The two-dimensional (2D) layered semiconductors such as MoS2 have attracted tremendous interest as a new class of electronic materials. However, there is considerable challenge in making reliable contacts to these atomically thin materials. Here we p
resent a new strategy by using graphene as back electrodes to achieve Ohmic contact to MoS2. With a finite density of states, the Fermi level of graphene can be readily modified by gate potential to ensure a nearly perfect band alignment with MoS2. We demonstrate, for the first time, a transparent contact can be made to MoS2 with essentially zero contact barrier and linear output behaviour at cryogenic temperatures (down to 1.9 K) for both monolayer and multilayer MoS2. Benefiting from the barrier-free transparent contacts, we show that a metal-insulator-transition (MIT) can be observed in a two-terminal MoS2 device, a phenomenon that could be easily masked by Schottky barrier and only seen in four-terminal devices in conventional metal-contacted MoS2 system. With further passivation y born nitride encapsulation, we demonstrate a record high extrinsic (two-terminal) field effect mobility over 1300 cm2/Vs in MoS2.
Computing the equilibrium properties of complex systems, such as free energy differences, is often hampered by rare events in the dynamics. Enhanced sampling methods may be used in order to speed up sampling by, for example, using high temperatures,
as in parallel tempering, or simulating with a biasing potential such as in the case of umbrella sampling. The equilibrium properties of the thermodynamic state of interest (e.g., lowest temperature or unbiased potential) can be computed using reweighting estimators such as the weighted histogram analysis method or the multistate Bennett acceptance ratio (MBAR). weighted histogram analysis method and MBAR produce unbiased estimates, the simulation samples from the global equilibria at their respective thermodynamic state--a requirement that can be prohibitively expensive for some simulations such as a large parallel tempering ensemble of an explicitly solvated biomolecule. Here, we introduce the transition-based reweighting analysis method (TRAM)--a class of estimators that exploit ideas from Markov modeling and only require the simulation data to be in local equilibrium within subsets of the configuration space. We formulate the expanded TRAM (xTRAM) estimator that is shown to be asymptotically unbiased and a generalization of MBAR. Using four exemplary systems of varying complexity, we demonstrate the improved convergence (ranging from a twofold improvement to several orders of magnitude) of xTRAM in comparison to a direct counting estimator and MBAR, with respect to the invested simulation effort. Lastly, we introduce a random-swapping simulation protocol that can be used with xTRAM, gaining orders-of-magnitude advantages over simulation protocols that require the constraint of sampling from a global equilibrium.
We study the well-posedness of a coupled Cahn-Hilliard-Stokes-Darcy system which is a diffuse-interface model for essentially immiscible two phase incompressible flows with matched density in a karstic geometry. Existence of finite energy weak soluti
on that is global in time is established in both 2D and 3D. Weak-strong uniqueness property of the weak solutions is provided as well.
We consider the modified phase-field crystal (MPFC) equation that has recently been proposed by P. Stefanovic et al. This is a variant of the phase-field crystal (PFC) equation, introduced by K.-R. Elder et al., which is characterized by the presence
of an inertial term $betaphi_{tt}$. Here $phi$ is the phase function standing for the number density of atoms and $betageq 0$ is a relaxation time. The associated dynamical system for the MPFC equation with respect to the parameter $beta$ is analyzed. More precisely, we establish the existence of a family of exponential attractors $mathcal{M}_beta$ that are Holder continuous with respect to $beta$.
We consider a non-isothermal modified Cahn--Hilliard equation which was previously analyzed by M. Grasselli et al. Such an equation is characterized by an inertial term and a viscous term and it is coupled with a hyperbolic heat equation. The resulti
ng system was studied in the case of no-flux boundary conditions. Here we analyze the case in which the order parameter is subject to a dynamic boundary condition. This assumption requires a more refined strategy to extend the previous results to the present case. More precisely, we first prove the well-posedness for solutions with bounded energy as well as for weak solutions. Then we establish the existence of a global attractor. Finally, we prove the convergence of any given weak solution to a single equilibrium by using a suitable Lojasiewicz--Simon inequality.
Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dyna
mics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has therefore been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase- space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecular observables of interest that are often computed from MSMs can be computed from HMMs / PMMs. The new framework is applicable to both, simulation and single-molecule experimental data. We demonstrate its versatility by applications to educative model systems, an 1 ms Anton MD simulation of the BPTI protein, and an optical tweezer force probe trajectory of an RNA hairpin.
We consider a modification of the so-called phase-field crystal (PFC) equation introduced by K.R. Elder et al. This variant has recently been proposed by P. Stefanovic et al. to distinguish between elastic relaxation and diffusion time scales. It con
sists of adding an inertial term (i.e. a second-order time derivative) into the PFC equation. The mathematical analysis of the resulting equation is more challenging with respect to the PFC equation, even at the well-posedness level. Moreover, its solutions do not regularize in finite time as in the case of PFC equation. Here we analyze the modified PFC (MPFC) equation endowed with periodic boundary conditions. We first prove the existence and uniqueness of a solution with initial data in a bounded energy space. This solution satisfies some uniform dissipative estimates which allow us to study the global longtime behavior of the corresponding dynamical system. In particular, we establish the existence of an exponential attractor. Then we demonstrate that any trajectory originating from the bounded energy phase space does converge to a unique equilibrium. This is done by means of a suitable version of the {L}ojasiewicz-Simon inequality. A convergence rate estimate is also given.
We consider a hydrodynamic system that models the Smectic-A liquid crystal flow. The model consists of the Navier-Stokes equation for the fluid velocity coupled with a fourth-order equation for the layer variable $vp$, endowed with periodic boundary
conditions. We analyze the long-time behavior of the solutions within the theory of infinite-dimensional dissipative dynamical systems. We first prove that in 2D, the problem possesses a global attractor $mathcal{A}$ in certain phase space. Then we establish the existence of an exponential attractor $mathcal{M}$ which entails that the global attractor $mathcal{A}$ has finite fractal dimension. Moreover, we show that each trajectory converges to a single equilibrium by means of a suitable Lojasiewicz--Simon inequality. Corresponding results in 3D are also discussed.
