ocean, as well as industrial applications in
aerodynamics, oil production, free-space optical communications, and
nano-fabrication.
Even with nearly two
hundred RT-related papers published each year in peer-reviewed mathematical,
scientific and engineering journals, our knowledge of the mixing process is
still limited. On the side of experiments, it is a challenge to systematically
probe and gather precise and accurate data on RT flow, owing to its sensitive
and transient dynamics. On the side of simulations, numerical modeling of RT
instability and mixing is a severe task for both Eulerian and Lagrangian
methods even for illustrative simulations using leadership-class computers. It
is because the numerical solution has to track interfaces, accurately account
for the dynamics at small scales, capture dissipation and shocks, and span
substantial dynamic range in space and time. On the side of acquiring knowledge
from data, a systematic interpretation of RT flows from experimental and
numerical data alone is neither easy nor straightforward, and requires
identification of a set of robust parameters that can be precisely diagnosed in
the observations. On the side of theoretical analysis, evolution of RT flows is
an intellectually rich theoretical problem, as it has to balance numerous
competing requirements and demands due attention to the multi-scale, nonlinear,
non-local and statistically unsteady character of the dynamics. We wish to
identify universal asymptotic solutions if they exist, establish whether memory
of deterministic and initial conditions persists, and capture the order
prevalent in RT flows. Despite these challenges, significant success has been
achieved in the past decades on the sides of experiments, technology,
simulations, and theory in our understanding of RT instabilities and mixing.
Group theory approach provides accurate solutions of the scale-dependent and
the self-similar RT dynamics for various conditions and explains a broad range
of experiments and simulations in fluids, plasmas, materials.
Self-similar Rayleigh-Taylor
mixing: scaling, invariance, correlations, spectra, statistics
Relevant papers: Abarzhi a,b (in processing); Abarzhi 2024b; Abarzhi
2023a,c; Abarzhi & Sreenivasan 2022; Abarzhi 2021; Pandian et al 2021;
Meshkov & Abarzhi 2019; Abarzhi et al 2019a; Pandian et al 2017a,b; Swisher
et al 2015; Abarzhi et al 2013; Anisimov et al 2013; Sreenivasan & Abarzhi
2013; Abarzhi & Rosner 2010; Abarzhi 2010a,b; Abarzhi et al 2007; Abarzhi
et al 2005.
Relevant conference proceedings: Abarzhi 2011.
Relevant video recordings: Abarzhi 2023a,d.
To understand the fundamentals of RT mixing one has to go above and
beyond the domain of idealized canonical considerations. RT mixing is
inhomogeneous (i.e. the flow fields are essentially non-uniform, even in a
statistical sense), anisotropic (i.e. the dynamics in the direction of
acceleration differ from those in the normal plane), non-local (i.e. the flow
evolution depends on the initial conditions and on the contributions from all
the scales) and statistically unsteady (i.e. the mean values of the flow
quantities vary with time, and there are also the time-dependent fluctuations
around these means). Its properties depart from those of canonical turbulence.
Capturing fundamentals of RT mixing can improve our knowledge of realistic
turbulent processes and can help to elaborate the methods of control of the
non-equilibrium dynamics in nature and technology.
I developed the new theoretical concepts - the invariance of the
modified rate of momentum loss for variable acceleration, and the invariance of
the rate of momentum loss for constant acceleration - in order to describe the
transports of mass, momentum and energy in RT mixing and to capture its
anisotropic, non-uniform and statistically unsteady character.
For
variable acceleration, by analyzing symmetries of RT dynamics, we
discovered a special class of self-similar solutions and
identified their
scaling, correlations and spectra. We found that dynamics of RT
mixing can
vary from super-ballistics to sub-diffusion depending on the
acceleration and
can retain memory of deterministic conditions for any acceleration.
These rich
dynamic properties considerably impact the understanding and control of
RT
relevant phenomena in fluids, plasmas, materials, and reveal conditions
at
which turbulence can be realized in RT mixing. Particularly, they
reveal the
new mechanism of energy accumulation and transport at small scales in
supernovae.
