scholarly journals Localization in Stationary Non-equilibrium Solutions for Multicomponent Coagulation Systems

2021 ◽  
Author(s):  
Marina A. Ferreira ◽  
Jani Lukkarinen ◽  
Alessia Nota ◽  
Juan J. L. Velázquez
Keyword(s):  
Source Term ◽  
Equilibrium Solutions ◽  
Equilibrium Conditions ◽  
Measure Concentration ◽  
Localization Property ◽  
Smoluchowski Coagulation Equation ◽  
Coagulation Equation ◽  
Asymptotic Scaling ◽  
Coagulation Kernel ◽  
Non Equilibrium

AbstractWe consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that the corresponding stationary non-equilibrium solutions have a universal localization property. More precisely, we show that these solutions asymptotically localize into a direction determined by the source or by a flux constraint: the ratio between monomers of a given type to the total number of monomers in the cluster becomes ever closer to a predetermined ratio as the cluster size is increased. The assumptions on the coagulation kernel are quite general, with isotropic power law bounds. The proof relies on a particular measure concentration estimate and on the control of asymptotic scaling of the solutions which is allowed by previously derived estimates on the mass current observable of the system.

scholarly journals Stationary Non-equilibrium Solutions for Coagulation Systems

2021 ◽  
Vol 240 (2) ◽  
pp. 809-875
Author(s):  
Marina A. Ferreira ◽  
Jani Lukkarinen ◽  
Alessia Nota ◽  
Juan J. L. Velázquez
Keyword(s):  
Power Law ◽  
Source Term ◽  
Continuous Model ◽  
Stationary Solutions ◽  
Weight Functions ◽  
Equilibrium Solutions ◽  
Coagulation Rate ◽  
Diffusion Limited Aggregation ◽  
Coagulation Equations ◽  
Non Equilibrium

AbstractWe study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of coagulation rate kernels, with the main restriction being boundedness from above and below by certain weight functions. The weight functions depend on two power law parameters, and the assumptions cover, in particular, the commonly used free molecular and diffusion limited aggregation coagulation kernels. Our main result shows that the two weight function parameters already determine whether there exists a stationary solution under the presence of a source term. In particular, we find that the diffusive kernel allows for the existence of stationary solutions while there cannot be any such solutions for the free molecular kernel. The argument to prove the non-existence of solutions relies on a novel power law lower bound, valid in the appropriate parameter regime, for the decay of stationary solutions with a constant flux. We obtain optimal lower and upper estimates of the solutions for large cluster sizes, and prove that the solutions of the discrete model behave asymptotically as solutions of the continuous model.

scholarly journals Mass-conserving solutions to the Smoluchowski coagulation equation with singular kernel

2019 ◽  
Vol 150 (4) ◽  
pp. 1805-1825 ◽  
Author(s):  
Prasanta Kumar Barik ◽  
Ankik Kumar Giri ◽  
Philippe Laurençot
Keyword(s):  
Weak Solutions ◽  
Linear Growth ◽  
Weak Compactness ◽  
Singular Kernel ◽  
Initial Condition ◽  
Existence Proof ◽  
Global Weak Solutions ◽  
Smoluchowski Coagulation Equation ◽  
Coagulation Equation ◽  
Coagulation Kernel

AbstractGlobal weak solutions to the continuous Smoluchowski coagulation equation (SCE) are constructed for coagulation kernels featuring an algebraic singularity for small volumes and growing linearly for large volumes, thereby extending previous results obtained in Norris (1999) and Cueto Camejo & Warnecke (2015). In particular, linear growth at infinity of the coagulation kernel is included and the initial condition may have an infinite second moment. Furthermore, all weak solutions (in a suitable sense) including the ones constructed herein are shown to be mass-conserving, a property which was proved in Norris (1999) under stronger assumptions. The existence proof relies on a weak compactness method in L1 and a by-product of the analysis is that both conservative and non-conservative approximations to the SCE lead to weak solutions which are then mass-conserving.

scholarly journals A time-domain phase diagram of metastable states in a charge ordered quantum material

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jan Ravnik ◽  
Michele Diego ◽  
Yaroslav Gerasimenko ◽  
Yevhenii Vaskivskyi ◽  
Igor Vaskivskyi ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Time Domain ◽  
Metastable States ◽  
Scanning Tunneling ◽  
Photon Density ◽  
Tunneling Microscopy ◽  
Equilibrium Conditions ◽  
Time Resolved ◽  
A Charge ◽  
Non Equilibrium

