Remarks on the stability of the Navier-Stokes equations supplemented with stress-free boundary conditions

The purpose of this note is to analyze the long term stability of the Navier-Stokes equations supplemented with the Coriolis force and the stress-free boundary condition. It is shown that, if the flow domain is axisymmetric, spurious stability behaviors can occur depending whether the Coriolis force is active or not

QCD Multipole Expansion and Hadronic Transitions in Heavy Quarkonium Systems

We review the developments of QCD multipole expansion and its applications to hadronic transitions and some radiative decays of heavy quarkonia. Theoretical predictions are compsred with updated experimental results.Comment: 23 pages, 7 figures. Some typos corrected, and 3 references adde

Quantum dense coding in multiparticle entangled states via local measurements

In this paper, we study quantum dense coding between two arbitrarily fixed particles in a (N+2)-particle maximally-entangled states through introducing an auxiliary qubit and carrying out local measurements. It is shown that the transmitted classical information amount through such an entangled quantum channel usually is less than two classical bits. However, the information amount may reach two classical bits of information, and the classical information capacity is independent of the number of the entangled particles in the initial entangled state under certain conditions. The results offer deeper insights to quantum dense coding via quantum channels of multi-particle entangled states.Comment: 3 pages, no figur

A Tensor-Based Forensics Framework for Virtualized Network Functions in the Internet of Things: Utilizing Tensor Algebra in Facilitating More Efficient Network Forensic Investigations

With the ever-increasing network traffic and Internet connectivity of smart devices, more attack events are being reported. As a result, network forensics remains a topic of ongoing research interest in the Internet of Things (IoT). In this article, we present a novel tensor-based forensics approach for virtualized network functions (VNFs). An event tensor model is proposed to formalize the network events, and then, it is used for effectively updating the core event tensor. We then introduce a similarity tensor model to integrate the core event tensors on the orchestration and management layer in the network function virtualization (NFV) framework. Finally, we present an evidence tensor model for network forensics, where we demonstrate how evidence tensors can be merged

Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

Thermal Impact on Spiking Properties in Hodgkin-Huxley Neuron with Synaptic Stimulus

The effect of environmental temperature on neuronal spiking behaviors is investigated by numerically simulating the temperature dependence of spiking threshold of the Hodgkin-Huxley neuron subject to synaptic stimulus. We find that the spiking threshold exhibits a global minimum in a "comfortable temperature" range where spike initiation needs weakest synaptic strength, indicating the occurrence of optimal use of synaptic transmission in neural system. We further explore the biophysical origin of this phenomenon in ion channel gating kinetics and also discuss its possible biological relevance in information processing in neural systems.Comment: 10 pages, 4 figure

Search for Bc(ns)B_c(ns) via the Bc(ns)→Bc(ms)π+π−B_c(ns)\to B_c(ms)\pi^+\pi^- transition at LHCb and Z0Z_0 factory

It is interesting to study the characteristics of the whole family of $B_c$ which contains two different heavy flavors. LHC and the proposed $Z^0$ factory provide an opportunity because a large database on the $B_c$ family will be achieved. $B_c$ and its excited states can be identified via their decay modes. As suggested by experimentalists, $B_c^*(ns)\to B_c+\gamma$ is not easy to be clearly measured, instead, the trajectories of $\pi^+$ and $\pi^-$ occurring in the decay of $B_c(ns)\to B_c(ms)+\pi^+\pi^-$ ($n>m$) can be unambiguously identified, thus the measurement seems easier and more reliable, therefore this mode is more favorable at early running stage of LHCb and the proposed $Z^0$ factory. In this work, we calculate the rate of $B_c(ns)\to B_c(ms)+\pi^+\pi^-$ in terms of the QCD multipole-expansion and the numerical results indicate that the experimental measurements with the luminosity of LHC and $Z^0$ factory are feasible.Comment: 12 pages, 1 figures and 4 tables, acceptted by SCIENCE CHINA Physics, Mechanics & Astronomy (Science in China Series G

Coulomb drag between quantum wires with different electron densities

We study the way back-scattering electron--electron interaction generates Coulomb drag between quantum wires with different densities. At low temperature $T$ the system can undergo a commensurate-- incommensurate transition as the potential difference $|W|$ between the two wires passes a critical value $\Delta$, and this transition is reflected in a marked change in the dependence of drag resistivity on $W$ and $T$. At high temperature a density difference between the wires suppresses Coulomb drag induced by back scattering, and we use the Tomonaga--Luttinger model to study this suppression in detail.Comment: 6 pages, 4 figure