scholarly journals Effective interactions mediated between two permeable disks in an active fluid

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Mahmoud Sebtosheikh ◽  
Ali Naji
Keyword(s):  
Spatial Distribution ◽  
Steady State ◽  
Phase Diagrams ◽  
Effective Interaction ◽  
Two Dimensions ◽  
Effective Interactions ◽  
Active Fluid ◽  
Brownian Particles ◽  
Exterior Regions ◽  
Pass Through

Abstract We study steady-state properties of a bath of active Brownian particles (ABPs) in two dimensions in the presence of two fixed, permeable (hollow) disklike inclusions, whose interior and exterior regions can exhibit mismatching motility (self-propulsion) strengths for the ABPs. We show that such a discontinuous motility field strongly affects spatial distribution of ABPs and thus also the effective interaction mediated between the inclusions through the active bath. Such net interactions arise from soft interfacial repulsions between ABPs that sterically interact with and/or pass through permeable membranes assumed to enclose the inclusions. Both regimes of repulsion and attractive (albeit with different mechanisms) are reported and summarized in overall phase diagrams.

scholarly journals Two-loop superstring five-point amplitudes. Part II. Low energy expansion and S-duality

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Eric D’Hoker ◽  
Carlos R. Mafra ◽  
Boris Pioline ◽  
Oliver Schlotterer
Keyword(s):  
Moduli Space ◽  
Effective Interaction ◽  
Type Ii ◽  
Leading Order ◽  
Effective Interactions ◽  
Heterotic String Theory ◽  
Genus Two ◽  
Genus One ◽  
Graph Function ◽  
Point Amplitude

Abstract In an earlier paper, we constructed the genus-two amplitudes for five external massless states in Type II and Heterotic string theory, and showed that the α′ expansion of the Type II amplitude reproduces the corresponding supergravity amplitude to leading order. In this paper, we analyze the effective interactions induced by Type IIB superstrings beyond supergravity, both for U(1)R-preserving amplitudes such as for five gravitons, and for U(1)R-violating amplitudes such as for one dilaton and four gravitons. At each order in α′, the coefficients of the effective interactions are given by integrals over moduli space of genus-two modular graph functions, generalizing those already encountered for four external massless states. To leading and sub-leading orders, the coefficients of the effective interactions D2ℛ5 and D4ℛ5 are found to match those of D4ℛ4 and D6ℛ4, respectively, as required by non-linear supersymmetry. To the next order, a D6ℛ5 effective interaction arises, which is independent of the supersymmetric completion of D8ℛ4, and already arose at genus one. A novel identity on genus-two modular graph functions, which we prove, ensures that up to order D6ℛ5, the five-point amplitudes require only a single new modular graph function in addition to those needed for the four-point amplitude. We check that the supergravity limit of U(1)R-violating amplitudes is free of UV divergences to this order, consistently with the known structure of divergences in Type IIB supergravity. Our results give strong consistency tests on the full five-point amplitude, and pave the way for understanding S-duality beyond the BPS-protected sector.

scholarly journals Polythermal conditions in arctic glaciers

1991 ◽  
Vol 37 (126) ◽  
pp. 261-269 ◽  
Author(s):  
Heinz Blatter ◽  
Kolumban Hutter
Keyword(s):  
Steady State ◽  
Continuum Hypothesis ◽  
Basal Layer ◽  
Moisture Diffusion ◽  
Moisture Diffusivity ◽  
Climatic Conditions ◽  
Two Dimensions ◽  
Water Mixture ◽  
Plane Flow ◽  
Transition Surface

AbstractEnglacial temperature measurements in Arctic valley glaciers suggest in the ablation zone the existence of a basal layer of temperate ice lying below the bulk of cold ice. For such a polythermal glacier, a mathematical model is presented that calculates the temperature in the cold part and the position of the cold-temperate transition surface (CTS). The model is based on the continuum hypothesis for ice and the ice-water mixture, and on the conservation laws for moisture and energy. Temperate ice is treated as a binary mixture of ice and water at the melting point of pure ice. Boundary and transition conditions are formulated for the free surface, the base and the intraglacial cold-temperate transition surface. The model is reduced to two dimensions (plane flow) and the shallow-ice approximation is invoked. The limit of very small moisture diffusivity is analysed by using a stationary model with further reduction to one dimension (parallel-sided slab), thus providing the means of a consistent formulation of the transition conditions for moisture and heat flux through the CTS at the limit of negligibly small moisture diffusion.The application of the model to the steady-state Laika Glacier, using present-day conditions, results in a wholly cold glacier with a cold sole, in sharp contrast to observations. The present polythermal state of this glacier is suspected to be a remnant of the varying climatic conditions and glacier geometry during the past few centuries. Steady-state solutions representing apolythermalstructure can indeed be found within a range of prescribed conditions which are judged to be realistic for Laika Glacier at the last maximum extent of the glacier.

