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Total Posts 32

Homomorphisms of trees into a path

Zhicong Lin | SIAM Journal on Discrete Mathematics 29 (2015)

Let ${{hom}}(G,H)$ denote the number of homomorphisms from a graph $G$ to a graph $H$. In this paper we study the number of homomorphisms of trees into a path, and prove that ${{hom}}(P_m,P_n)\leq {{hom}}(T_m,P_n)\leq {{hom}}(S_m,P_n),$ where $T_m$ is any tree on $m$ vertices, and $P_m$ and $S_m$ denote the path and star on $m$ vertices, respectively. This completes the study of extremal problems concerning the number of homomorphisms between trees started in the paper Graph Homomorphisms Between Trees



Physical Properties of Tidal Features of Interacting Disk Galaxies: Three-Dimensional Self-Consistent Models

SangHoonOh(Woong-Tae Kim, Hyung Mok Lee) | Astrophysical Journal 807 (2015)

Using self-consistent three-dimensional (3D) N-body simulations, we investigate the physical properties of nonaxisymmetric features in a disk galaxy created by a tidal interaction with its companion. The primary galaxy consists of a stellar disk, a bulge, and a live halo, corresponding to Milky-Way-type galaxies, while the companion is represented by a halo alone. We vary the companion mass and the pericenter distance to explore situations with differing tidal strength parameterized by either the relative tidal force P or the relative imparted momentum S. We find that the formation of a tidal tail in the outer parts requires or . A stronger interaction results in a stronger, less wound tail that forms earlier. Similarly, a stronger tidal forcing produces stronger, more loosely wound spiral arms in the inner parts. The arms are approximately logarithmic in shape, with both amplitude and pitch angle decaying with time. The derived pattern speed decreases with radius and is close to the curve at late time, with Ω and κ denoting the angular and epicycle frequencies, respectively. This suggests that the tidally induced spiral arms are most likely kinematic density waves weakly modified by self-gravity. Compared to the razor-thin counterparts, arms in the 3D models are weaker, have a smaller pitch angle, and wind and decay more rapidly. The 3D density structure of the arms is well described by the concentrated and sinusoidal models when the arms are in the nonlinear and linear regimes, respectively. We demonstrate that dynamical friction between interacting galaxies transfers the orbital angular momentum of one galaxy to the spin angular momentum of the companion halo.



Searches for Continuous Gravitational Waves from Nine Young Supernova Remnants

J.Aasi (S. H. Oh, J. J. Oh, E. J. Son) | Astrophysical Journal 813/1 (2015)

015? We describe directed searches for continuous gravitational waves (GWs) in data from the sixth Laser Interferometer Gravitational-wave Observatory (LIGO) science data run. The targets were nine young supernova remnants not associated with pulsars; eight of the remnants are associated with non-pulsing suspected neutron stars. One target's parameters are uncertain enough to warrant two searches, for a total of 10. Each search covered a broad band of frequencies and first and second frequency derivatives for a fixed sky direction. The searches coherently integrated data from the two LIGO interferometers over time spans from 5.3–25.3 days using the matched-filtering -statistic. We found no evidence of GW signals. We set 95% confidence upper limits as strong (low) as 4 × 10−25 on intrinsic strain, 2 × 10−7 on fiducial ellipticity, and 4 × 10−5 on r-mode amplitude. These beat the indirect limits from energy conservation and are within the range of theoretical predictions for neutron-star ellipticities and r-mode amplitudes.



Note on uncertainty relations in doubly special relativity and rainbow gravity

EdwinJ.Son (Wontae Kim) | Modern Physics Letters A 30 (2015)

We present commutation relations depending on the rainbow functions which are slightly different from the well-known results. However, the advantage of these new commutation relations are compatible with the calculation of the Hawking temperature in the rainbow Schwarzschild black hole.



Application of Artificial Neural Network to Search for Gravitational-Wave Signals Associated with Short Gamma-Ray Bursts

KyungminKim | Classical and Quantum Gravity 32 (2015)

We apply a machine learning algorithm, the artificial neural network, to the search for gravitational-wave signals associated with short gamma-ray bursts (GRBs). The multi-dimensional samples consisting of data corresponding to the statistical and physical quantities from the coherent search pipeline are fed into the artificial neural network to distinguish simulated gravitational-wave signals from background noise artifacts. Our result shows that the data classification efficiency at a fixed false alarm probability (FAP) is improved by the artificial neural network in comparison to the conventional detection statistic. Specifically, the distance at 50% detection probability at a fixed false positive rate is increased about 8%–14% for the considered waveform models. We also evaluate a few seconds of the gravitational-wave data segment using the trained networks and obtain the FAP. We suggest that the artificial neural network can be a complementary method to the conventional detection statistic for identifying gravitational-wave signals related to the short GRBs.