For sustained acceleration, it has been found that the invariant,
scaling and spectral properties of RT mixing differ substantially from those of
isotropic and homogeneous turbulence. In particular, the invariance of the rate
of momentum loss leads to non-dissipative momentum transfer in physical space,
to 1/2 and 3/2 power-law scale-dependences of the velocity and Reynolds number
and to non-Kolmogorov spectra. At the same time, viscous and dissipation scales
of the mixing flow remain finite and are set by the flow acceleration. By
generalizing Kolmogorov’s ideas on statistical symmetries of turbulent flows to
non-canonical circumstances of self-similar RT dynamics, it has been discovered
that RT mixing exhibits more order, and has steeper spectra, stronger
correlations, and weaker fluctuations when compared to canonical turbulence.
Accurate
description of fluctuations in RT mixing is a challenge, since
the fluctuations are ‘frozen’ to deterministic conditions, and since RT
mixing
is a statistically unsteady process. To describe the random character
of the
statistically unsteady RT dynamics, we employed invariant
measures, and identified robust diagnostic parameters of the
dynamics. For variable
acceleration, the transition has been found from Rayleigh-Taylor-type
to
Richtmyer-Meshkov type of self-similar mixing with variations of the
acceleration parameters. For constant acceleration, our approach has
resolved
the so-called alpha problem – a central puzzled RT community for some
twenty
years.
Our theoretical analysis is consistent with the existing experiments
and simulations including high Reynolds number RT mixing flows in high energy
density plasmas and in strongly accelerated gases and liquids, and low-Reynolds
number RT mixing in fluids. Detailed quantitative and qualitative comparison of
our theoretical results with experiments and simulations shows that scale
coupling in RT mixing flow has a complex character. On one hand, strongly
accelerated high Reynolds number mixing flows may indeed keep a significant
degree of order. On the other, at low-to-moderate Reynolds numbers,
statistically steady RT flows may resemble properties of canonical turbulence.
The ordered character and re-laminarization of strongly accelerated RT mixing
is the principal result that is discovered by our theory and that may help to
comprehend the fundamentals of a variety of natural phenomena (such as early
Universe evolution, supernova explosions and stellar and planetary convection) and
to better control the technological applications (such as mixing mitigation in
inertial confinement fusion).
Scale-dependent Rayleigh-Taylor
dynamics: conservation laws, boundary value problem, and group theory
Relevant papers: Rahimyar et al 2023; Hill & Abarzhi 2023; Chan et
al 2023; Abarzhi et al 2022a,b; Hill & Abarzhi 2022; Hwang et al 2021;
Williams & Abarzhi 2021; Hill & Abarzhi 2020a,b; Naveh et al 2020;
Abarzhi et al 2019a; Hill et al 2019 a,b; Pandian et al 2017; Bhowmick &
Abarzhi 2016; Velikovich et al 2014a,b; Abarzhi 2008a,b; Herrmann et al 2008;
Herrmann & Abarzhi 2007; Abarzhi et al 2006; Abarzhi & Herrmann 2005;
Abarzhi et al 2003a,b; Abarzhi 2003; Abarzhi 2002a,b; Abarzhi 2001a,b; Abarzhi
2000; Abarzhi 1999a,b,c; Oparin & Abarzhi 1999; Abarzhi 1998; Abarzhi
1996a,b; Abarzhi & Inogamov 1995, Inogamov & Abarzhi 1995.
Relevant book chapters: Williams et al 2021; Hwang & Abarzhi
2020a,b,c; Abarzhi & Herrmann 2003; Abarzhi 2003.
Rayleigh-Taylor dynamics is governed by the conservation laws, which
are nonlinear partial differential (Navier-Stokes or Euler) equations, and
requires solution of a boundary value problem at a freely evolving
discontinuity (interface) with account for the initial and boundary conditions
at the discontinuity and at the boundaries of the domain. In the past, these
problems were attacked by brilliant scientists and mathematicians, including
Fermi, von Neumann, Chandrasekhar, Birkhoff, Garabedian, Taylor, and Richtmyer.
