Casimir interactions in strained graphene systems

We theoretically study the strain effect on the Casimir interactions in graphene based systems. We found that the interactions between two strained graphene sheets are strongly dependent on the direction of stretching. The influence of the strain on the dispersion interactions is still strong in the presence of dielectric substrates but is relatively weak when the substrate is metallic. Our studies would suggest new ways to design next generation devices.Comment: 5 pages, 4 figure

Adaptive Point-to-Multipoint Transmission for Multimedia Broadcast Multicast Services in LTE

This paper investigates point-to-multipoint (PTM) transmission supporting adaptive modulation and coding (AMC) as well as retransmissions based on incremental redundancy. In contrast to the classical PTM transmission which was introduced by the Multimedia Broadcast Multicast Service (MBMS), the adaptiveness requires user individual feedback channels that allow the receivers to report their radio conditions and send positive or negative acknowledgments (ACK/NACK) for a Layer 1 transport block to the eNodeB. In this work, an adaptive PTM scheme based on feedback from multiple users is presented and evaluated. Furthermore, a simple NACK-oriented feedback mechanism is introduced to relieve the feedback channel that is used in the uplink. Finally, the performance of different single-cell MBMS transmission modes is evaluated by dynamic radio network simulations. It is shown that adaptive PTM transmission outperforms the conventional MBMS configurations in terms of radio resource consumption and user satisfaction rate.Comment: 6 pages, 7 figure

Theory of Activated Glassy Dynamics in Randomly Pinned Fluids

We generalize the force-level, microscopic, Nonlinear Langevin Equation (NLE) theory and its elastically collective generalization (ECNLE theory) of activated dynamics in bulk spherical particle liquids to address the influence of random particle pinning on structural relaxation. The simplest neutral confinement model is analyzed for hard spheres where there is no change of the equilibrium pair structure upon particle pinning. As the pinned fraction grows, cage scale dynamical constraints are intensified in a manner that increases with density. This results in the mobile particles becoming more transiently localized, with increases of the jump distance, cage scale barrier and NLE theory mean hopping time; subtle changes of the dynamic shear modulus are predicted. The results are contrasted with recent simulations. Similarities in relaxation behavior are identified in the dynamic precursor regime, including a roughly exponential, or weakly supra-exponential, growth of the alpha time with pinning fraction and a reduction of dynamic fragility. However, the increase of the alpha time with pinning predicted by the local NLE theory is too small, and severely so at very high volume fractions. The strong deviations are argued to be due to the longer range collective elasticity aspect of the problem which is expected to be modified by random pinning in a complex manner. A qualitative physical scenario is offered for how the three distinct aspects that quantify the elastic barrier may change with pinning. ECNLE theory calculations of the alpha time are then presented based on the simplest effective-medium-like treatment for how random pinning modifies the elastic barrier. The results appear to be consistent with most, but not all, trends seen in recent simulations. Key open problems are discussed with regards to both theory and simulation.Comment: 14 pages, 10 figures, under revie

The pH-dependent electrostatic interaction of a metal nanoparticle with the MS2 virus-like particles

The electrostatic interaction of metal nanoparticles with viruses is attracting great interest due to their antiviral activity and their role in enhancing the detection of viruses at ultra-low concentrations. We model the MS2 virus devoid of its single strand RNA core using a core-shell model. The dependence of the inner and outer surface charge density on the pH is taken into account in our model of the interaction. Varying the pH causes a change in the sign of the outer surface charge leading to the attractive-repulsive transition in the electrostatic interaction between the MS2 virus and metal nanoparticle at pH = 4.Comment: 6 pages, 4 figures, accepted for publication on Chemical Physics Lette

Theory of the Spatial Transfer of Interface-Nucleated Changes of Dynamical Constraints and Its Consequences in Glass-Forming Films

We formulate a new theory for how caging constraints in glass-forming liquids at a surface or interface are modified and then spatially transferred, in a layer-by-layer bootstrapped manner, into the film interior in the context of the dynamic free energy concept of the Nonlinear Langevin Equation theory approach. The dynamic free energy at any mean location involves contributions from two adjacent layers where confining forces are not the same. At the most fundamental level of the theory, the caging component of the dynamic free energy varies essentially exponentially with distance from the interface, saturating deep enough into the film with a correlation length of modest size and weak sensitivity to thermodynamic state. This imparts a roughly exponential spatial variation of all the key features of the dynamic free energy required to compute gradients of dynamical quantities including the localization length, jump distance, cage barrier, collective elastic barrier and alpha relaxation time. The spatial gradients are entire of dynamical, not structural nor thermodynamic, origin. The theory is implemented for the hard sphere fluid and diverse interfaces which can be a vapor, a rough pinned particle solid, a vibrating pinned particle solid, or a smooth hard wall. Their basic description at the level of the spatially-heterogeneous dynamic free energy is identical, with the crucial difference arising from the first layer where dynamical constraints can be weakened, softened, or hardly changed depending on the specific interface. Numerical calculations establish the spatial dependence and fluid volume fraction sensitivity of the key dynamical property gradients for five different model interfaces. Comparison of the theoretical predictions for the dynamic localization length and glassy modulus with simulations and experiments for systems with a vapor interface reveals good agreement.Comment: 17 pages, 11 figures, Accepted on Journal of Chemical Physic

