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Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise
No full textWe introduce an agent-based model for co-evolving opinions and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents’ movements are governed by the positions and opinions of other agents and similarly, the opinion dynamics are influenced by agents’ spatial proximity and their opinion similarity. Using numerical simulations and formal analyses, we study this feedback loop between opinion dynamics and the mobility of agents in a social space. We investigate the behaviour of this ABM in different regimes and explore the influence of various factors on the appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples, we show that a resulting PDE model is a good approximation of the original AB
Slab-derived devolatilization fluids oxidized by subducted metasedimentary rocks
No full textMetamorphic devolatilization of subducted slabs generates aqueous fluids that ascend into the mantle wedge, driving the partial melting that produces arc magmas. These magmas have oxygen fugacities some 10–1,000 times higher than magmas generated at mid-ocean ridges. Whether this oxidized magmatic character is imparted by slab fluids or is acquired during ascent and interaction with the surrounding mantle or crust is debated. Here we study the petrology of metasedimentary rocks from two Tertiary Aegean subduction complexes in combination with reactive transport modelling to investigate the oxidative potential of the sedimentary rocks that cover slabs. We find that the metasedimentary rocks preserve evidence for fluid-mediated redox reactions and could be highly oxidized. Furthermore, the modelling demonstrates that layers of these oxidized rocks less than about 200 m thick have the capacity to oxidize the ascending slab dehydration flux via redox reactions that remove H2, CH4 and/or H2S from the fluids. These fluids can then oxidize the overlying mantle wedge at rates comparable to arc magma generation rates, primarily via reactions involving sulfur species. Oxidized metasedimentary rocks need not generate large amounts of fluid themselves but could instead oxidize slab dehydration fluids ascending through them. Proposed Phanerozoic increases in arc magma oxygen fugacity may reflect the recycling of oxidative weathering products following Neoproterozoic–Palaeozoic marine and atmospheric oxygenation
Connection between Macroscopic Hydrodynamics and Molecular Friction in Liquids
Get PDFA fundamental problem in molecular dynamics is the relation between the frequency-dependent
friction of a molecule in a liquid and the underlying hydrodynamic equations. We investigate this
connection for the case of a water molecule moving in liquid water using all-atomistic molecular dy�namics simulations and linear hydrodynamic theory. For this we calculate the frequency-dependent
friction of a sphere with finite surface slip moving in a non-Newtonian compressible fluid by solving
the linear transient Stokes equation, including frequency-dependent shear and volume viscosities,
which are determined from MD simulations of bulk liquid water. We investigate in detail the in�fluence of the volume viscosity on the sphere friction and find that the high-frequency decay of
the volume viscosity crucially influences the friction. We also determine the frequency-dependent
friction of a single water molecule moving in liquid water, as defined by the generalized Langevin
equation, from MD simulation trajectories. By fitting the effective sphere radius and the slip length
in the solution of the Stokes equation, the two frequency-dependent frictions are shown to agree well.
This shows that the transient Stokes equation describes the frequency-dependent friction of a single
water molecule in liquid water and thus applies down to molecular length and time scales, provided
accurate frequency-dependent viscosities are used. In particular the pronounced maximum of the
sphere friction around 7 THz is shown to be caused by a pronounced maximum of the shear viscosity
at the same frequency. We also find non-negligible slip effects for the motion of a water molecule, in
quantitative agreement with a recent study of the translational and rotational diffusion of a water
molecule in liquid water. For a methane molecule moving in water, the friction function cannot
be predicted based on our simple hydrodynamic model, which suggests that a methane molecule is
surrounded by a hydration layer with viscous properties that are very different from bulk water.
Subject Areas: Soft Matter, Statistical Physics, Fluid Dynamics, Biological Physics, Complex System
Upper plate dynamic response to a sequential elastic rebound and slab acceleration in laboratory-scale subduction megathrust
No full textAn earthquake-induced stress drop on a megathrust instigates different responses on the upper plate and slab. We mimic homogenous and heterogeneous megathrust interfaces at the laboratory scale to monitor the strain relaxation on the two elastically bi-material plates by establishing analog velocity weakening and neutral materials. A sequential elastic rebound follows the coseismic shear-stress drop in our elastic-frictional models: a fast rebound of the upper plate and the delayed and smaller rebound on the slab. A combination of the rebound of the slab and the rapid relaxation (i.e., elastic restoration) of the upper plate after an elastic overshooting may accelerate the relocking of the megathrust. This acceleration triggers/antedates the failure of a nearby asperity and enhances the early slip reversal in the rupture area. Hence, the trench-normal rearward displacement in the upper plate may reach a significant amount of the entire interseismic slip reversal and speeds up the stress build-up on upper plate backthrust. Moreover, the backthrust switches its kinematic mode from a normal to reverse mechanism reflecting the sense of shear on the interface during coseismic and postseismic stages
Nuclear Quantum Effects in Fullerene-Fullerene Aggregation in Water
No full textWe studied the effects of the quantum delocalization in space of the hydrogen
atoms of water in the aggregation process of two fullerene molecules. We
considered a case using a purely repulsive water–fullerene interaction, as such a
situation has shown that water-mediated effects play a key role in the
aggregation process. This study becomes feasible, at a reduced
computational price, by combining the path integral (PI) molecular dynamics
(MD) method with a recently developed open-system MD technique.