I developed and successfully applied the original theoretical
approach based on group theory to capture the scale-dependent dynamics of the
early-time and late-time nonlinear Rayleigh-Taylor instabilities. The strength
of group theory consideration is that it strictly obeys conservation laws,
allows for a solution of a boundary value problem, clearly outlines the
theoretical approximation, and is applicable in a broad range of parameters and
conditions. First proposed in the mid-1990th this approach enabled
the understanding of fundamental properties of nonlinear Rayleigh-Taylor (RT)
and Richtmyer-Meshkov (RM) instabilities, and the derivation of analytical
solutions for these nonlinear boundary value problems. It accurately described
local properties of interface evolution, such as asymptotic dynamics of the
front, as well as its global properties, such as classification of interactions
and pattern formation. The group theory approach was the first to introduce the
concept of coherent structures in the RT/RM research field, and to identify a
set of invariant measures of unstable interfacial dynamics. This approach also
clearly outlined the range of applicability and limitations of the main stream
heuristic models, and suggested a set of robust parameters that should be
precisely quantified in observations.
We were the first to find that
there is a family of regular asymptotic solutions describing nonlinear dynamics
of the interface in 3D and 2D RTI and RMI. We established the relation
between non-local and singular character of the flow evolution and the
multiplicity of regular asymptotic solutions, and showed that the number
of family parameters is set by the flow symmetry. We were the first to
analyze stability of the regular asymptotic solutions, and to identify the
similarities and differences in the asymptotic dynamics of 3D and 2D RTI and
RMI. For instance, both RT and RM structure tend to conserve isotropy in the
plane, the dynamics of highly symmetric 3D flows is universal, and the
dimensional 3D–2D crossover is discontinuous. In both RTI and RMI, nonlinear
evolution is essentially multi-scale and is characterized by independent
contributions of the wavelength and the amplitude of the front. Yet the shape
of the RT-bubble is curved as the flow is steady, and shape of RM-bubble is
flattened as the flow decelerates. We were the first to solve the early-time
linearized and late-time non-linear scale-dependent Rayleigh-Taylor dynamics
with variable acceleration. We discovered the direct link between the
nonlinear asymptotic solutions and the interfacial shear, found the
essentially interfacial character of Rayleigh-Taylor dynamics, and
identified the transition from Rayleigh-Taylor type to Richtmyer-Meshkov type
of dynamics with the variation of the acceleration parameters.
For pattern formation, the group theory approach found that in 2D and
3D the interactions essentially distinct characters and that in 3D with
hexagonal symmetry the growth of horizontal scales may not occur. We were the
first to identify the effect of interference of the waves constituting the
initial perturbation on order and disorder of the Rayleigh-Taylor and
Richtmyer-Meshkov dynamics and to study this effect qualitatively and
quantitatively.
Qualitative and quantitative results found within the group theory
approach been confirmed in accurate experiments and simulations. These
include multi-pole interactions in 3D RTI, flattening of RM bubbles, curved
shape of RT bubbles, ‘universality’ of highly symmetric 3D flows, discontinuity
of the dimensional 3D–2D crossover, etc. Our analysis suggested new directions
for interpretation of experimental and numerical data sets, as well as for
improvement of experimental diagnostics and numerical modeling techniques.
Our current research interests are focused on the problem of evolution
of a phase boundary with and without fluxes of scalar and vector fields across
it, and on connection between these fluxes and vortical structures at the
interface and in the bulk. This approach opens new avenues for rigorous
consideration of a broad range of nonlinear problems in multi-phase flows
previously inaccessible to analysis, including instability of flames,
non-Boussinesq convection, and ablative RTI. We are also interested in space-
and time-variable accelerations.
Far from equilibrium dynamics and
Lagrangian modeling of matter at the extremes
Relevant papers: Wright & Abarzhi 2021; Abarzhi et al 2020; Abarzhi
et al 2019a; Dell et al 2017; Pandian et al 2017; Dell et al 2015; Stanic et al
2013; Stanic et al 2012; Cassibry et al 2012; Zybin et al 2006; Zhakhovsky et
al 2006.
Relevant book chapters: Wright & Abarzhi 2021.
Relevant conference proceedings: Stanic et al 2011; Zybin et al 2006;
Zhakhovsky et al 2006.
One of my research interests is to understand connections between
Lagrangian (kinetic) and Eulerian (continuous) descriptions in non-equilibrium
systems. This is a fundamental scientific problem, since at micro-scopic and
meso-scales, the non-equilibrium dynamics depart from the scenario of
quasi-statistic Boltzmann equation. This difference becomes even more dramatic
under conditions of high energy density, for instance, in inertial confinement
and magneto-inertial fusion. To understand the coupling of microscopic to
macroscopic scales, we applied the theoretical analysis and the particle
simulations.