scholarly journals Levitation of non-magnetizable droplet inside ferrofluid

2018 ◽  
Vol 857 ◽  
pp. 398-448 ◽  
Author(s):  
Chamkor Singh ◽  
Arup K. Das ◽  
Prasanta K. Das
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Viscosity Ratio ◽  
Temporal Dynamics ◽  
Liquid Droplet ◽  
Droplet Surface ◽  
Two Dimensions ◽  
Projection Algorithm ◽  
The Stability ◽  
The Individual

The central theme of this work is that a stable levitation of a denser non-magnetizable liquid droplet, against gravity, inside a relatively lighter ferrofluid – a system barely considered in ferrohydrodynamics – is possible, and exhibits unique interfacial features; the stability of the levitation trajectory, however, is subject to an appropriate magnetic field modulation. We explore the shapes and the temporal dynamics of a plane non-magnetizable droplet levitating inside a ferrofluid against gravity due to a spatially complex, but systematically generated, magnetic field in two dimensions. The coupled set of Maxwell’s magnetostatic equations and the flow dynamic equations is integrated computationally, utilizing a conservative finite-volume-based second-order pressure projection algorithm combined with the front-tracking algorithm for the advection of the interface of the droplet. The dynamics of the droplet is studied under both the constant ferrofluid magnetic permeability assumption as well as for more realistic field-dependent permeability described by Langevin’s nonlinear magnetization model. Due to the non-homogeneous nature of the magnetic field, unique shapes of the droplet during its levitation, and at its steady state, are realized. The complete spatio-temporal response of the droplet is a function of the Laplace number $La$ , the magnetic Laplace number $La_{m}$ and the Galilei number $Ga$ ; through detailed simulations we separate out the individual roles played by these non-dimensional parameters. The effect of the viscosity ratio, the stability of the levitation path and the possibility of existence of multiple stable equilibrium states is investigated. We find, for certain conditions on the viscosity ratio, that there can be developments of cusps and singularities at the droplet surface; we also observe this phenomenon experimentally and compare with the simulations. Our simulations closely replicate the singular projection on the surface of the levitating droplet. Finally, we present a dynamical model for the vertical trajectory of the droplet. This model reveals a condition for the onset of levitation and the relation for the equilibrium levitation height. The linearization of the model around the steady state captures that the nature of the equilibrium point goes under a transition from being a spiral to a node depending upon the control parameters, which essentially means that the temporal route to the equilibrium can be either monotonic or undulating. The analytical model for the droplet trajectory is in close agreement with the detailed simulations.

scholarly journals FORMAL RELATION AMONG VARIOUS HERMITIAN AND NON-HERMITIAN EFFECTIVE INTERACTIONS

2005 ◽  
Vol 14 (01) ◽  
pp. 21-28 ◽  
Author(s):  
RYOJI OKAMOTO ◽  
SHINICHIRO FUJII ◽  
KENJI SUZUKI
Keyword(s):  
Effective Interaction ◽  
Model Space ◽  
General Definition ◽  
Effective Interactions ◽  
Formal Relation ◽  
Definition Of ◽  
Effective Hamiltonians

A general definition of the model-space effective interaction is given. The energy-independent effective Hamiltonians derived in a time-independent way are classified systematically.

scholarly journals THE ACCUMULATION OF ELECTROLYTES

1932 ◽  
Vol 15 (6) ◽  
pp. 667-689 ◽  
Author(s):  
W. J. V. Osterhout ◽  
W. M. Stanley
Keyword(s):  
Steady State ◽  
Osmotic Pressure ◽  
Aqueous Phase ◽  
Thermodynamic Potential ◽  
Ph Value ◽  
Molecular Form ◽  
External Solution ◽  
Aqueous Layer ◽  
The Difference ◽  
Pass Through