Effect of vision angle on the phase transition in flocking behavior of animal groups

P.TheNguyen (Sang-Hee Lee) | PHYSICAL REVIEW E 92 (2015)

The nature of the phase transition in a system of self-propelling particles has been extensively studied during the past few decades. A theoretical model was proposed by [T. Vicsek et al. Phys. Rev. Lett. 75, 1226 (1995)] with a simple rule for updating the direction of motion of each particle. Based on the model of Vicsek et al., in this paper, we consider a group of animals as particles moving freely in a two-dimensional space. Due to the fact that the viewable area of animals depends on the species, we consider the motion of each individual within an angle φ=?/2 (? is called the angle of view) of a circle centered at its position of radius R . We obtained a phase diagram in the space (φ,ηc) with ηc being the critical noise. We show that the phase transition exists only in the case of a wide view's angle φ≥0.5π . The flocking of animals is a universal behavior of the species of prey but not the one of the predator. Our simulation results are in good agreement with experimental observation [C. Beccoa et al., Physica A 367, 487 (2006)].



Characterization of the Crawling Activity of Caenorhabditis elegans by Using a Hidden Markov Model

Sang-HeeLee (Seung Ho Kang) | Theory in Biosciences 134 (2015)

The locomotion behavior of Caenorhabditis elegans has been studied extensively to understand the respective roles of neural control and biomechanics as well as the interaction between them. Constructing a mathematical model is helpful to understand the locomotion behavior in various surrounding conditions that are difficult to realize in experiments. In this study, we built three hidden Markov models (HMMs) for the crawling behavior of C. elegans in a controlled environment with no chemical treatment and in a formaldehyde-treated environment (0.1 and 0.5 ppm). The organism’s crawling activity was recorded using a digital camcorder for 20 min at a rate of 24 frames per second. All shape patterns were quantified by branch length similarity (BLS) entropy and classified into four groups using the self-organizing map (SOM). Comparison of the simulated behavior generated by HMMs and the actual crawling behavior demonstrated that the HMM coupled with the SOM was successful in characterizing the crawling behavior. In addition, we briefly discussed the possibility of using the HMM together with BLS entropy to develop bio-monitoring systems to determine water quality.



A multiscale model of cardiovascular system including an immersed whole-heart in the cases of normal and ventricular septal defect (VSD)

WanhoLee (Eunok Jung) | Bulletin of Mathematical Biology 77 (2015)

A mathematical and computational model combining the heart and circulatory system has been developed to understand the hemodynamics of circulation under normal conditions and ventricular septal defect (VSD). The immersed boundary method has been introduced to describe the interaction between the moving two-dimensional heart and intracardiac blood flow. The whole-heart model is governed by the Navier–Stokes system; this system is combined with a multi-compartment model of circulation using pressure–flow relations and the linearity of the discretized Navier–Stokes system. We investigate the velocity field, flowmeters, and pressure–volume loop in both normal and VSD cases. Simulation results show qualitatively good agreements with others found in the literature. This model, combining the heart and circulation, is useful for understanding the complex, hemodynamic mechanisms involved in normal circulation and cardiac diseases.



An immersed boundary method for a contractile elastic ring in a three-dimensional Newtonian fluid

SeunggyuLee (Darae Jeong, Wanho Lee, and Junseok Kim) | Journal of Scientific Computing 67 (2015)

In this paper, we present an immersed boundary method for modeling a contractile elastic ring in a three-dimensional Newtonian fluid. The governing equations are the modified Navier–Stokes equations with an elastic force from the contractile ring. The length of the elastic ring is time dependent and the ring shrinks with time because of its elastic nature in our proposed model. We dynamically reduce the number of Lagrangian boundary points when the distance between adjacent points is too small. This point-deleting algorithm helps keep the number of immersed boundary points in a single Cartesian mesh grid from becoming too high. We perform numerical experiments with various initial configurations of the contractile elastic ring, and numerical simulations to investigate the effects of the parameters are also conducted. The numerical results show that the proposed method can model and simulate the time-dependent contractile elastic ring in a three-dimensional Newtonian fluid.



Multidimensional Open System for Valveless Pumping

JonggulLee (Eunok Jung, Do Wan, Kim, and Wanho Lee) | Bulletin of the Korean Mathematical Society 52 (2015)

In this study, we present a multidimensional open system for valveless pumping (VP). This system consists of an elastic tube connected to two open tanks filled with a fluid under gravity. The two-dimensional elastic tube model is constructed based on the immersed boundary method, and the tank model is governed by a system of ordinary differential equations based on the work-energy principle. The flows into and out of the elastic tube are modeled in terms of the source/sink patches inside the tube. The fluid dynamics of this system is generated by the periodic compress-and-release action applied to an asymmetric region of the elastic tube. We have developed an algorithm to couple these partial differential equations and ordinary differential equations using the pressure-flow relationship and the linearity of the discretized Navier-Stokes equations. We have observed the most important feature of VP, namely, the existence of a unidirectional net flow in the system. Our computations are focused on the factors that strongly influence the occurrence of unidirectional flows, for example, the frequency, compression duration, and location of pumping. Based on these investigations, some case studies are performed to observe the details of the ow features.