Finite Dissipation Research Articles

Operator size growth in Lindbladian SYK

We investigate the growth of operator size in the Lindbladian Sachdev-Ye-Kitaev model with q-body interaction terms and linear jump terms at finite dissipation strength. We compute the operator size as well as its distribution numerically at finite q and analytically at large q. With dissipative (productive) jump terms, the size converges to a value smaller (larger) than half the number of Majorana fermions. At weak dissipation, the evolution of operator size displays a quadratic-exponential-plateau behavior. The plateau value is determined by the ratios between the coupling of the interaction and the linear jump term in the large q limit. The operator size distribution remains localized in the finite size region even at late times, contrasting with the unitary case. Moreover, we also derived the time-independent orthogonal basis for operator expansion which exhibits the operator size concentration at finite dissipation. Finally, we observe that the uncertainty relation for operator size growth is saturated at large q, leading to classical dynamics of the operator size growth with dissipation.

A computational study of solidification kinetics in multicomponent alloys

Recent advances in materials processing technologies highlight the need to understand solidification kinetics in multicomponent alloys. Using a finite interface dissipation phase field model, we investigate planar front solidification rates in ternary alloys, used as a model system, as a function of various mass transport processes and nonequilibrium conditions. Simulation results reveal that the off-diagonal diffusion coefficients play an important role in controlling the solid–liquid (S–L) interface velocity and solute partition coefficients. Specifically, under various rapid solidification conditions negative values for the off-diagonal diffusion coefficients increase the solute partition coefficients due to the depletion of liquid phase concentrations ahead of the S–L interface. Given an undercooling, the S–L interface velocity increases with decreasing the off-diagonal diffusion coefficients. In broad terms, our work quantifies the role of coupled mass transport processes and nonequilibrium effects in solidification rates of multicomponent alloys.

Multi-physics simulation of non-equilibrium solidification in Ti-Nb alloy during selective laser melting

This paper underscores the critical role of temperature distribution in the molten pool on the resulting solidification microstructure during selective laser melting (SLM) process. A powder-resolved computational fluid dynamics (CFD) model of Ti-Nb alloy is established to investigate heat transfer and fluid flow in the molten pool. When comparing the bulk model to the powder bed model, discrepancies in temperature gradient and cooling rate can reach up to 26.29 % and 18.32 %, respectively. Utilizing the powder bed CFD model, temperature gradient and cooling rate data at the molten pool boundary are integrated into the finite interface dissipation phase-field model. The simulation results illuminate the non-equilibrium solidification microstructure in the SLMed Ti-Nb alloy. Results indicate that the rapid solidification fosters a pronounced solute trapping effect, mitigating solute microsegregation. The microstructure manifests as cellular and dendritic structures, with Nb concentration in cellular cores and depletion in intercellular region. Predicted primary dendrite arm spacing (PDAS) or cell size range between 0.4 to 0.6 μm, consistent with experimental observations. In particular, the study reveals a transition from dendritic to cellular and from cellular to planar structures, with an accompanying analysis of the underlying mechanisms.

Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry

We study the quench dynamics of noninteracting fermionic quantum many-body systems that are subjected to Markovian drive and dissipation and are described by a quadratic Liouvillian which has parity-time (PT) symmetry. In recent work, we have shown that such systems relax locally to a maximum entropy ensemble that we have dubbed the PT-symmetric generalized Gibbs ensemble (PTGGE), in analogy to the generalized Gibbs ensemble that describes the steady state of isolated integrable quantum many-body systems after a quench. Here, using driven-dissipative versions of the Su-Schrieffer-Heeger (SSH) model and the Kitaev chain as paradigmatic model systems, we corroborate and substantially expand upon our previous results. In particular, we confirm the validity of a dissipative quasiparticle picture at finite dissipation by demonstrating light cone spreading of correlations and the linear growth and saturation to the PTGGE prediction of the quasiparticle-pair contribution to the subsystem entropy in the PT-symmetric phase. Further, we introduce the concept of directional pumping phases, which is related to the non-Hermitian topology of the Liouvillian and based upon qualitatively different dynamics of the dual string order parameter and the subsystem fermion parity in the SSH model and the Kitaev chain, respectively: depending on the postquench parameters, there can be pumping of string order and fermion parity through both ends of a subsystem corresponding to a finite segment of the one-dimensional lattice, through only one end, or there can be no pumping at all. We show that transitions between dynamical pumping phases give rise to a new and independent type of dynamical critical behavior of the rates of directional pumping, which are determined by the soft modes of the PTGGE. Published by the American Physical Society 2024

