Branching Behavior Research Articles

Occurrence of strain nonuniformity in thin‐walled cylinders subjected to constant axial compressive force and cyclic torsion

Hysteretic behaviour numerical analysis has been carried out for elastic–plastic thin‐walled cylinders subjected to a constant axial compressive force and cyclic torsion. It is shown that various deformation modes appear, which are different from those under constant axial contraction, and that those modes cause rapid growth of strain nonuniformity. Also branching analysis for the same model has been performed according to symmetry limit theory and the predicted multiple branching behaviour is compared with the hysteretic behaviour.

Quasiscarred modes and their branching behavior at an exceptional point

We study quasiscarring phenomena and mode branching at an exceptional point (EP) in typically deformed microcavities. It is shown that quasiscarred (QS) modes are dominant in some mode group and their pattern can be understood by short-time ray dynamics near the critical line. As cavity deformation increases, high-Q and low-Q QS modes are branching in opposite ways, at an EP, into two robust mode types showing QS and diamond patterns, respectively. Similar branching behavior can also be found at another EP appearing at a higher deformation. This branching behavior of QS modes has its origin in the fact that an EP is a square-root branch point.

Determination of Propagation Rate Coefficients for Methyl and 2-Ethylhexyl Acrylate via High Frequency PLP−SEC under Consideration of the Impact of Chain Branching

The radical propagation rate coefficients, kp, of methyl acrylate (MA) and 2-ethylhexyl acrylate (EHA) have been determined in bulk via high frequency (500 Hz) pulsed laser polymerization coupled to size exclusion chromatography (PLP−SEC) up to elevated temperatures (20 ≤ T/°C ≤ 80). Prior to the analysis of the generated polymeric material, an investigation into the branching behavior of the generated polymers has been undertaken, employing the concept of local dispersity, D(Ve). In addition, the Mark-Houwkink-Kuhn-Sakurada parameters for both poly(MA) and polyEHA were determined at each studied reaction temperature. The temperature averaged values read (K = 10.2 × 10−5 dL g−1; α = 0.741) and (K = 9.85 × 10−5 dL g−1; α = 0.719) for poly(MA) and polyEHA, respectively. The local dispersity data indicate that branching in polyEHA may be considerably more prevalent than in poly(MA), as with increasing temperature polymer microinhomogeneities are observed. Consequently, the Arrhenius parameters for kp of EHA ...

Automated Sholl analysis of digitized neuronal morphology at multiple scales: Whole cell Sholl analysis versus Sholl analysis of arbor subregions

The morphology of dendrites and the axon determines how a neuron processes and transmits information. Neurite morphology is frequently analyzed by Sholl analysis or by counting the total number of neurites and branch tips. However, the time and resources required to perform such analysis by hand is prohibitive for the processing of large data sets and introduces problems with data auditing and reproducibility. Furthermore, analyses performed by hand or using course-grained morphometric data extraction tools can obscure subtle differences in data sets because they do not store the data in a form that facilitates the application of multiple analytical tools. To address these shortcomings, we have developed a program (titled "Bonfire") to facilitate digitization of neurite morphology and subsequent Sholl analysis. Our program builds upon other available open-source morphological analysis tools by performing Sholl analysis on subregions of the neuritic arbor, enabling the detection of local level changes in dendrite and axon branching behavior. To validate this new tool, we applied Bonfire analysis to images of hippocampal neurons treated with 25 ng/ml brain-derived neurotrophic factor (BDNF) and untreated control neurons. Consistent with prior findings, conventional Sholl analysis revealed that global exposure to BDNF increases the number of neuritic intersections proximal to the soma. Bonfire analysis additionally uncovers that BDNF treatment affects both root processes and terminal processes with no effect on intermediate neurites. Taken together, our data suggest that global exposure of hippocampal neurons to BDNF results in a reorganization of neuritic segments within their arbors, but not necessarily a change in their number or length. These findings were only made possible by the neurite-specific Sholl data returned by Bonfire analysis.

