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Dynamics of various Polymer/Graphene Interfacial Systems through Atomistic Molecular Dynamics Simulations
Get PDFThe current work refers to a simulation study on hybrid polymer/graphene interfacial systems. We explore the effect of graphene on the mobility of polymers, by studying three well known and widely used polymers, polyethylene (PE), polystyrene (PS) and poly(methyl-methacrylate) (PMMA). Qualitative and quantitative differences in the dynamic properties of the polymer chains in particular at the polymer/graphene interface are detected. Results concerning both the segmental and the terminal dynamics render PE much faster than the other two polymers, PS follows, while PMMA is the slowest one. Clear spatial dynamic heterogeneity has been observed for all model systems, with different dynamical behavior of the adsorbed polymer segments. The segmental relaxation time of polymer (τseg) as a function of the distance from graphene shows an abrupt decrease beyond the first adsorption layer for PE, as a result of its the well-ordered layered structure close to graphene, though a more gradual decay for PS and PMMA. The distribution of the relaxation times of adsorbed segments was also found to be broader than the bulk ones for all three polymer/graphene systems
Evolution PDEs and augmented eigenfunctions. I finite interval
Get PDFThe so-called unified method expresses the solution of an initial-boundary value problem for an evolution PDE in the finite interval in terms of an integral in the complex Fourier (spectral) plane. Simple initial-boundary value problems, which will be referred to as problems of type~I, can be solved via a classical transform pair. For example, the Dirichlet problem of the heat equation can be solved in terms of the transform pair associated with the Fourier sine series. Such transform pairs can be constructed via the spectral analysis of the associated spatial operator. For more complicated initial-boundary value problems, which will be referred to as problems of type~II, there does \emph{not} exist a classical transform pair and the solution \emph{cannot} be expressed in terms of an infinite series. Here we pose and answer two related questions: first, does there exist a (non-classical) transform pair capable of solving a type~II problem, and second, can this transform pair be constructed via spectral analysis? The answer to both of these questions is positive and this motivates the introduction of a novel class of spectral entities. We call these spectral entities augmented eigenfunctions, to distinguish them from the generalised eigenfunctions introduced in the sixties by Gel'fand and his co-authors
Spectral gap in stationary non-equilibrium processes
Get PDFIn this paper we study the spectral gap for a family of interacting particles systems
on , proving that it is of the order . The system arises as a natural
model for current reservoirs and Fick's law
A mathematical model for mechanotransduction at the early steps of suture formation
Get PDFGrowth and patterning of craniofacial sutures are subjected to the effects of mechanical stress. Mechanotransduction processes occurring at the margins of the sutures are not precisely understood. Here, we propose a simple theoretical model based on the orientation of collagen fibres within the suture in response to local stress. We demonstrate that fibre alignment generates an instability leading to the emergence of interdigitations. We confirm the appearance of this instability both analytically and numerically. To support our model, we use histology and synchrotron x-ray microtomography and reveal the fine structure of fibres within the sutural mesenchyme and their insertion into the bone. Furthermore, using a mouse model with impaired mechanotransduction, we show that the architecture of sutures is disturbed when forces are not interpreted properly. Finally, by studying the structure of sutures in the mouse, the rat, an actinopterygian (\emph{Polypterus bichir}) and a placoderm (\emph{Compagopiscis croucheri}), we show that bone deposition patterns during dermal bone growth are conserved within jawed vertebrates. In total, these results support the role of mechanical constraints in the growth and patterning of craniofacial sutures, a process that was probably effective at the emergence of gnathostomes, and provide new directions for the understanding of normal and pathological suture fusion
Low Mach Asymptotic Preserving Scheme for the Euler-Korteweg Model
Get PDFWe present an all speed scheme for the Euler-Korteweg model.
We study a semi-implicit time-discretisation which treats the terms, which are stiff for low Mach numbers, implicitly and thereby avoids a dependence of the timestep restriction on the Mach number.
Based on this we present a fully discrete finite difference scheme.
In particular, the scheme is asymptotic preserving, i.e., it converges to a stable discretisation of the incompressible limit
of the Euler-Korteweg model when the Mach number tends to zero
On the construction and properties of weak solutions describing dynamic cavitation
Get PDFWe consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations
of radial elasticity we construct self-similar weak solutions that describe a cavity emanating from a state of uniform deformation.
For dimensions d =2, 3 we show that cavity formation is necessarily associated with a unique precursor shock.
We also study the bifurcation diagram and do a detailed analysis of the singular asymptotics associated to cavity initiation
as a function of the cavity speed of the self-similar profiles. We show that
for stress free cavities the critical stretching associated with dynamically cavitating solutions coincides with the critical stretching in the bifurcation diagram of equilibrium elasticity. Our analysis treats both stress-free cavities and cavities with contents
Magnetization oscillations by vortex-antivortex dipoles
Get PDFA vortex-antivortex dipole can be generated due to current with in-plane spin-polarization,
flowing into a magnetic element,
which then behaves as a spin transfer oscillator.
Its dynamics is analyzed using the Landau-Lifshitz equation including
a Slonczewski spin-torque term.
We establish that the vortex dipole is set in steady state rotational motion due to
the interaction between the vortices,
while an external in-plane magnetic field can tune the frequency of rotation.
The rotational motion is linked to the nonzero skyrmion number of the dipole.
The spin-torque acts to stabilize the vortex dipole at a definite vortex-antivortex separation distance.
In contrast to a free vortex dipole, the rotating pair under spin-polarized current
is an attractor of the motion, therefore a stable state.
Three types of vortex-antivortex pairs are obtained as we vary the external field and spin-torque strength.
We give a guide for the frequency of rotation based on analytical relations
Finite Element Approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise
Get PDFWe consider an initial- and Dirichlet boundary- value problem for
a linear Cahn-Hilliard-Cook equation, in one space dimension,
forced by the space derivative of a space-time white noise.
First, we propose an approximate regularized stochastic parabolic
problem discretizing the noise using linear splines. Then
fully-discrete approximations to the solution of the
regularized problem are constructed using, for the discretization
in space, a Galerkin finite element method based on
piecewise polynomials, and, for time-stepping, the Backward
Euler method.
Finally, we derive strong a priori estimates for the modeling error and
for the numerical approximation error to the solution of the regularized problem
Effect of Solvent on the Self-Assembly of Dialanine and Diphenylalanine Peptides
Get PDFDiphenylalanine (FF) is a very common peptide with many potential applications, both biological and technological, due to a large number of different nanostructures which it attains. The current work concerns a detailed study of the self assembled structures of FF in two different solvents, an aqueous (H2O) and an organic (CH3OH) through simulations and experiments. Detailed atomistic Molecular Dynamics (MD) simulations of FF in both solvents have been performed, using an explicit solvent model. The self assembling propensity of FF in water is obvious while in methanol a very weak self assembling propensity is observed. We studied and compared structural properties of FF in the two different solvents and a comparison with a system of dialanine (AA) in the corresponding solvents was also performed. In addition, temperature dependence studies were carried out. Finally, the simulation predictions were compared to new experimental data, which were produced in the framework of the present work. A very good qualitative agreement between simulation and experimental observations was found
Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model
Get PDFWe design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen--Cahn/Cahn--Hilliard/Navier--Stokes--Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system