In particular, we were the first to conduct molecular dynamic
simulations of RMI in solids and to find the dependence of the material melting
on the strength and orientation of the shock. We also were the first to
systematically study the Richtmyer-Meshkov instability induced by strong shocks
for fluids with contrasting densities and with small and large amplitude
initial perturbations imposed at the fluid interface by means of Lagrangian
approach.
We employed the Smooth Particle Hydrodynamics Code (SPHC) to
ensure the shock capturing and the interface tracking, and to accurately
account for the dissipation processes. We achieved excellent agreement
with existing experiments and with theoretical analyses including zero-order
theory that describes the post-shock background motion of the fluids, linear
theory that provides RMI growth-rate in a broad range of the Mach and Atwood
numbers, and highly nonlinear theory that describes the nonlinear evolution of
RM bubble front. Particularly, the nonlinear dynamics is shown to the
essentially multi-scale and interfacial character. We further found that
for strong-shock-driven RMI a significant part of the shock deposited energy
goes into compression and background motion of the fluids, and only a small
fraction of it remains for interfacial mixing. According to our results, the
initial perturbation amplitude is a key factor of RMI evolution that strongly
influences the dynamics of the interface, in the fluid bulk, and the
transmitted shock.
One interesting result is a non-monotone dependence of the initial
growth-rate of RMI on the initial amplitude and the maximum initial growth-rate
of strong-shock-driven RMI. It suggests that the amount of energy that can be
deposited by the shock at the interface is finite and depends only on the shock
strength, the density ratio, and the adiabatic indexes. We developed a
theoretical model for the RMI growth-rate and achieved the excellent,
within 3 significant digits and free from adjustable parameters, agreement with
accurate experiments.
We further found that in addition to vortical structures at the
interface, the vector and scalar fields in the fluid bulk are non-uniform at
small scales. These heterogeneities include the reverse cumulative jets, the
checkerboard velocity patterns, the shock-focusing effects, the localized hot
(cold) spots with temperature substantially higher (smaller) than that in the
ambient, and the high and the low pressure regions. These small-scale
heterogeneities can play a critical role for energy transport and accumulation
at small scales in supernovae.
For the near future, we would like to further understand the coupling
of microscopic to meso- and macroscopic scales in shock-driven multiphase flows
and apply this knowledge to describe the non-equilibrium transport in fluids,
plasmas, and materials, and to conduct detailed quantitative and qualitative
comparisons of the Lagrangian (kinetic) and Eulerian (continuous) simulations
results with one another and with the theory.
Dynamical systems: Influence of
heterogeneities and noise on pattern formation and chaos
Relevant papers: Nepomnyashchy
& Abarzhi 2010; Abarzhi et al 2007.
Relevant book
chapters: Fedotov & Abarzhi 2006; Abarzhi et al 2003.
Pattern forming
systems exhibits some universal features of the nonlinear dynamics. For ideal
spatially extended systems, this universality is well captured by
low-dimensional models. Realistic systems are often multi-scale and
inhomogeneous. This raises a problem on qualitative and quantitative
correspondence between the idealized low-dimensional description and the
realistic multi-scale phenomenon. This problem can be viewed on one hand as a
sensitivity of the model results to heterogeneities and noise, and, on the
other hand, -- as a control of a pattern formation and chaos development by
means of heterogeneities. We considered the effect of heterogeneities on the
dynamics of nonlinear wave patterns within the framework of a complex
Ginzburg-Landau equation with parametric non-resonant forcing. The forcing
preserves the gauge invariance of the system and is non-intrusive. We found
that the forcing results in occurrence of traveling waves with new dispersion
properties, leads to appearance of waves with quasi-periodic and an-harmonic
spatial structures, and may completely suppress development of intermittent
chaos.
Data analysis and design of
experiments and simulations
Relevant papers: Abarzhi c (in processing); Suchandra et al (in
processing); Abarzhi & Williams (in processing); Abarzhi et al 2025; Abarzhi
& Williams 2024a,b; Wiliams & Abarzhi 2023; Williams & Abarzhi
2022; Pfefferle & Abarzhi 2022; Jacobs et al 2021; Pfefferle & Abarzhi
2020; Abarzhi & Sreenivasan 2020; Swisher et al 2015; Anisimov et al 2013;
Orlov et al 2010; Fisher et al 2008; Abarzhi 2008; Orlov et al 2007a,b.
