We study the heterogeneous nucleation of Ising model on complex networks under a non-equilibrium situation where the impurities perform degree-biased motion controlled by a parameter alpha. Through the forward flux sampling and detailed analysis on t
he nucleating clusters, we find that the nucleation rate shows a nonmonotonic dependence on alpha for small number of impurities, in which a maximal nucleation rate occurs at alpha=0 corresponding to the degree-uncorrelated random motion. Furthermore, we demonstrate the distinct features of the nucleating clusters along the pathway for different preference of impurities motion, which may be used to understand the resonance-like dependence of nucleation rate on the motion bias of impurities. Our theoretical analysis shows that the nonequilibrium diffusion of impurities can always induce a positive energy flux that can facilitate the barrier-crossing nucleation process. The nonmonotonic feature of the average value of the energy flux with alpha may be the origin of our simulation results.
Study of general purpose computation by GPU (Graphics Processing Unit) can improve the image processing capability of micro-computer system. This paper studies the parallelism of the different stages of decimation in time radix 2 FFT algorithm, desig
ns the butterfly and scramble kernels and implements 2D FFT on GPU. The experiment result demonstrates the validity and advantage over general CPU, especially in the condition of large input size. The approach can also be generalized to other transforms alike.
We show that the graph of the classical Weierstrass function $sum_{n=0}^infty lambda^n cos (2pi b^n x)$ has Hausdorff dimension $2+loglambda/log b$, for every integer $bge 2$ and every $lambdain (1/b,1)$. Replacing $cos(2pi x)$ by a general non-const
ant $C^2$ periodic function, we obtain the same result under a further assumption that $lambda b$ is close to $1$.
Near infrared images from the COBE satellite presented the first clear evidence that our Milky Way galaxy contains a boxy shaped bulge. Recent years have witnessed a gradual paradigm shift in the formation and evolution of the Galactic bulge. Bulges
were commonly believed to form in the dynamical violence of galaxy mergers. However, it has become increasingly clear that the main body of the Milky Way bulge is not a classical bulge made by previous major mergers, instead it appears to be a bar seen somewhat end-on. The Milky Way bar can form naturally from a precursor disk and thicken vertically by the internal firehose/buckling instability, giving rise to the boxy appearance. This picture is supported by many lines of evidence, including the asymmetric parallelogram shape, the strong cylindrical rotation (i.e., nearly constant rotation regardless of the height above the disk plane), the existence of an intriguing X-shaped structure in the bulge, and perhaps the metallicity gradients. We review the major theoretical models and techniques to understand the Milky Way bulge. Despite the progresses in recent theoretical attempts, a complete bulge formation model that explains the full kinematics and metallicity distribution is still not fully understood. Upcoming large surveys are expected to shed new light on the formation history of the Galactic bulge.
In this paper, we try to answer two questions about any given scientific discipline: First, how important is each subfield and second, how does a specific subfield influence other subfields? We modify the well-known open-system Leontief Input-Output
Analysis in economics into a closed-system analysis focusing on eigenvalues and eigenvectors and the effects of removing one subfield. We apply this method to the subfields of physics. This analysis has yielded some promising results for identifying important subfields (for example the field of statistical physics has large influence while it is not among the largest subfields) and describing their influences on each other (for example the subfield of mechanical control of atoms is not among the largest subfields cited by quantum mechanics, but our analysis suggests that these fields are strongly connected). This method is potentially applicable to more general systems that have input-output relations among their elements.
We explore the kinematics (both the radial velocity and the proper motion) of the vertical X-shaped feature in the Milky Way with an N-body bar/bulge model. From the solar perspective, the distance distribution of particles is double-peaked in fields
passing through the X-shape. The separation and amplitude ratio between the two peaks qualitatively match the observed trends towards the Galactic bulge. We confirm clear signatures of cylindrical rotation in the pattern of mean radial velocity across the bar/bulge region. We also find possible imprints of coherent orbital motion inside the bar structure in the radial velocity distribution along l=0 degree, where the near and far sides of the bar/bulge show excesses of approaching and receding particles. The coherent orbital motion is also reflected in the slight displacement of the zero-velocity-line in the mean radial velocity, and the displacement of the maximum/minimum in the mean longitudinal proper motion across the bulge region. We find some degree of anisotropy in the stellar velocity within the X-shape, but the underlying orbital family of the X-shape cannot be clearly distinguished. Two potential applications of the X-shape in previous literature are tested, i.e., bulge rotation and Galactic center measurements. We find that the proper motion difference between the two sides of the X-shape can be used to estimate the mean azimuthal streaming motion of the bulge, but not the pattern speed of the bar. We also demonstrate that the Galactic center can be located with the X-shape, but the accuracy depends on the fitting scheme, the number of fields, and their latitudinal coverage.
