Based on some important properties of dS space, we present a Beltrami model BΛ that may shed light on the observable puzzle of dS space and the paradox between the special relativity principle and cosmological principle. In BΛ, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson-Walkerlike metric. It is of positive spatial curvature of order Λ. This is more or less indicated already by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.

The transport of water molecules through nanopores is not only crucial to biological activities but also useful for designing novel nanofluidic devices. Despite considerable effort and progress that has been made, a controllable and unidirectional water flow is still difficult to achieve and the underlying mechanism is far from being understood. In this paper, using molecular dynamics simulations, we systematically investigate the effects of an external electric field on the transport of single-file water molecules through a carbon nanotube (CNT). We find that the orientation of water molecules inside the CNT can be well-tuned by the electric field and is strongly coupled to the water flux. This orientation-induced water flux is energetically due to the asymmetrical water-water interaction along the CNT axis. The wavelike water density profiles are disturbed under strong field strengths. The frequency of flipping for the water dipoles will decrease as the field strength is increased, and the flipping events vanish completely for the relatively large field strengths. Most importantly, a critical field strength E(c) related to the water flux is found. The water flux is increased as E is increased for E ≤ E(c), while it is almost unchanged for E > E(c). Thus, the electric field offers a level of governing for unidirectional water flow, which may have some biological applications and provides a route for designing efficient nanopumps.

It has recently been pointed out that the spinning Kerr black hole with maximal spin could act as a particle collider with arbitrarily high center-of-mass energy. In this paper, we will extend the result to the charged spinning black hole, the Kerr-Newman black hole. The center-of-mass energy of collision for two uncharged particles falling freely from rest at infinity depends not only on the spin a but also on the charge Q of the black hole. We find that an unlimited center-of-mass energy can be approached with the conditions: (1) the collision takes place at the horizon of an extremal black hole; (2) one of the colliding particles has critical angular momentum; (3) the spin a of the extremal black hole satisfies 1 ffiffi 3 p a M 1, where M is the mass of the Kerr-Newman black hole. The third condition implies that to obtain an arbitrarily high energy, the extremal Kerr-Newman black hole must have a large value of spin, which is a significant difference between the Kerr and Kerr-Newman black holes. Furthermore, we also show that, for a near-extremal black hole, there always exists a finite upper bound for center-of-mass energy, which decreases with the increase of the charge Q.

Between Snyder's quantized space-time model in de Sitter space of momenta and the dS special relativity on dS-spacetime of radius R with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with Planck length ℓ P , R ≃ (3/Λ) 1/2 should be a fundamental constant. They lead to a dimensionless constant g∼ ℓ P R −1 = (G c −3 Λ/3) 1/2 ∼ 10 −61 . These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local dS-invariance characterized by g. A simple model of dS-gravity with a gauge-like action on umbilical manifolds may show these characters. It can pass the observation tests and support the duality.

In this paper we obtain a new solution of a brane made up of a scalar field coupled to a dilaton.There is a unique parameter b in the solution, which decides the distribution of the energy density and will effect the localization of bulk matter fields. For free vector fields, we find that the zero mode for left-chiral fermion also can be localized.

From the perspectives of biological applications and material sciences, it is essential to understand the transport properties of water molecules through nanochannels. Although considerable effort and progress has been made in recent years, a systematic understanding of the effect of nanochannel dimension is still lacking. In this paper, we use molecular dynamics (MD) simulations to study the transport of water molecules through carbon nanotubes (CNTs) with various dimensions under pressure differences. We find an exponential decay describing the relation of the water flow and CNT lengths (L) for different pressures. The average translocation time of individual water molecules yields to a power law relation with L. We also exploit these results by comparing with the single-file transport, where some interesting relations were figured. Meanwhile, for a given CNT length, the water flow vs CNT diameters (R) can be depicted by a power law, which is found to be relevant to the water occupancy inside the nanochannel. In addition, we compare our MD results with predictions from the no-slip Hagen-Poisseuille (HP) relation. The dependence of the enhancement of the simulated water flux over the HP prediction on the CNT length and diameter supports previous MD and experimental studies. Actually, the effect of nanotube dimension is not only originated from the motion of water molecules inside the CNT but also related to thermal fluctuations in the bulk water outside the CNT. These results enrich our knowledge about the channel size effect on the water transportation, which should have deep implications for the design of nanofluidic devices.

We focus on the dynamical aspects on Newton-Hooke space-time N H + mainly from the viewpoint of geometric contraction of the de Sitter spacetime with Beltrami metric. (The term spacetime is used to denote a space with non-degenerate metric, while the term space-time is used to denote a space with degenerate metric.) We first discuss the Newton-Hooke classical mechanics, especially the continuous medium mechanics, in this framework. Then, we establish a consistent theory of gravity on the Newton-Hooke space-time as a kind of Newton-Cartan-like theory, parallel to the Newton's gravity in the Galilei space-time. Finally, we give the Newton-Hooke invariant Schrödinger equation from the geometric contraction, where we can relate the conservative probability in some sense to the mass density in the Newton-Hooke continuous medium mechanics. Similar consideration may apply to the Newton-Hooke space-time N H − contracted from anti-de Sitter spacetime.

Liquid crystals playing a crucial role in material sciences show increasing potential applications in nanotechnology and industry. Generally, thermodynamic and dynamic properties of liquid crystals strongly depend on the corresponding force fields (FF); thus, it is necessary and urgent for us to establish a reliable force field for a given liquid crystal system. In this paper, we develop a new set of FF parameters for the 5CB (4-cyano-4'-pentylbiphenyl) molecule by reoptimizing some parameters of TraPPE-UA in order to reproduce the bulk density. This strategy for the construction of 5CB FF is rather advisable as it not only provides reliable values for the Lennard-Jones parameters but also reduces the computational cost and maintains FF transferability. Indeed, our simulation results show that the phase behavior, the order parameter, conformational features, neighboring molecular pair arrangements, and diffusion properties of 5CB can be reproduced very well. We further validate the transferability of this 5CB FF by extending it to the 8CB (4-cyano-4'-octylbiphenyl) system. As a result, both the nematic and the partial bilayer smectic phases (Sm-A(d)) and the nematic-isotropic and the smectic-nematic transition temperatures as well as the diffusion properties of 8CB are successfully reproduced. Therefore, this set of FF parameters originally designed for the 5CB molecule is reliable and transferable. Its effectiveness to model nCB series and molecules with similar chemical structures is expected.