Relevant book chapters: Rahimyar & Abarzhi (in processing); Williams & Abarzhi 2024; Hwang et al 2020;
Tieszen et al 2004.
Relevant conference proceedings: Orlov et al 2007.
For traditional physical systems (that are stable, single-scale,
‘linear,’ local and are bounded in a narrow parameter regime) an optimally
designed experiment ensures statistical quality of collected data. The systems
that are studied in contemporary physics are often non-equilibrium, multi-scale,
nonlinear, non-local and multi-parameter. In these systems the formulation and
solution of the optimization problem is a formidable task, and the statistical
quality is a challenge to evaluate. The problem complexity can be reduced when
symmetry principles are applied. We successfully employed the principles
of symmetry theory in experiments and simulations in order to identify a set of
robust parameters and a useful metrics that should be precisely diagnosed. We
found that, beyond their important role in understanding fundamental properties
of nature, the symmetry principles can also serve to identify the quantitative
criteria for the estimate of the quality and information capacity of
experimental and numerical data sets, and to elaborate the new methods for
mitigation and control of complex processes in technology, such as fusion and
nano-electronics. Furthermore, we showed how to leverage modern technologies in
order to achieve significant improvement in precision, accuracy, dynamic range
and reproducibility of data.
Quantitative biology: topological comparison of protein structures
Relevant conference proceedings: Upadhyay et al 2011.
Comparison of protein structures has critical importance
for understanding the functionality, specificity, flexibility, and evolution of
proteins. Existing comparison methods usually optimize a global structural
similarity. The original highly efficient method TOPOFIT is topology based and is
capable to align protein structures and produce elastic alignments through the Delaunay
tessellations, with representations employing Voronoi polyhedrons and Delaunay
simplexes. The method naturally detects and finds non-sequential alignments and
flexible alignments, with accuracy over-performing that of other methods. We
set the comparison of protein structures as a mathematical and computational
problem of finding error-tolerant largest common sub-graphs of the Delaunay
tessellation graphs representing the compared proteins. We found the statistically
confident quantitative metrics for evaluating protein alignments, and confirmed
and justified this metrics in the computational experiments involving the non-homologous
proteins and the large structure families. This research was within the
collaborative project ‘Accurate protein structural comparisons by TOPOFIT’ (PI
Prof. Ilyin, Boston College & Northeastern University, USA).
Condensed matter physics:
spin dynamics of low-dimensional magnetic systems (PhD, MS)
Relevant papers: Abarzhi et al 1993; Abarzhi 1993; Abarzhi et al 1992;
Abarzhi & Chubukov 1990.
PhD Thesis advisors: Prof. Anisimov (Landau Institute for Theoretical
Physics, Academy of Sciences), Prof. Prozorova (Kapitza Institute for Physical
Problems, Academy of Sciences).
Low-dimensional non-collinear magnetic systems are characterized by
strong influence of frustrations and quantum fluctuations on their ground state
and spectral properties. To understand these influences, we considered
static and dynamical properties of quasi one-dimensional antiferromagnets on a
stacked triangular lattice. Previous studies interpreted experimental spectra
of these compounds either as a direct observation of the so-called Haldane (2016 Nobel Laureate) gap
in 1D spin chain or
as an influence of 2D frustrations. We employed the 3D Heisenberg
spin model and a phenomenological 3D model to understand
the microscopic and macroscopic properties of the system. We found the
key
parameter – the ratio between the relativistic anisotropy and weak
exchange
interaction – that governs the system dynamics, and showed that
re-normalized
3D spin-wave theory adequately describes the experiments in either
quasi-1D or
quasi-2D limit. We conducted test experiments, employed direct
measurements and
confirmed the new qualitative and quantitative results predicted the
theory,
including transversal magnetization in an oblique magnetic field,
dependences
of the dynamics on the parameter, and quantum phase transition.
Statistical physics:
spin glass theory of nonlinear Hopfiled model (MS)
Hopfield model is a standard model of neutral
networks. We introduced a Hamiltonian system extending the Hopfield model with the
nonlinearity. Statistical attributes of the extended nonlinear model were investigated
by employing the spin glass theory. The sustainability of the ground states
under the thermal noise was analyzed by using the replica method. We found that
the nonlinearity can substantially enlarge the information capacity of the
standard Hopfield model and increase the ratio of the thermally stable states to
all ground states.