Automated Sholl Analysis of Digitized Neuronal Morphology at Multiple Scales

Neuronal morphology plays a significant role in determining how neurons function and communicate. Specifically, it affects the ability of neurons to receive inputs from other cells and contributes to the propagation of action potentials. The morphology of the neurites also affects how information is processed. The diversity of dendrite morphologies facilitate local and long range signaling and allow individual neurons or groups of neurons to carry out specialized functions within the neuronal network. Alterations in dendrite morphology, including fragmentation of dendrites and changes in branching patterns, have been observed in a number of disease states, including Alzheimer's disease, schizophrenia, and mental retardation. The ability to both understand the factors that shape dendrite morphologies and to identify changes in dendrite morphologies is essential in the understanding of nervous system function and dysfunction. Neurite morphology is often analyzed by Sholl analysis and by counting the number of neurites and the number of branch tips. This analysis is generally applied to dendrites, but it can also be applied to axons. Performing this analysis by hand is both time consuming and inevitably introduces variability due to experimenter bias and inconsistency. The Bonfire program is a semi-automated approach to the analysis of dendrite and axon morphology that builds upon available open-source morphological analysis tools. Our program enables the detection of local changes in dendrite and axon branching behaviors by performing Sholl analysis on subregions of the neuritic arbor. For example, Sholl analysis is performed on both the neuron as a whole as well as on each subset of processes (primary, secondary, terminal, root, etc.) Dendrite and axon patterning is influenced by a number of intracellular and extracellular factors, many acting locally. Thus, the resulting arbor morphology is a result of specific processes acting on specific neurites, making it necessary to perform morphological analysis on a smaller scale in order to observe these local variations. The Bonfire program requires the use of two open-source analysis tools, the NeuronJ plugin to ImageJ and NeuronStudio. Neurons are traced in ImageJ, and NeuronStudio is used to define the connectivity between neurites. Bonfire contains a number of custom scripts written in MATLAB (MathWorks) that are used to convert the data into the appropriate format for further analysis, check for user errors, and ultimately perform Sholl analysis. Finally, data are exported into Excel for statistical analysis. A flow chart of the Bonfire program is shown in Figure 1.

Branching and rheological behavior after electron irradiation in metallocene ethylene- co-norbornene copolymers

The effect of Electron beam (EB) irradiation on a cycloolefin copolymer based on ethylene and norbornene with intermediate molar content of norbornene has been evaluated. Crosslinking is not observed at any dose analyzed. Scission and branching of the chains simultaneously occur at low and high irradiation doses. Scission prevails for doses up to 167 kGy and, then, branching becomes dominant in the rheological bulk response at the highest dose. These side chains favor the development of reversible physical networks through entanglements and, accordingly, the G N 0 value and the dynamic and zero-shear viscosities increase at high levels of irradiation compared with the same parameters found at smaller EB doses. The resulting structures attained after irradiation at different doses are inactivated to microorganism development and exhibit higher thermal stability and a broader temperature window for its standard applications in comparison with the pristine non-irradiated ethylene- co-norbornene (EN) copolymer.

Dynamical polarization of graphene under strain

We study the dependence of the plasmon dispersion relation of graphene on applied uniaxial strain. Besides electron correlation at the RPA level, we also include local field effects specific for the honeycomb lattice. As a consequence of the two-band character of the electronic band structure, we find two distinct plasmon branches. We recover the square-root behavior of the low-energy branch, and find a nonmonotonic dependence of the strain-induced modification of its stiffness, as a function of the wavevector orientation with respect to applied strain.

Phonons and superconductivity in fcc and dhcp lanthanum

We have investigated the structural and electronic properties of lanthanum in the face-centered-cubic (fcc) and double hexagonal-close-packed (dhcp) phases using a generalized gradient approximation of the density functional theory and the ab initio pseudopotential method. It is found that double hexagonal-close-packed is the more stable phase for lanthanum. Differences in the density of states at the Fermi level between these two phases are pointed out and discussed in detail. Using the calculated lattice constant and electronic band structure for both phases, a linear response approach based on the density functional theory has been applied to study phonon modes, polarization characteristics of phonon modes, and electron-phonon interaction. Our phonon results show a softening behavior of the transverse acoustic branch along the $\ensuremath{\Gamma}\text{\ensuremath{-}}L$ direction and the $\ensuremath{\Gamma}\text{\ensuremath{-}}M$ direction for face-centered-cubic and double hexagonal-close-packed phases, respectively. Thus, the transverse-phonon linewidth shows a maximum at the zone boundary $M(L)$ for the double hexagonal-close-packed phase (face-centered-cubic phase), where the transverse-phonon branch exhibits a dip. The electron-phonon coupling parameter $\ensuremath{\lambda}$ is found to be 0.97 (1.06) for the double hexagonal-close-packed phase (face-centered-cubic phase), and the superconducting critical temperature is estimated to be 4.87 (dhcp) and 5.88 K (fcc), in good agreement with experimental values of around 5.0 (dhcp) and 6.0 K (fcc). A few superconducting parameters for the double hexagonal-close-packed phase have been calculated and compared with available theoretical and experimental results. Furthermore, the calculated superconducting parameters for both phases are compared between each other in detail.