AbstractMetastable self-organized electronic states in quantum materials are of fundamental importance, displaying emergent dynamical properties that may be used in new generations of sensors and memory devices. Such states are typically formed through phase transitions under non-equilibrium conditions and the final state is reached through processes that span a large range of timescales. Conventionally, phase diagrams of materials are thought of as static, without temporal evolution. However, many functional properties of materials arise as a result of complex temporal changes in the material occurring on different timescales. Hitherto, such properties were not considered within the context of a temporally-evolving phase diagram, even though, under non-equilibrium conditions, different phases typically evolve on different timescales. Here, by using time-resolved optical techniques and femtosecond-pulse-excited scanning tunneling microscopy (STM), we track the evolution of the metastable states in a material that has been of wide recent interest, the quasi-two-dimensional dichalcogenide 1T-TaS2. We map out its temporal phase diagram using the photon density and temperature as control parameters on timescales ranging from 10−12 to 103 s. The introduction of a time-domain axis in the phase diagram enables us to follow the evolution of metastable emergent states created by different phase transition mechanisms on different timescales, thus enabling comparison with theoretical predictions of the phase diagram, and opening the way to understanding of the complex ordering processes in metastable materials.

Emergence of a Promiscuous Peroxidase Under Non‐Equilibrium Conditions

2021 ◽  
Author(s):  
Sumit Pal ◽  
Antara Reja ◽  
Subhajit Bal ◽  
Baishakhi Tikader ◽  
Dibyendu Das
Keyword(s):  
Equilibrium Conditions ◽  
Non Equilibrium

scholarly journals Quantification of fast molecular adhesion by fluorescence footprinting

2021 ◽  
Author(s):  
Adam B. Yasunaga ◽  
Isaac T.S. Li
Keyword(s):  
Shear Stress ◽  
Dynamic Range ◽  
Force Distribution ◽  
Equilibrium Conditions ◽  
Ligand Dissociation ◽  
Molecular Adhesion ◽  
Molecular Force ◽  
Adhesion Complex ◽  
Non Equilibrium

AbstractRolling adhesion is a unique process in which the adhesion events are short-lived and operate under highly non-equilibrium conditions. These characteristics pose a challenge in molecular force quantification, where in situ measurement of such forces cannot be achieved with most molecular force sensors that probe near equilibrium. In this report, we demonstrated a quantitative adhesion footprint assay combining DNA-based non-equilibrium force probes and modelling to measure the molecular force involved in fast rolling adhesion. We were able to directly profile the ensemble molecular force distribution during rolling adhesion with a dynamic range between 0 – 18 pN. Our results showed that the shear stress driving bead rolling motility directly controls the molecular tension on the probe-conjugated adhesion complex. Furthermore, the shear stress can steer the dissociation bias of components within the molecular force probe complex, favouring either DNA probe dissociation or receptor-ligand dissociation.

scholarly journals Formation of Hydrides in the Surface Layer of Aluminum in NonEquilibrium Conditions of Electrolyte Plasma

2019 ◽  
Vol 20 (2) ◽  
pp. 181-184
Author(s):  
L. Fedorenkova
Keyword(s):  
Diffusion Layer ◽  
Hydrogen Atoms ◽  
Equilibrium Conditions ◽  
Heating And Cooling ◽  
Polymorphic Modifications ◽  
High Heating ◽  
Aluminum Hydrides ◽  
Micromechanical Characteristics ◽  
Nonequilibrium Conditions ◽  
Non Equilibrium

In this paper, the formation of a diffusion layer on aluminum, which includes aluminum hydrides, in non-equilibrium conditions of electrolyte plasma with high local temperatures, high heating and cooling rates were studied. As a result of the research it was obtained that in the diffusion layer formed complex nanosized inclusions of polymorphic modifications (AlН3)n and AlB3H12. The diffusion in the non-equilibrium conditions of the electrolyte plasma is carried out in hydrogen environment, where the hydrogen atoms have the greatest energy and is one of the main forces that activate the diffusion process and influence the structure, composition and micromechanical characteristics of the diffusion layer.

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