Scientific program ‘Turbulent Mixing and
Beyond’
Relevant research books: Abarzhi et al (in processing); Abarzhi & Glimm (in processing), Abarzhi &
Goddard (in processing); Abarzhi 2025a,b; Abarzhi 2022; Abarzhi &
Nepomnyashchy 2022; Abarzhi & Gekelman 2022; Abarzhi et al. 2021; Abarzhi
et al 2019; Abarzhi & Gauthier 2017; Abarzhi et al 2013a,b; Abarzhi et al
2014; Abarzhi et al 2013; Abarzhi & Sreenivasan 2010; Abarzhi et al 2010;
Abarzhi & Gauthier 2008.
Relevant editorial papers: Abarzhi a,b (in processing); Abarzhi 2025; Abarzhi
2022a,b; Abarzhi & Gekelman 2022; Abarzhi & Goddard 2019; Abarzhi 2018;
Gautier et al 2018; Abarzhi et al 2015; Abarzhi et al 2013a,b,c,d; Gauthier et
al 2013; Abarzhi & Sreenivasan 2010a,b; Abarzhi et al 2010; Gauthier et al
2010; Abarzhi et al 2008.
Relevant proceedings with ISBN: Abarzhi et al 2017; Abarzhi et al 2014;
Abarzhi et al 2011; Abarzhi et al 2009; Abarzhi 2007.
Relevant conference proceedings: Abarzhi & Goddard 2023; Abarzhi
2023; Abarzhi et al 2017; Abarzhi et al 2014; Abarzhi et al 2011; Abarzhi et al
2009; Abarzhi 2007.
Relevant video / audio recordings: Abarzhi & Goddard 2023a,b;
Abarzhi 2019 a,b; Abarzhi 2012; Abarzhi & Sreenivasan 2017; Abarzhi 2011;
Abarzhi et al 2009; Abarzhi 2007.
We developed the program
‘Turbulent Mixing and Beyond’ (TMB) to bring together researchers from
different areas of science, engineering and mathematics and to focus their
attention on the fundamental problem of non-equilibrium dynamics and
interfacial and turbulent mixing. Interfacial mixing and turbulent mixing are non-equilibrium
processes that occur in a broad variety of natural phenomena and technological
applications, ranging from astrophysical to atomistic scales and from high- to
low- energy-density regimes. Examples include inertial confinement fusion,
light–matter interaction, strong shock waves, explosions, supernovae and
accretion discs, convection in stellar and planetary interiors, premixed and
non-premixed combustion, hypersonic and supersonic flows — both wall-bounded and
boundary-free — as well as the atmosphere and the ocean. A good grasp on
interfacial mixing and turbulent mixing is crucial for the cutting-edge
technology in laser micro-machining and free-space optical telecommunications,
and for traditional industrial applications in the areas of aeronautics and
aerodynamics. In some of these applications (e.g. combustion processes),
turbulent mixing should be enhanced, whereas in some others (e.g. inertial
confinement fusion) it should be mitigated. In all these circumstances, we
to understand the fundamentals of non-equilibrium dynamics, interfacial mixing
and turbulent mixing, be able to gather high-quality data and derive knowledge
from these data, and, ultimately, achieve a better control of these complex
processes.
In 2007, with the support of international scientific
community, national and international funding agencies and institutions,
we founded the TMB program. The
program goals are in the development of new ideas for understanding the
fundamentals of non-equilibrium dynamics, interfacial mixing and turbulent mixing,
in applications of novel approaches for description of a broad range of
phenomena where these processes occur, and in the potential impact on
technology development. The TMB program spans fluid dynamics, plasmas,
high-energy-density physics, astrophysics, material science, combustion, Earth
sciences, nonlinear physics, applied mathematics, probability, statistics, data
processing, computations, optics and communications, and other areas. To date,
the TMB community unites a few thousand researchers worldwide including
scientists from academia, national laboratories, corporations and industry, at
experienced and early stages of their carrier working. Google.com returns over ~7,000,000 results for
‘turbulent mixing and beyond’.
Please see for
details the program web-site, the recordings and the video-interviews:
http://www.tmbw.org
http://www.tmbw.org/tmbconferences
https://vimeo.com/352943627
https://vimeo.com/48922680