The structure of IR divergences in celestial gluon amplitudes

The all-loop resummation of SU(N) gauge theory amplitudes is known to factorize into an IR-divergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a process-dependent quantity.We prove that this factorization persists for the corresponding celestial amplitudes. Moreover, the soft/collinear factor becomes a scalar correlator of the product of renormalized Wilson lines defined in terms of celestial data. Their effect on the hard amplitude is a shift in the scaling dimensions by an infinite amount, proportional to the cusp anomalous dimension. This leads us to conclude that the celestial-IR-safe gluon amplitude corresponds to a expectation value of operators dressed with Wilson line primaries. These results hold for finite N.In the large N limit, we show that the soft/collinear correlator can be described in terms of vertex operators in a Coulomb gas of colored scalar primaries with nearest neighbor interactions. In the particular cases of four and five gluons in planar $$ \mathcal{N} $$ N = 4 SYM theory, where the hard factor is known to exponentiate, we establish that the Mellin transform converges in the UV thanks to the fact that the cusp anomalous dimension is a positive quantity. In other words, the very existence of the full celestial amplitude is owed to the positivity of the cusp anomalous dimension.

Scale-free percolation in continuous space: quenched degree and clustering coefficient

Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuous-space version of scale-free percolation introduced in [14]. This is an undirected inhomogeneous random graph whose vertices are given by a Poisson point process in $\mathbb{R}^d$. Each vertex is equipped with a random weight, and the probability that two vertices are connected by an edge depends on their weights and on their distance. Under suitable conditions on the parameters of the model, we show that, for almost all realizations of the point process, the degree distributions of all the nodes of the graph follow a power law with the same tail at infinity. We also show that the averaged clustering coefficient of the graph is self-averaging. In particular, it is almost surely equal to the annealed clustering coefficient of one point, which is a strictly positive quantity.

Strength Characteristics of Recycled Aggregate Concrete by Ann

Development Practices is the Key to the Next Generation for having a progressively imperative and better work concerning Engineering Perspectives. Various sorts of research have been done previously and are being done in the present on building materials extensively used for Constructions. With the ultimate objective to shield the future and proportion the trademark resources, various examinations have been coordinated over some vague period on reactions and wastes leaving undertakings, fantastically warm power plants, to facilitate the use of wastes thusly reusing them and screen the normal resources which are comprehensively using being developed practices[1-5]. A positive quantity of mortar and cement paste from the authentic concrete stays connected to stone particles in the recycled combination when demolished concrete is crushed [11,15]. The adhered mortar presence at the surface of an overwhelmed concrete mixture usually degrades the great of the recycled mixture and therefore the fresh and hardened residences of concrete crafted from it compared to herbal aggregates. As per the investigation, the compressive strength of cement was anticipated utilizing artificial neural system models Firstly, to prepare the ANN model to anticipate the compressive strength of RAC, The predicted compressive strength was contrasted and the exploratory compressive strength and correlation are carried out[12-14]. Training and testing of the ANN model are done utilizing compressive strength results of RAC collected from literature, the practical values obtained are used to validate the ANN model. Then the percentage error between the experiment and predicted compressive strength is obtained

How the node’s vital and tie strength effect rumor spreading on social network

The spread of rumors on complex networks has attracted wide attention in the field of management. In this paper, the generalized rumor spreading model is modified to take into account the vital of the spreader and the tie strength for the pairwise contacts between nodes in complex networks at degree-dependent spreading rate. Concretely, we introduce the infectivity exponent [Formula: see text], and the degree influenced real exponent [Formula: see text] into the analytical rumor spreading model. Rumor infectivity, [Formula: see text], where [Formula: see text], defines that each spreader node may contact [Formula: see text] neighbors within one time step. The tie strength between two nodes with degrees [Formula: see text] and [Formula: see text] are measured by [Formula: see text], [Formula: see text] is the degree influenced real exponent which depends on the type of complex networks and [Formula: see text] is a positive quantity. We use a tuning parameter [Formula: see text] to combine both the effect of the vital nodes and the strength of connectivity between nodes. We use analytical and numerical solutions to examine the threshold behavior and dynamics of the model on several models of social network. It was found that the infectivity exponent [Formula: see text], the degree influenced real exponent [Formula: see text] and tuning parameter [Formula: see text] affect the rumor threshold, one can adjust the parameters to control the rumor threshold which is absent for the standard rumor spreading model.

Entropy and Geometric Objects

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object—a black hole—having a mass, a momentum, a temperature, a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast, the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes like an area A—which is the area of the event horizon of the black hole-, a length LP—which is the Planck length - and a factor ¼. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function, with this extension drawing on the phase-field concept of diffuse interfaces. Entropy enters into the local, statistical description of contrast respectively gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formula eventually is derived for a geometric sphere based on mere geometric-statistic considerations.