Chu connections and back diagonals are introduced as morphisms for distributors between categories enriched in a small quantaloid $mathcal{Q}$. These notions, meaningful for closed bicategories, dualize the constructions of arrow categories and the F
reyd completion of categories. It is shown that, for a small quantaloid $mathcal{Q}$, the category of complete $mathcal{Q}$-categories and left adjoints is a retract of the dual of the category of $mathcal{Q}$-distributors and Chu connections, and it is dually equivalent to the category of $mathcal{Q}$-distributors and back diagonals. As an application of Chu connections, a postulation of the intuitive idea of reduction of formal contexts in the theory of formal concept analysis is presented, and a characterization of reducts of formal contexts is obtained.
Dust lanes, nuclear rings, and nuclear spirals are typical gas structures in the inner region of barred galaxies. Their shapes and properties are linked to the physical parameters of the host galaxy. We use high-resolution hydrodynamical simulations
to study 2D gas flows in simple barred galaxy models. The nuclear rings formed in our simulations can be divided into two groups: one group is nearly round and the other is highly elongated. We find that roundish rings may not form when the bar pattern speed is too high or the bulge central density is too low. We also study the periodic orbits in our galaxy models, and find that the concept of inner Lindblad resonance (ILR) may be generalized by the extent of $x_2$ orbits. All roundish nuclear rings in our simulations settle in the range of $x_2$ orbits (or ILRs). However, knowing the resonances is insufficient to pin down the exact location of these nuclear rings. We suggest that the backbone of round nuclear rings is the $x_2$ orbital family, i.e. round nuclear rings are allowed only in the radial range of $x_2$ orbits. A round nuclear ring forms exactly at the radius where the residual angular momentum of infalling gas balances the centrifugal force, which can be described by a parameter $f_{rm ring}$ measured from the rotation curve. The gravitational torque on gas in high pattern speed models is larger, leading to a smaller ring size than in the low pattern speed models. Our result may have important implications for using nuclear rings to measure the parameters of real barred galaxies with 2D gas kinematics.
About one third of early-type barred galaxies host small-scale secondary bars. The formation and evolution of such double-barred galaxies remain far from being well understood. In order to understand the formation of such systems, we explore a large
parameter space of isolated pure-disk simulations. We show that a dynamically cool inner disk embedded in a hotter outer disk can naturally generate a steady secondary bar while the outer disk forms a large-scale primary bar. The independent bar instabilities of inner and outer disks result in long-lived double-barred structures whose dynamical properties are comparable with observations. This formation scenario indicates that the secondary bar might form from the general bar instability, the same as the primary bar. Under some circumstances, the interaction of the bars and the disk leads to the two bars aligning or single, nuclear, bars only. Simulations that are cool enough of the center to experience clump instabilities may also generate steady double-barred galaxies. In this case, the secondary bars are fast, i.e., the bar length is close to the co-rotation radius. This is the first time that double-barred galaxies containing a fast secondary bar are reported. Previous orbit-based studies had suggested that fast secondary bars are not dynamically possible.
In this paper, we consider permutation manipulations by any subset of women in the Gale-Shapley algorithm. This paper is motivated by the college admissions process in China. Our results also answer Gusfield and Irvings open problem on what can be ac
hieved by permutation manipulations. We present an efficient algorithm to find a strategy profile such that the induced matching is stable and Pareto-optimal while the strategy profile itself is inconspicuous. Surprisingly, we show that such a strategy profile actually forms a Nash equilibrium of the manipulation game. We also show that a strong Nash equilibrium or a super-strong Nash equilibrium does not always exist in general and it is NP-hard to check the existence of these equilibria. We consider an alternative notion of strong Nash equilibria and super-strong Nash equilibrium. Under such notions, we characterize the super-strong Nash equilibrium by Pareto-optimal strategy profiles. In the end, we show that it is NP-complete to find a manipulation that is strictly better for all members of the coalition. This result demonstrates a sharp contrast between weakly better-off outcomes and strictly better-off outcomes.