Specifically, only the mandatory solvation shell of the two fullerene
molecules was considered at full quantum resolution, while the rest of the
system was represented as a mean-field macroscopic reservoir of particles and
energy. Our results showed that the quantum nature of the hydrogen atoms
leads to a sizable difference in the curve of the free energy of aggregation; that
is, that nuclear quantum effects play a relevant role
Direct Bayesian model reduction of smaller scale convective activity conditioned on large-scale dynamics
Get PDFAbstract. We pursue a simplified stochastic representation of smaller scale convective activity conditioned on large scale
dynamics in the atmosphere. For identifying a Bayesian model describing the relation of different scales we use a probabilistic
approach (Gerber and Horenko, 2017) called Direct Bayesian Model Reduction (DBMR). The convective available potential
energy (CAPE) is applied as large scale flow variable combined with a subgrid smaller scale time series for the vertical velocity.
We found a probabilistic relation of CAPE and vertical up- and downdraft for day and night. The categorization is based on the5
conservation of total probability. This strategy is part of a development process for parametrizations in models of atmospheric
dynamics representing the effective influence of unresolved vertical motion on the large scale flows. The direct probabilistic
approach provides a basis for further research of smaller scale convective activity conditioned on other possible large scale
drivers
Simulation of a Particle Domain in a Continuum, Fluctuating Hydrodynamics Reservoir
No full textIn molecular simulation and fluid mechanics, the coupling of a particle domain with a continuum representation of its embedding environment is an ongoing challenge. In this Letter, we show a novel approach where the latest version of the adaptive resolution scheme (AdResS), with noninteracting tracers as particles’ reservoir, is combined with a fluctuating hydrodynamics (FHD) solver. The resulting algorithm, supported by a solid mathematical model, allows for a physically consistent exchange of matter and energy between the particle domain and its fluctuating continuum reservoir. Numerical tests are performed to show the validity of the algorithm. Differently from previous algorithms of the same kind, the current approach allows for simulations where, in addition to density fluctuations, also thermal fluctuations can be accounted for, thus large complex molecular systems, as, for example, hydrated biological membranes in a thermal field, can now be efficiently treated
Generalized Langevin equation with a nonlinear potential of mean force and nonlinear memory friction from a hybrid projection scheme
No full textWe introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig
projection techniques and use it to derive a generalized Langevin equation (GLE) for a general interacting
many-body system. The resulting GLE includes (i) explicitly the potential of mean force (PMF) that describes
the equilibrium distribution of the system in the chosen space of reaction coordinates, (ii) a random force
term that explicitly depends on the initial state of the system, and (iii) a memory friction contribution that
splits into two parts: a part that is linear in the past reaction-coordinate velocity and a part that is in general
nonlinear in the past reaction coordinates but does not depend on velocities. Our hybrid scheme thus combines
all desirable properties of the Zwanzig and Mori projection schemes. The nonlinear memory friction contribution
is shown to be related to correlations between the reaction-coordinate velocity and the random force.We present
a numerical method to compute all parameters of our GLE, in particular the nonlinear memory friction function
and the random force distribution, from a trajectory in reaction coordinate space. We apply our method on the
dihedral-angle dynamics of a butane molecule in water obtained from atomistic molecular dynamics simulations.
For this example, we demonstrate that nonlinear memory friction is present and that the random force exhibits
significant non-Gaussian corrections. We also present the derivation of the GLE for multidimensional reaction
coordinates that are general functions of all positions in the phase-space of the underlying many-body system;
this corresponds to a systematic coarse-graining procedure that preserves not only the correct equilibrium
behavior but also the correct dynamics of the coarse-grained system
QG-DL-Ekman: Dynamics of a diabatic layer in the quasi-geostrophic framework
No full textQuasigeostrophic (QG) theory describes the dynamics of synoptic-scale flows in the troposphere that are balanced with respect to both acoustic and internal gravity waves. Within this framework, effects of (turbulent) friction near the ground are usually represented by Ekman layer theory. The troposphere covers roughly the lowest 10 km of the atmosphere while Ekman layer heights are typically just a few hundred meters. However, this two-layer asymptotic theory does not explicitly account for substantial changes of the potential temperature stratification due to diabatic heating associated with cloud formation or with radiative and turbulent heat fluxes which can be significant in about the lowest 3 km and in the middle latitudes. To address this deficiency, this paper extends the classical QG–Ekman layer model by introducing an intermediate dynamically and thermodynamically active layer, called the “diabatic layer” (DL) from here on. The flow in this layer is also in acoustic, hydrostatic, and geostrophic balance but, in contrast to QG flow, variations of potential temperature are not restricted to small deviations from a stable and time-independent background stratification. Instead, within the DL diabatic processes are allowed to affect the leading-order stratification. As a consequence, this layer modifies the pressure field at the top of the Ekman layer, and with it the intensity of Ekman pumping seen by the quasigeostrophic bulk flow. The result is the proposed extended quasigeostrophic three-layer QG–DL–Ekman model for midlatitude dynamics
Variational Approach to Fluid–Structure Interaction via GENERIC
No full textWe present a framework to systematically derive variational formulations for fluid–structure interaction problems based on thermodynamical driving functionals and geometric structures in different coordinate systems by suitable transformations within this formulation. Our approach provides a promising basis to construct structure-preserving discretization strategies