On the Dissolution of WC in WC-Co Alloys

Transitional metals, such as V, Nb, Mo and Ti, were used to control the growth of ultrafine WC particles. Based on a study of the microstructures these metals were effective in inhibiting the growth of WC. The interaction parameter measured between those metals and W in a Co melt was a positive quantity. This indicates that the presence of V, Nb, Mo or Ti would tend to reduce the solubility of W in a Co melt, thus inhibiting the dissolution and growth of WC.

COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE-GAS MODEL WITH FOURTH-RANK INTERACTIONS

We have considered a classical lattice-gas model, consisting of a three-dimensional simple-cubic lattice, whose sites host three-component unit vectors; pairs of nearestneighboring sites interact via the nematogenic potential [Formula: see text] here P4(τ) denotes the fourth Legendre polynomial, nuj=0,1 are occupation numbers, uj are unit vectors (classical spins), and ∊ is a positive quantity setting the energy and temperature scales (i.e. T* =k B T / ∊). The total Hamiltonian is given by [Formula: see text] where ∑{j < k} denotes sum over all distinct nearest-neighboring pairs of lattice sites. The saturated-lattice version of this model defines a nematogenic lattice model, already studied in the literature, and found to possess a transition to an orientationally ordered phase at low temperature; moreover, according to available rigorous results, there exists a μ0<0, such that, for all μ>μ0, the system supports an ordering transition at a finite, μ-dependent, temperature. We present here a detailed study of the case μ=0, and characterize it by means of Monte Carlo simulation, Mean Field and Two Site Cluster treatments; the latter significantly improves the agreement with simulation results.

COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE-GAS MODEL BASED ON THE NEHRING–SAUPE INTERACTION POTENTIAL

Over 25 years ago, Nehring and Saupe proposed an anisotropic nematogenic lattice model, whose restriction to nearest neighbours has the form [Formula: see text] Here the three-component vectors xj∈Z3define centre-of-mass coordinates of the particles, and ukare three-component unit vectors defining their orientations; ∊ is a positive quantity setting energy and temperature scales (i.e. T*=kBT/∊); this model is seen to be the anisotropic counterpart to the generic Lebwohl–Lasher lattice model. It has often been used for approximate calculations of elastic properties, and has recently been studied by simulation [Hashim and Romano, Int. J. Mod. Phys.B13, 3879 (1999)]. We study here its lattice-gas extension, whose Hamiltonian is defined by [Formula: see text] where νk=0,1 denote occupation numbers, ∑{j<k}denotes sum over all distinct nearest-neighbouring pairs of lattice sites, and μ is the chemical potential. The model has been addressed by Monte Carlo simulation; comparisons are reported with Mean Field theory as well as with the Lebwohl–Lasher counterpart.

MEAN FIELD, TWO-SITE CLUSTER, AND COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE-GAS MODEL

We have considered a classical lattice-gas model, consisting of a three-dimensional simple-cubic lattice, whose sites host three-component unit vectors; pairs of nearest-neighbouring sites interact via the nematogenic potential [Formula: see text] here P2(τ) denotes the second Legendre polynomial, νj = 0, 1 are occupation numbers, uj are unit vectors (classical spins), and ∊ is a positive quantity setting energy and temperature scales (i.e. T* = k B T/∊); the total Hamiltonian is given by [Formula: see text] where ∑{j<k} denotes sum over all distinct nearest-neighbouring pairs of lattice sites. The saturated-lattice version of this model defines the extensively studied Lebwohl–Lasher model, possessing a transition to an orientationally ordered phase at low temperature; according to available rigorous results, there exists a μ0 < 0, such that, for all μ > μ0, the system supports an ordering transition at a finite, μ-dependent, temperature. Continuing along the lines of our previous communication [S. Romano, Int. J. Mod. Phys.B14, 1195 (2000)], we present here a detailed study of the case μ = 0, using Monte Carlo simulation, Mean Field and Two Site Cluster treatments; the latter significantly improves the agreement with simulation results.

A Biphasic, Anisotropic Model of the Aortic Wall

A biphasic, anisotropic elastic model of the aortic wall is developed and compared to literature values of experimental measurements of vessel wall radii, thickness, and hydraulic conductivity as a function of intraluminal pressure. The model gives good predictions using a constant wall modulus for pressures less than 60 mmHg, but requires a strain-dependent modulus for pressures greater than this. In both bovine and rabbit aorta, the tangential modulus is found to be approximately 20 times greater than the radial modulus. These moduli lead to predictions that, when perfused in a cylindrical geometry, the aortic volume and its specific hydraulic conductivity are relatively independent of perfusion pressure, in agreement with experimental measurements. M, the parameter that relates specific hydraulic conductivity to tissue dilation, is found to be a positive quantity correcting a previous error in the literature.