Thixo-elastoviscoplastic modeling of human blood

We propose an enhanced model for the rheological characterization of human blood that accounts for thixotropy, viscoelasticity, and yield-stress. Blood plasma is assumed to act as a Newtonian solvent. We introduce a scalar variable, λ, to macroscopically describe the structure of blood. The temporal evolution of λ is governed by an equation that accounts for aggregation of red blood cells and breakdown of rouleaux structures. We introduce a Gaussian function that qualitatively describes experimental findings on rouleaux restructuring and the expression that was proposed by Stephanou and Georgiou for the breakdown term. The constitutive equation for stresses is based on the elastoviscoplastic formalism by Saramito. However, the max term of the viscoplastic deformation rate has been replaced by a continuous function of λ to account for smooth solid-fluid transition, following the experimental evidence. The continuous yielding description provides improved rheological predictions, especially in small amplitude oscillatory shear. The model predicts finite viscous dissipation at small amplitude oscillation, as we would expect from a gel material-like human blood. Overall, it has nine adjustable parameters that are fitted simultaneously to experimental data by nonlinear regression. The model can accurately predict numerous flow conditions: steady shear, step shear, hysteresis loops, and oscillatory shear. We compare this model (TEVP 9) to our previous formulation for human blood (TEVP 11), and we show that the predictions of the new model are more accurate, despite using fewer parameters. We provide additional predictions for uniaxial elongation, which include finite normal stress difference, extensional hardening at large values of the extensional rate, and extensional thinning at extremely large extensional rates.

Entropía y análisis de Hurst para la determinación de la complejidad de series temporales de flujo bifásico

In this work is presented a hydrodynamic and mass transfer study using the computational fluid dynamic (CFD) for typical experimental measurements and theoretical calculations for pyrite (FeS2) dissolution in acid media using ozone as an oxidizing agent, which occurs in a laboratory glass reactor. The hydrodynamics for the reactor employed, was evaluated with the Navier-Stokes equations (κ-ɛ) RNG turbulence model and the VOF multi-phase model. The results of the hydrodynamic simulation study show that the reactor can operate at a speed range of 1.2 to 4.4 m/s at a total pressure of 12.5 Pa; the Reynolds numerical profile indicates that the flow has a turbulent behavior inside the reactor. For the mass transfer simulation, the model of finite velocity-Eddy dissipation was used for solving the kinetic of the reaction, and was performed for 3 different particle fractions: -106 +75 µm, -38 +25 µm and -25 µm. The simulation results present satisfactorily differences of 17%, 13% and 2% respectively, in comparison with experimental data for pyrite dissolved.

Dynamic Crack-Front Deformations in Cohesive Materials.

Crack fronts deform due to heterogeneities, and inspecting these deformations can reveal local variations of material properties, and help predict out-of-plane damage. Current models neglect the influence of a finite dissipation length scale behind the crack tip, called the process zone size. The latter introduces scale effects in the deformation of the crack front, that are mitigated by the dynamics of the crack. We provide and numerically validate a theoretical framework for dynamic crack-front deformations in heterogeneous cohesive materials, a key step toward identifying the effective properties of a microstructure.

Bistability and nonequilibrium condensation in a driven-dissipative Josephson array: A c-field model

Developing theoretical models for nonequilibrium quantum systems poses significant challenges. Here we develop and study a multimode model of a driven-dissipative Josephson junction chain of atomic Bose-Einstein condensates, as realised in the experiment of Labouvie et al. [Phys. Rev. Lett. 116, 235302 (2016)]. The model is based on c-field theory, a beyond-mean-field approach to Bose-Einstein condensates that incorporates fluctuations due to finite temperature and dissipation. We find the c-field model is capable of capturing all key features of the nonequilibrium phase diagram, including bistability and a critical slowing down in the lower branch of the bistable region. Our model is closely related to the so-called Lugiato-Lefever equation, and thus establishes new connections between nonequilibrium dynamics of ultracold atoms with nonlinear optics, exciton-polariton superfluids, and driven damped sine-Gordon systems.