Elastically Collective Nonlinear Langevin Equation Theory of Dynamics in Glass-Forming Liquids: Transient Localization, Thermodynamic Mapping and Cooperativity

We analyze multiple new issues concerning activated relaxation in glassy hard sphere fluids and molecular and polymer liquids based on the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory. By invoking a high temperature reference state, a near universality of the apparent dynamic localization length scale is predicted for liquids of widely varying fragility, a result that is relevant to recent simulation studies and quasi-elastic neutron scattering measurements. In contrast, in the same format strongly non-universal behavior is found for the activation barrier that controls long time relaxation. Two measures of cooperativity in ECNLE theory are analyzed. A particle-level total displacement associated with the alpha relaxation event is found to be only of order 1-2 particle diameters and weakly increases with cooling. In contrast, an alternative cooperativity length is defined as the spatial scale required to recover the full barrier and bulk alpha time. This length scale grows strongly with cooling due to the emergence in the deeply supercooled regime of collective long range elastic fluctuations required to allow local hopping. It becomes very large as the laboratory Tg is approached, though is relatively modest at degrees of supercooling accessible with molecular dynamics simulation. The alpha time is found to be exponentially related to this cooperativity length over an enormous number of decades of relaxation time that span the lightly to deeply supercooled regimes. Moreover, the effective barrier height increases almost linearly with the growing cooperativity length scale. An alternative calculation of the collective elastic barrier based on a literal continuum mechanics approach is shown to result in very little change of the theoretical results for bulk properties, but leads to a much smaller and less temperature-sensitive cooperativity length scale.Comment: 12 pages, 10 figure

Modification of the Statistical Moment Method for the High-Pressure Melting Curve by the Inclusion of Thermal Vacancies

Melting behaviors of defective crystals under extreme conditions are theoretically investigated using the statistical moment method. In our theoretical model, heating processes cause missing atoms or vacancies in crystal structures via dislocating them from their equilibrium positions. The coordination number of some atoms is assumed to be removed by one unit and the defect depends on temperature and external pressure. We formulate analytical expressions to directly connect the equilibrium vacancy concentration, the elastic modulus, and the melting temperature. Numerical calculations are carried out for six transition metals including Cu, Ag, Au, Mo, Ta, and W up to 400 GPa. The obtained results show that vacancies strongly drive the melting transition. Ignoring the vacancy formation leads to incorrect predictions of the melting point. The good agreement between our numerical data and prior experimental works validates the accuracy of our approach.Comment: 9 pages, 5 figures, accepted for publication on Vacuum 202

CANDECOMP/PARAFAC Decomposition of High-order Tensors Through Tensor Reshaping

In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easily to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding, and they are often not applicable to higher order and relatively large scale tensors. In this paper, by exploiting the uniqueness of CPD and the relation of a tensor in Kruskal form and its unfolded tensor, we propose a fast approach to deal with this problem. Instead of directly factorizing the high order data tensor, the method decomposes an unfolded tensor with lower order, e.g., order-3 tensor. On basis of the order-3 estimated tensor, a structured Kruskal tensor of the same dimension as the data tensor is then generated, and decomposed to find the final solution using fast algorithms for the structured CPD. In addition, strategies to unfold tensors are suggested and practically verified in the paper

Best Rank-One Tensor Approximation and Parallel Update Algorithm for CPD

A novel algorithm is proposed for CANDECOMP/PARAFAC tensor decomposition to exploit best rank-1 tensor approximation. Different from the existing algorithms, our algorithm updates rank-1 tensors simultaneously in parallel. In order to achieve this, we develop new all-at-once algorithms for best rank-1 tensor approximation based on the Levenberg-Marquardt method and the rotational update. We show that the LM algorithm has the same complexity of first-order optimisation algorithms, while the rotational method leads to solving the best rank-1 approximation of tensors of size $2 \times 2 \times \cdots \times 2$. We derive a closed-form expression of the best rank-1 tensor of $2\times 2 \times 2$ tensors and present an ALS algorithm which updates 3 component at a time for higher order tensors. The proposed algorithm is illustrated in decomposition of difficult tensors which are associated with multiplication of two matrices.Comment: 33 page

Non-Orthogonal Tensor Diagonalization

Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate joint diagonalization (AJD) of a set of matrices. In particular, we derive (1) a new algorithm for symmetric AJD, which is called two-sided symmetric diagonalization of order-three tensor, (2) a similar algorithm for non-symmetric AJD, also called general two-sided diagonalization of an order-3 tensor, and (3) an algorithm for three-sided diagonalization of order-3 or order-4 tensors. The latter two algorithms may serve for canonical polyadic (CP) tensor decomposition, and they can outperform other CP tensor decomposition methods in terms of computational speed under the restriction that the tensor rank does not exceed the tensor multilinear rank. Finally, we propose (4) similar algorithms for tensor block diagonalization, which is related to the tensor block-term decomposition.Comment: The manuscript was revised deeply, but the main idea is the same. The algorithm has changed significantl