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Register a new userCorrelated flares in models of a magnetized canopy
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Added by
Bidzina Shergelashvili
Publication date
2007
fields
Physics
and research's language is
English
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A model of the Lu-Hamilton kind is applied to the study of critical behavior of the magnetized solar atmosphere. The main novelty is that its driving is done via sources undergoing a diffusion. This mimics the effect of a virtual turbulent substrate forcing the system. The system exhibits power-law statistics not only in the size of the flares, but also in the distribution of the waiting times.
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In some systems, the connecting probability (and thus the percolation process) between two sites depends on the geometric distance between them. To understand such process, we propose gravitationally correlated percolation models for link-adding networks on the two-dimensional lattice $G$ with two strategies $S_{rm max}$ and $S_{rm min}$, to add a link $l_{i,j}$ to connect site $i$ and site $j$ with mass $m_i$ and $m_j$, respectively; $m_i$ and $m_j$ are sizes of the clusters which contain site $i$ and site $j$, respectively. The probability to add the link $l_{i,j}$ is related to the generalized gravity $g_{ij} equiv m_i m_j/r_{ij}^d$, where $r_{ij}$ is the geometric distance between $i$ and $j$, and $d$ is an adjustable decaying exponent. In the beginning of the simulation, all sites of $G$ are occupied and there is no link. In the simulation process, two inter-cluster links $l_{i,j}$ and $l_{k,n}$ are randomly chosen and the generalized gravities $g_{ij}$ and $g_{kn}$ are computed. In the strategy $S_{rm max}$, the link with larger generalized gravity is added. In the strategy $S_{rm min}$, the link with smaller generalized gravity is added, which include percolation on the ErdH os-Renyi random graph and the Achlioptas process of explosive percolation as the limiting cases, $d to infty$ and $d to 0$, respectively. Adjustable strategies facilitate or inhibit the network percolation in a generic view. We calculate percolation thresholds $T_c$ and critical exponents $beta$ by numerical simulations. We also obtain various finite-size scaling functions for the node fractions in percolating clusters or arrival of saturation length with different intervening strategies.
We analyze the thermal conductivity of ions (equivalent to the conductivity of phonons in crystalline matter) in a neutron star envelope. We calculate the ion/phonon thermal conductivity in a crystal of atomic nuclei using variational formalism and performing momentum-space integration by Monte Carlo method. We take into account phonon-phonon and phonon-electron scattering mechanisms and show that phonon-electron scattering dominates at not too low densities. We extract the ion thermal conductivity in ion liquid or gas from literature. Numerical values of the ion/phonon conductivity are approximated by analytical expressions, valid for T>10^5 K and 10^5 g cm^-3 < rho < 10^14 g cm^-3. Typical magnetic fields B~10^12 G in neutron star envelopes do not affect this conductivity although they strongly reduce the electron thermal conductivity across the magnetic field. The ion thermal conductivity remains much smaller than the electron conductivity along the magnetic field. However, in the outer neutron star envelope it can be larger than the electron conductivity across the field, that is important for heat transport across magnetic field lines in cooling neutron stars. The ion conductivity can greatly reduce the anisotropy of heat conduction in outer envelopes of magnetized neutron stars.
We study the SYK$_{2}$ model of $N$ Majorana fermions with random quadratic interactions through a detailed spectral analysis and by coupling the model to 2- and 4-point sources. In particular, we define the generalized spectral form factor and level spacing distribution function by generalizing from the partition function to the generating function. For $N=2$, we obtain an exact solution of the generalized spectral form factor. It exhibits qualitatively similar behavior to the higher $N$ case with a source term. The exact solution helps understand the behavior of the generalized spectral form factor. We calculate the generalized level spacing distribution function and the mean value of the adjacent gap ratio defined by the generating function. For the SYK$_2$ model with a 4-point source term, we find a Gaussian unitary ensemble behavior in the near-integrable region of the theory, which indicates a transition to chaos. This behavior is confirmed by the connected part of the generalized spectral form factor with an unfolded spectrum. The departure from this Gaussian random matrix behavior as the relative strength of the source term is increased is consistent with the observation that the 4-point source term alone, without the SYK$_2$ couplings turned on, exhibits an integrable spectrum from the spectral form factor and level spacing distribution function in the large $N$ limit.
We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of the 4D Z_2 LGT. In this way, all classical spin models with apparently very different features are unified in a single complete model, and a physical relation between all models is established. As applications of this result, we present a new method to do mean field theory for abelian discrete LGTs with d>3, and we show that the computation of the partition function of the 4D Z_2 LGT is a computationally hard (#P-hard) problem. We also extend our results to abelian continuous models, where we show the approximate completeness of the 4D Z_2 LGT. All results are proven using quantum information techniques.
As a shock front interacts with turbulence, it develops corrugation which induces outgoing wave modes in the downstream plasma. For a fast shock wave, the incoming wave modes can either be fast magnetosonic waves originating from downstream, outrunning the shock, or eigenmodes of the upstream plasma drifting through the shock. Using linear perturbation theory in relativistic MHD, this paper provides a general analysis of the corrugation of relativistic magnetized fast shock waves resulting from their interaction with small amplitude disturbances. Transfer functions characterizing the linear response for each of the outgoing modes are calculated as a function of the magnetization of the upstream medium and as a function of the nature of the incoming wave. Interestingly, if the latter is an eigenmode of the upstream plasma, we find that there exists a resonance at which the (linear) response of the shock becomes large or even diverges. This result may have profound consequences on the phenomenology of astrophysical relativistic magnetized shock waves.
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