Characteristic Analysis of Finite Dissipation Zone in Directional Material Flow

Materials compress each other in a directional material flow, causing energy and momentum to overflow. Materials moving at a low velocity outside the boundary of a rigid moving component form a finite dissipation zone. A discrete element model is established to explore its characteristics. First, the mass of material driven by the disk increases linearly with an increase in the translation distance, and the mass of material moving at a low velocity increases significantly. Second, the movement state of materials depends on its distance from the disk. The material velocity at the boundary of the finite dissipation zone is verified to be 1 mm/s by analyzing the material velocity and contact force. When the operating parameters are different, the boundary curves of the finite dissipation zone are similar but the numerical values are different. Third, the maximum edge extends 0.7–3.0 mm beyond the boundary, and this value is linearly related to the translation velocity with little impact from the lowering depth. Studying the mechanism of finite dissipation zones contributes to forming an efficient directional material flow and the energy dissipation mechanism under a flexible constraint.

Problem of Longitudinal Vibrations of a Viscoelastic Rod of Maxwell Type

In this paper, we study well-posedness in the sense of Hadamard of the Cauchy problem for a one-dimensional hyperbolic system of partial differential equations describing the longitudinal vibrations of a viscoelastic rod of Maxwell type with constant cross-section. We discuss some properties of the system and its solutions: the conservation of modified “energy”, the finite propagation speed, dispersion, and dissipation of solutions.

Topological Vortexes, Asymptotic Freedom, and Multifractals

In this paper, we study the Kelvinons, which are monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, which is in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS.

Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits

Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transport theory concerns the means by which one can optimally transport a source distribution to a target distribution, deriving a useful metric between probability distributions, called the Wasserstein distance. Despite their seemingly unrelated nature, an intimate connection between these fields has been unveiled in the context of continuous-state Langevin dynamics, providing several important implications for nonequilibrium systems. In this study, we elucidate an analogous connection for discrete cases by developing a thermodynamic framework for discrete optimal transport. We first introduce a novel quantity called dynamical state mobility, which significantly improves the thermodynamic uncertainty relation and provides insights into the precision of currents in nonequilibrium Markov jump processes. We then derive variational formulas that connect the discrete Wasserstein distances to stochastic and quantum thermodynamics of discrete Markovian dynamics described by master equations. Specifically, we rigorously prove that the Wasserstein distance equals the minimum product of irreversible entropy production and dynamical state mobility over all admissible Markovian dynamics. These formulas not only unify the relationship between thermodynamics and the optimal transport theory for discrete and continuous cases, but also generalize it to the quantum case. In addition, we demonstrate that the obtained variational formulas lead to remarkable applications in stochastic and quantum thermodynamics, such as stringent thermodynamic speed limits and the finite-time Landauer principle. These bounds are tight and can be saturated for arbitrary temperatures, even in the zero-temperature limit. Notably, the finite-time Landauer principle can explain finite dissipation even at extremely low temperatures, which cannot be explained by the conventional Landauer principle.1 MoreReceived 26 July 2022Revised 1 December 2022Accepted 13 December 2022DOI:https://doi.org/10.1103/PhysRevX.13.011013Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntropy productionNonequilibrium & irreversible thermodynamicsNonequilibrium statistical mechanicsQuantum thermodynamicsStochastic processesStochastic thermodynamicsThermodynamics of computationTechniquesGraph theoryStatistical PhysicsInterdisciplinary PhysicsGeneral Physics

Evolution of dissipative fluid flows with imposed helicity conservation

We propose the helicity-conserved Navier–Stokes (HCNS) equation by modifying the non-ideal force term in the Navier–Stokes (NS) equation. The corresponding HCNS flow has strict helicity conservation, and retains major NS dynamics with finite dissipation. Using the helical wave decomposition, we show that the pentadic interaction of Fourier helical modes in the HCNS dynamics is more complex than the triadic interaction in the NS dynamics, and enhanced variations for left- and right-handed helicity components cancel each other in the HCNS flow to keep the invariant helicity. A comparative study of HCNS and NS flow evolutions with direct numerical simulation elucidates the influence of the helicity conservation on flow structures and statistics in the vortex reconnection and isotropic turbulence. First, the HCNS flow evolves towards a Beltrami state with a $-4$ scaling law of the energy spectrum at high wavenumbers at long times. Second, large-scale flow structures are almost identical during the viscous reconnection of vortex tubes in the two flows, whereas many more small-scale helical structures are generated via the pentadic mode interaction in the HCNS flow than in the NS flow. Moreover, we demonstrate that parity breaking at small scales can trigger a notable helicity variation in the NS flow. These findings hint that the helicity may not be conserved in the inviscid limit of the NS flow.