Interfacial instability due to evaporation and convection: linear and nonlinear analyses

Interfacial instability arising from evaporation of a single component liquid is investigated using linear and weakly nonlinear analysis. Evaporative convection is studied taking into account the fluid dynamics of both liquid and vapour phases as well as lateral rigid sidewalls. Both open and closed systems are addressed. The nature of the bifurcation and the change in heat flux in the nonlinear regime are determined. It is shown that depending upon the aspect ratio of the geometry, either supercritical or subcritical branching behaviour is possible.

One-magnon inelastic light scattering in the canted antiferromagnetNiF2

Experimental results concerning the temperature and polarization dependence of the one-magnon Raman light scattering in the canted antiferromagnet ${\text{NiF}}_{2}$ (N\'eel temperature ${T}_{N}=73\text{ }\text{K}$) are reported. The excitation frequencies, linewidths, and integrated intensities of the lower and upper magnon branches are obtained over the temperature range 5--65 K. A comparison between theory and experiment for the frequencies of the one-magnon branches shows good overall agreement for temperatures up to $0.3{T}_{N}$. A theoretical model that includes the effects of linear and quadratic magneto-optical coupling is used to account for the observed polarization characteristics of the Stokes and anti-Stokes peaks. The analysis takes account of the small canting angle of the spins which complicates the behavior of the lower magnon branch, in particular. The experimental data are indicative of a possible spin-reorientation transition at $\ensuremath{\sim}31\text{ }\text{K}$.

Three-dimensional analysis of microstructures in titanium

Samples of Ti–4.3Fe–6.7Mo–1.5Al were isothermally annealed in the temperature range of 730–780 °C for various times to study the β–α transformation. Serial sectioning in conjunction with both optical and EBSD analyses was applied to determine the three-dimensional (3-D) morphologies of primary α phase. The 3-D analysis proved to be essential for characterization of the complex morphologies of α grains and consequently for the identification of growth behavior. It showed that nucleation of α grains takes place at β–β grain boundaries and significant branching takes place after initial growth of α grains along β–β grain boundaries. Some branches grow inside the β grain interior. The branching behavior is shown to interact with β–β grain boundaries, leading to a zig-zag morphology. The presented 3-D analysis of α grains and their influence on β–β grain boundaries clearly show that 2-D observations of the microstructural morphologies are not sufficient to adequately represent the transformation characteristics.

Oscillations of stratified fluids

We study the problem on small motions and normal oscillations of a system of two heavy immiscible stratified fluids partially filling a fixed vessel. The lower fluid is assumed to be viscous, while the upper one is assumed to be ideal. We find sufficient existence conditions for a strong (with respect to the time variable) solution of the initial-boundary value problem describing the evolution of the specified hydraulic system. For the corresponding spectral system, we obtain results about the localization of the spectrum, asymptotic behavior of branches of eigenvalues, and existence of the substantial spectrum of the problem.

The Impact of Mergers on the Degree of Competition in the Banking Industry

This paper analyses the relation between competition and concentration in the banking sector. The empirical answer is given by testing a monopolistic competition model of bank branching behaviour on individual bank data at county level (departements and provinces) in France and Italy. We propose a measure of the degree of competiveness in each local market that is function also of market structure indicators. We then use the econometric model to evaluate the impact of horizontal mergers among incumbent banks on competition and discuss when, depending on the pre-merger structure of the market and geographic distribution of branches, the merger is anti-competitive. The paper has implications for competition policy as it suggests an applied tool to evaluate the potential anti-competitive impact of mergers.

Surface circulation in the Eastern Mediterranean using drifters (2005–2007)

Abstract. Within the framework of the EGITTO/EGYPT programs, the spatial structure and the temporal variability of the surface circulation in the eastern basin of the Mediterranean Sea was studied with satellite-tracked drifters. A total of 97 drifters drogued to 15-m nominal depth were released between September 2005 and March 2007, regularly along ship-of-opportunity routes in the Sicily Channel and within specific structures during dedicated campaigns in the Levantine sub-basin. This study complements previous ones in the former and in the Ionian, but it is the first one in the latter. After editing and low-pass filtering, the drifter trajectories were used to estimate pseudo-Eulerian statistics: mean current, variance ellipses, mean and eddy kinetic energies. A statistical analysis was also performed dividing the dataset in two extended seasons (winter and summer). A branching behaviour of the surface water after passing through the Sicily Channel is evidenced, together with a seasonal variability inducing a reversal of the circulation in the southern part of the Ionian. In the Levantine, the surface circulation describes an eastward flow along the Libyan and Egyptian slopes (the Libyo-Egyptian Current: LEC) that continues in a cyclonic circuit along the Middle East and Turkish slopes. This general alongslope circuit can be perturbed locally and temporally by the numerous anticyclonic eddies that co-exist in the Levantine, mainly created by the instability of the LEC in the south (Libyo-Egyptian Eddies: LEEs), but also by the wind (Ierapetra and Pelops), and by the topography (over the Eratosthenes Seamount and off Latakia). The most frequent perturbation is the entrainment of part of the flow seaward: the LEEs close to the slope can interact with the LEC, which then spreads more or less around them, so that a series of contiguous LEEs (paddle-wheel effect) can possibly result in an eastward offshore transport (the so-called Mid Mediterranean Jet). Additionally, when LEEs are close enough to the slope, most of the surface flow is spread seaward. Along the slope the current is then induced by the LEEs southern side which results in a westward current. Locally and temporally the circulation along the slope can thus be reversed.

