Stability of non-constant equilibrium solutions for two-fluid non-isentropic Euler-Maxwell systems arising in plasmas

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy estimates, the global smooth solution with small amplitude is established near a non-constant equilibrium solution with asymptotic stability properties. This improves the results obtained in \cite{LWF16a} for models with temperature diffusion terms by using the pressure functions $p^\nu$ in place of the unknown variables densities $n^\nu$

Deterministic Constructions of Binary Measurement Matrices from Finite Geometry

Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as {provably} good measurement matrices for compressed sensing under $\ell_1$-minimization. The performance of the proposed binary measurement matrices is mainly theoretically analyzed with the help of the analyzing methods and results from (finite geometry) LDPC codes. Particularly, several lower bounds of the spark (i.e., the smallest number of columns that are linearly dependent, which totally characterizes the recovery performance of $\ell_0$-minimization) of general binary matrices and finite geometry matrices are obtained and they improve the previously known results in most cases. Simulation results show that the proposed matrices perform comparably to, sometimes even better than, the corresponding Gaussian random matrices. Moreover, the proposed matrices are sparse, binary, and most of them have cyclic or quasi-cyclic structure, which will make the hardware realization convenient and easy.Comment: 12 pages, 11 figure

Signal Recognition Particle (SRP) and SRP Receptor: A New Paradigm for Multistate Regulatory GTPases

The GTP-binding proteins or GTPases comprise a superfamily of proteins that provide molecular switches in numerous cellular processes. The “GTPase switch” paradigm, in which a GTPase acts as a bimodal switch that is turned “on” and “off” by external regulatory factors, has been used to interpret the regulatory mechanism of many GTPases for more than two decades. Nevertheless, recent work has unveiled an emerging class of “multistate” regulatory GTPases that do not adhere to this classical paradigm. Instead of relying on external nucleotide exchange factors or GTPase activating proteins to switch between the on and off states, these GTPases have the intrinsic ability to exchange nucleotides and to sense and respond to upstream and downstream factors. In contrast to the bimodal nature of the GTPase switch, these GTPases undergo multiple conformational rearrangements, allowing multiple regulatory points to be built into a complex biological process to ensure the efficiency and fidelity of the pathway. We suggest that these multistate regulatory GTPases are uniquely suited to provide spatial and temporal control of complex cellular pathways that require multiple molecular events to occur in a highly coordinated fashion

Universal short time quantum critical dynamics of finite size systems

We investigate the short time quantum critical dynamics in the imaginary time relaxation processes of finite size systems. Universal scaling behaviors exist in the imaginary time evolution and in particular, the system undergoes a critical initial slip stage characterized by an exponent $\theta$, in which an initial power-law increase emerges in the imaginary time correlation function when the initial state has zero order parameter and vanishing correlation length. Under different initial conditions, the quantum critical point and critical exponents can be determined from the universal scaling behaviors. We apply the method to the one- and two-dimensional transverse field Ising models using quantum Monte Carlo simulations. In the one-dimensional case, we locate the quantum critical point at $(h/J)_{c}=1.00003(8)$ \thirdrevise{in the thermodynamic limit}, and estimate the critical initial slip exponent $\theta=0.3734(2)$, static exponent $\beta/\nu=0.1251(2)$ \thirdrevise{by analyzing data on chains of length $L=32\sim 256$ and $L=48\sim 256$, respectively}. For the two-dimensional square-lattice system, the critical coupling ratio is given by $3.04451(7)$ \thirdrevise{in the thermodynamic limit} while the critical exponents are \thirdrevise{$\theta=0.209(4)$ and $\beta/\nu=0.518(1)$ estimated by data on systems of size $L=24\sim 64$ and $L=32\sim 64$, correspondingly.} Remarkably, the critical initial slip exponents obtained in both models are notably distinct from their classical counterparts, owing to the essential differences between classical and quantum dynamics. The short time critical dynamics and the imaginary time relaxation QMC approach can be readily adapted to various models.Comment: 12 pages, 8 figure