A novel computational model for isotropic interfacial energies in multicomponent alloys and its coupling with phase-field model with finite interface dissipation

• A CALPHAD model for isotropic interfacial energies was developed and programmed. • Direct coupling between interfacial energy model and phase-field model was realized. • Isotropic interfacial energy databases in Ni-Al-Cr systems were established. • 3-D phase-field simulations of γ dendritic growth in two Ni alloys were conducted. • Effect of different interfacial energies on γ dendritic growth was analyzed. In this work, a novel computational model for the description of the temperature- and composition-dependent isotropic interfacial energy in multicomponent alloys was first developed in the framework of the CALculation of PHAse Diagram (CALPHAD) approach and implemented in a home-made code. By linking to the open-source code for interfacial energy calculation in alloys, OpenIEC, the databases for isotropic γ /liquid and γ / γ' interfacial energies in Ni-Al, Ni-Cr, Al-Cr, and Ni-Al-Cr systems were then efficiently established. After that, a direct coupling strategy between the current CALPHAD interfacial energy database and the phase-field model with finite interface dissipation was proposed and applied to three-dimensional (3-D) phase-field simulations of the primary γ dendritic growth in both Ni-Al and Ni-Al-Cr alloys during isothermal solidification. The effect of the interfacial energy on the morphology, tip growth rate, and partitioning coefficients in primary γ dendrites of binary Ni-Al and ternary Ni-Al-Cr alloys was investigated by comprehensively comparing the phase-filed simulation results using the composition-/temperature-dependent interfacial energies with those using the constant value. It is anticipated that the presently developed CALPHAD model for interfacial energy is of general validity for different multicomponent alloys and should be integrated with the phase-field model for quantitative simulation of their microstructure evolution.

Viscous flow through a finite-width slit: Boundary conditions and dissipation

We study the hydrodynamic viscous electronic transport in a two-dimensional sample separated into two semi-infinite planes by a one-dimensional infinite barrier. The semi-infinite planes are electrically connected via the finite-size slit in the barrier. We calculate the current through the slit assuming finite voltage drop between the planes and neglecting disorder-induced Ohmic resistance, so dissipation and resistance are purely viscosity induced. We find that the only solution to the Stokes equation in this geometry, which yields a finite dissipation at finite resistance (and, hence, is not self-contradictory), is the one that fulfills both the no-stress and no-slip boundary conditions simultaneously. As a remarkable consequence, the obtained velocity profile satisfies the so-called partial-slip (Maxwell) boundary condition for any value of the slip length, which drops out from all final results. We also calculate the electronic temperature profile for the small and large heat conductivity and find asymmetric (with respect to the barrier) temperature patterns in the former case.

Schrödinger cat state formation in small bosonic Josephson junctions at finite temperatures and dissipation

In this work, we consider the feasibility of Schrödinger cat (SC) and states formation by a convenient bosonic Josephson junction system in two-mode approximation. Starting with purely quantum description of two-mode Bose–Einstein condensate we investigate the effective potential approach that provides an accurate analytical description for the system with a large number of particles. We show that in the zero temperature limit SC states result from a quantum phase transition that occurs when the nonlinear strength becomes comparable with the Josephson coupling parameter. The Wigner function approach demonstrates the growth of the SC state halves separation and formation of -like states (a Fock state superposition) with the particle number increase. We examine the possibility to attain the SC state at finite temperatures and a weak dissipation leading to appearing of some critical temperature; it defines the second-order phase transition from classical activation process to the SC state formation through the quantum tunneling phenomenon. Numerical estimations demonstrate that the critical temperature is sufficiently below the temperature of atomic condensation. The results obtained may be useful for experimental observation of SC states with small condensate Josephson junctions.