Transient Dynamics of Coherent Waves Released from Quantum Billiards and Analogous Observation from Free-Space Propagation of Laser Modes

The transient dynamics of the eigenstates and coherent states released from a square quantum billiard is analytically and numerically investigated. It is experimentally verified that this transient dynamic can be analogously observed with the free-space propagation of the lasing modes emitted from the laterally confined, vertically emitted cavities. Furthermore, we exploit a chaotically shaped cavity to originally demonstrate the diffraction-in-time characteristics of the chaotic wave functions. It is found that the transient patterns of chaotic wave functions exhibit a striking feature of random branching behavior with the appearance of intricate interference fringes.

Fatigue crack propagation in 7050-T7451 plate alloy

A study has been accomplished to characterize the fatigue crack growth rates and mechanisms in thin and thick plate commercial 7050-T7451 aluminum plate in the L–S orientation. Crack growth and crack shielding with branching behavior of long, through thickness cracks is examined and compared to L–T and T–L oriented growth data. Compact tension specimens and the compliance method were used to determine crack growth rates. Constant Δ K data showed significant retardation of growth rate curves for the L–S orientation in the range of 10–13 MPa√m where branching and splitting parallel to the load axis are dominant growth mechanisms.

Subdivision rules and virtual endomorphisms

Suppose f : S 2 → S 2 is a postcritically finite branched covering without periodic branch points. If f is the subdivision map of a finite subdivision rule with mesh going to zero combinatorially, then the virtual endomorphism on the orbifold fundamental group associated to f is contracting. This is a first step in a program to clarify the relationships among various notions of expansion for noninvertible dynamical systems with branching behavior.

The evaluation of the possibility of determining the function characterizing the connectedness of pores of various sizes from adsorption measurements

The possibility of determining the function characterizing the connectedness of pores of different types and sizes from the experimental adsorption isotherms is discussed. It is shown that the presence of joints of pores manifests itself by two indications in phase diagrams and adsorption isotherms that contain hysteresis loops. The first indication is related to the appearance of an additional phase transition in the phase diagram and/or a density jump in the isotherm. The second indication is related to different numbers of density jumps in the desorption and adsorption branches of adsorption isotherms. The character of the behavior of the adsorption branch of the isotherm in the case of the presence of regions of joints in a porous system is established.

Ground state, phonon spectrum, and superconducting properties of the nonoxide perovskiteCdCNi3

We have made theoretical investigations of the structural, elastic, electronic, lattice-dynamical, and superconducting properties of the antiperovskite compound ${\text{CdCNi}}_{3}$. The structural, elastic, and electronic properties of this material have been calculated by using the generalized gradient approximation of the density-functional theory and ab initio pseudopotentials. Using our structural and electronic results, the phonon spectrum, phonon linewidths, and electron-phonon coupling parameter have been calculated by employing a linear-response approach based on density-functional theory. We have observed a softening behavior of the lowest acoustic phonon branch along the $X\text{\ensuremath{-}}R$ symmetry direction. The electron-phonon coupling parameter is found to be 0.80.

Ab initio investigations of the phonon anomaly and superconductivity in fcc La

We have employed the ab initio plane wave pseudopotential method within a generalized gradient approximation of the density functional theory and a linear response approach to investigate the phonon anomaly and superconductivity in fcc La. Our results confirm the presence of the experimentally observed softening behavior of the transverse acoustic branch along the [111] direction for both zero pressure. This behavior is found to be present even at a pressure of 50 kbar. With a reasonable choice of 0.1 for the Coulomb pseudopotential μ∗, our estimate of the superconducting critical temperature of 6.44 K at zero pressure is in good agreement with the experimental value of 6.0 K. Our work further suggests that at 50 kbar the critical temperature will increase to 9.26 K.