Inasmuch as attempts to explain accumulation by the Donnan principle have failed in the case of Valonia, a hypothesis of the steady state has been formulated to explain what occurs. In order to see whether this hypothesis is in harmony with physico-chemical laws attempts have been made to imitate its chief features by means of a model. The model consists of a non-aqueous layer (representing the protoplasmic surface) placed between an alkaline aqueous phase (representing the external solution) and a more acid aqueous phase (representing the cell sap). The model reproduces most of the features of the hypothesis. Attention may be called to the following points. 1. The semipermeable surface is a continuous non-aqueous phase. 2. Potassium penetrates by combining with an acid HX in the non-aqueous layer to form KX which in turn reacts with an acid HA in the sap to form KA. Since KX is little dissociated in the non-aqueous layer potassium appears to pass through it chiefly in molecular form. 3. The internal composition depends on permeability, e.g., sodium penetrates less rapidly than potassium and in consequence potassium predominates over sodium in the "artificial sap." The order of penetration in the model is the same as in Valonia, i.e., K > Na > Ca > Mg, and Cl > SO4, but the quantitative resemblance is not close, e.g., the difference between potassium and sodium, and chloride and sulfate is much less in the model. 4. The formation of KA and NaA in the sap raises its osmotic pressure and water enters. 5. The concentration of potassium and sodium and the osmotic pressure become much greater inside than outside. For example, potassium may become 200 times as concentrated inside as outside. 6. No equilibrium occurs but a steady state is reached in which water and salt enter at the same rate so that the composition of the sap remains constant as its volume increases. 7. Since no equilibrium occurs there is a difference of thermodynamic potential between inside and outside. At the start the thermodynamic potential of KOH is much greater outside than inside. This difference gradually diminishes and in the steady state has about the same value as in Valonia. The difference in pH value between the internal and external solutions is also similar in both cases (about 2 pH units). 8. Accumulation does not depend on the presence of molecules or ions inside which are unable to pass out. One important feature of the hypothesis is not seen in the model: this is the exchange of HCO3 for Cl-. Experiments on this point are in progress.

scholarly journals Evaluating Spatial Distribution Randomness of Overlap Permissive Second Phase in Three- and Two-Dimensions

2007 ◽  
Vol 48 (10) ◽  
pp. 2762-2767 ◽  
Author(s):  
Kenjiro Sugio ◽  
Yasutaka Momota ◽  
Di Zhang ◽  
Hiroshi Fukushima ◽  
Osamu Yanagisawa
Keyword(s):  
Spatial Distribution ◽  
Two Dimensions ◽  
Second Phase

scholarly journals Phase diagrams of simple models of colloidal nanocrystals in two dimensions

2020 ◽  
Vol 4 (1) ◽  
pp. 015006
Author(s):  
Luis A Padilla ◽  
Abelardo Ramírez-Hernández
Keyword(s):  
Phase Diagrams ◽  
Two Dimensions ◽  
Colloidal Nanocrystals ◽  
Simple Models

scholarly journals Correction: Dynamical self-assembly of dipolar active Brownian particles in two dimensions

Soft Matter ◽  
2020 ◽  
Vol 16 (27) ◽  
pp. 6443-6443
Author(s):  
Guo-Jun Liao ◽  
Carol K. Hall ◽  
Sabine H. L. Klapp
Keyword(s):  
Self Assembly ◽  
Soft Matter ◽  
Two Dimensions ◽  
Brownian Particles

Correction for ‘Dynamical self-assembly of dipolar active Brownian particles in two dimensions’ by Guo-Jun Liao et al., Soft Matter, 2020, 16, 2208–2223, DOI: 10.1039/C9SM01539F.

Volume transition effects on the correlations and effective interactions among highly charged microgels

Soft Matter ◽  
2020 ◽  
Vol 16 (21) ◽  
pp. 5081-5093 ◽  
Author(s):  
L. A. Aguirre-Manzo ◽  
P. González-Mozuelos
Keyword(s):  
Effective Interaction ◽  
Counterion Condensation ◽  
Effective Interactions ◽  
Volume Transition ◽  
Transition Effects

Microgels shrinkage promotes counterion condensation, which in the highly charged regime markedly inhibits the effective interaction and induces strong counterion–counterion correlations that deviate this potential from the traditional Yukawa shape.

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