Dissipation and geometry in nonlinear quantum transports of multiband electronic systems

Nonlinear responses in condensed matters attract recent intensive interest because they provide rich information about the materials and hold the possibility of being applied in diodes or high-frequency optical devices. Nonlinear responses are often closely related to the multiband nature of the system which can be taken into account by the geometric quantities such as the Berry curvature as shown in the nonlinear Hall effect. Theoretically, the semi-classical Boltzmann treatment or the reduced density matrix method have been often employed, in which the effect of dissipation is included through the relaxation time approximation. In the diagrammatic method, the relaxation is treated through the imaginary part of the self-energy of the Green function and the consequent broadening of the spectral function for the integration over the real frequency. Therefore, the poles of the Green function do not play explicit pole when there is finite dissipation. In this paper, in stark contrast to this conventional picture, we show that the poles of the Green function determine mostly the nonlinear response functions with dissipation, which leads to the terms with the Fermi distribution function of complex argument and results in the dissipation-induced geometric term. We elucidate the geometric origin of the nonreciprocal conductivity, which is related to the Berry curvature generalized to the higher derivative. Finally, we derive the analytical results on the geometric terms of the nonlinear conductivities in the type-I and type-II Weyl Hamiltonian to demonstrate their crucial roles.

A thermomechanical finite strain shape memory alloy model and its application to bistable actuators

This work presents a thermomechanical finite strain shape memory alloy model that utilizes a projection method to deal with the incompressibility constraint on inelastic strains. Due to its finite strain formulation, it is able to accurately predict the behavior of shape memory alloys with high transformation strains. The key feature of this model is the thermomechanical modeling of the shape memory effect and superelastic behavior by optimizing a global, incremental mixed thermomechanical potential, the variation of which yields the linear momentum balance, the energy balance, the evolution equations of the internal variables as well as boundary conditions of Neumann- and Robin-type. The proposed thermal strain model allows to properly capture transformation induced volume changes, which occur in some shape memory alloys. A finite strain dissipation potential is formulated, which incorporates the disappearance of inelastic strains upon austenite transformation. This important property is consistently transferred to the time-discrete potential using a logarithmic strain formulation. Yield and transformation criteria are derived from the dual dissipation potential. The implementation based on an active set search and the algorithmically consistent linearization are discussed in detail. The model is applied in three-dimensional simulations of a bistable actuator design to explore its capabilities.

Effect of oblique shock wave induced from a wavy-wall combustor surface for a splitter plate scramjet combustor

The shorter residence period of supersonic air in a scramjet combustor makes mixing and combustion challenging. Mixing augmentation occurs at the fuel-supersonic air interface. Multiple interactions between shock waves and the shear layer may significantly affect this inter surface. In this research, an attempt has been made to analyze how multiple oblique shock waves interact with the shear layer. The primary splitter plate combustor bottom wall is modified with a wavy-wall surface to ensure the development of multiple oblique shock waves. The internal flow field with and without a wavy wall surface has been analyzed by solving the two-dimensional Reynolds averaged Navier-Stokes equations and SST k-ω turbulence model. The reaction between ethylene fuel and the air is modeled with a global one-step reaction mechanism with finite rate eddy dissipation turbulence chemistry interaction. The flow disturbances with the wavy-wall surface have been evaluated by analyzing the numerical results like the flow structure, pressure, velocity, reaction rate, vortices, turbulence intensity, and interactions among shock wave, shear mixing, and boundary layers. The oblique shock waves induced from the wavy-wall surface significantly impact the mixing of fuel and air and successful reaction mechanism from the visualization of flow structure and concern results.

Hybrid microstructure-defect printability map in laser powder bed fusion additive manufacturing

This work presents a methodology for predicting a hybrid microstructure and defect processing map for laser powder bed fusion (LPBF) additive manufacturing (AM). A finite element (FE) analysis based thermal model is coupled with a phase field model (PFM) in order to predict both defect formation and microstructure across the LPBF process parameter space. The parameter space is first categorized into defect regions such as keyholing, balling, and lack of fusion. These regions are predicted using the FE thermal model, allowing a defect map to be generated based on the geometries of the melt pools for a defined powder layer thickness. A region of the parameter space that leads to successful AM of defect-free parts is then identified. Segregation across the parameter space is predicted by an integrated computational model, which couples a finite interface dissipation PFM and the aforementioned FE thermal model. The parameter space is then separated into regions that result in cellular or planar microstructures based on the area fraction of cellular-dendritic segregation predicted within the melt pools. By merging the microstructure and defect maps, a hybrid microstructure-defect printability map is generated that distinguishes a process parameter region for fabricating defect-free parts with homogeneous microstructures. This hybrid map is validated with experimental observations for a Ni-5wt.%Nb alloy. The hybrid printability map can be used in the rapid selection and optimization of process parameters for additively manufacturing any alloy (provided models and their parameterization are available, and the alloy is printable), and can potentially help design alloys best suited for AM.