Palestinian Conference on Modern Trends in Mathematics and Physics II

Multiphysics scientific and engineering applications have added a new dimension to the challenges of computational complexities associated with geometry, mesh, and field manipulation tasks. While many research issues still remain in meshing methods for single-physics applications, multiphysics simulation adds additional complications that arise from the need to incorporate requirements from many, possibly tightly-coupled phenomena into the meshing process. Unfortunately, requirements for different equations systems may be orthogonal, necessitating the use of different meshes for each physics model and the need for accurate transfer of data between these meshes. The advent of supercomputing creates new opportunities for the representation of the entire fully-integrated designs via meshing at an unprecedented fidelity, particularly as computer architectures move toward the petascale/exascale.The premise of this talk is to present an overview of the challenges in meshing, geometry, and intermesh data transfer for multiphysics simulation and presents methodologies of tackling some of the issues that arise. In addition, we will present ongoing research in the development of adaptive mesh refinement tailored to application areas and highlight its use in several different simulation fields; e.g., climate modeling, astrophysics simulation, Neutron Science and reactor modeling, and materials science. The adaptive meshing approach and its underlying methods are attractive to many application areas when solving three-dimensional, multi-physics, multi-scale, and time-dependent problems.

The interactions between operator theory and complex analysis of one variable are now well known but are still an active _eld of research. The theory of truncated Toeplitz operators is a nice illustration of these interactions. In this project we will study the paper of Donald Sarason titled by Algebraic Properties of Truncated Toeplitz Operators.

The operators of the paper's title are compression of multiplication operators to proper invariant subspace of the bakward shift operator on H2. The paper inspired much subsequent work because of the questions are raised.

We will investigate both autonomous and non autonomous periodic competition models. Our main focus is to study invariant stable, unstable, and center manifolds using analytical and numerical methods. In addition, bifurcation analysis will be presented. Finally some open problems and conjectures will be discussed.

There is evidence that every galaxy contains at least a central super massive black hole (mass range 10^6-10^8 solar masses).The mass of the black hole is estimated to be about 1/1000 the mass of its host galaxy. Further, the best studied cases show a correlation between the mass of the black hole and the amplitude of the potential depth of the galaxy.

I will explore physical mechanisms for this intriguing correlation and its implication on the effect of black holes on shaping the properties of galaxies.

This paper is about the relation between the closeness centrality of the first infected node in the network and each of the total infection time that needs to infect all nodes in that network ,the infection rate for spreading epidemics in that network ,which measures the fraction of nodes those infected per unit time and the infection spreading power of that node,that masures the power for each node to spread the epidemic to other uninfected nodes in that network .
In this paper I deal with two types of networks , unweighted networks and weighted networks and studied that relation in those two types . The importance of this work is when we find the closeness centrality and the infection spreading power of any node that help us understand which weakness or advantages this node has for maintenance or blocking dangers at the right time .
In this work I made some development in the SI model for the epidemic network in which most of authors consider the infection rate in that model assumed and constant. In this work I found that this infection rate is not constant but it depends on the closeness centrality of the first infected node in the network ,hence I suggested to replace the the infection rate in the SI model by the closeness centrality of the first infected node in the network . The obtained results from this work show that each of the total infection time, the infection rate and the infection spreading power when any node infected first in the network depend on the closeness centrality for that node .

A comparative study by FP-LAPW calculations based on DFT within LDA, PBE- GGA, PW-EV-GGA, and EV-GGA schemes is introduced for the structural and Electronic properties of ScN in RS, ZB, WZ, and CsCl phases. According to all Approximations used in this work, the RS phase is the stable ground state structure and makes a transition to CsCl phase at high transition pressure. While PBE-GGA and PW-EV-GGA's have provided better structural features such as equilibrium lattice constant and bulk modulus, only PW-EV-GGA and EV-GGA's have given the non zero, positive indirect energy gap for RS-ScN, comparable with the Experimental ones. The indirect band gap of RS-ScN may be enlarged to the measured value by PW-EV-GGA calculations corrected with an on-site and angular dependent Coulomb potential approximation (USIC). The PW-EV-GGA calculations have also provided good results for the structural and electronic features of ScN in ZB, WZ, and CsCl phases comparable with the theoretical data available in the literature.
PW-EV-GGA and PW-EV-GGA+USIC schemes are considered to be the best ones among the others when the structural and electronic features of ScN are aimed to be calculated by the same exchange - correlation energy approximations.

In the first part of the talk, and in order to set the stage, we will offer a multi-scale and averaging strategy to compute the solution of a singularly perturbed system when the fast dynamics oscillates rapidly; namely, the fast dynamics forms cycle-like limits which advance along with the slow dynamics. We describe the limit as a Young measure with values being supported on the limit cycles, averaging with respect to which induces the equation for the slow dynamics. In particular, computing the tube of the limit cycles establishes a good approximation for arbitrarily small singular parameters. We will demonstrate this by exhibiting concrete numerical examples.
In the second part of the talk we will examine singularly perturbed systems which may not possess a natural split into fast and slow state variables. Once again, our approach depicts the limit behavior as a Young measure with values being invariant measure of the fast contribution to the flow. These invariant measures are drifted by the slow contribution to the value. We keep track of this drift via slowly evolving observables. Averaging equations for the latter lead to computation of characteristic features of the motion and the location the invariant measures.
To demonstrate our ideas computationally, we will present some numerical experiments involving a system derived from a spatial discretization of a Korteweg-de Vries-Burgers type equation, with fast dispersion and slow diffusion.
This is a joint work with Z. Artstein, W. Gear, I. Kevrekidis, J. Linshiz and M. Slemrod

The Schrödinger equation for the confined H-atom in N dimensional spherical cavity has been solved. It has been shown that the wave functions are dimension-dependent and having the same form as those of the free hydrogen atom in N- dimensions.The ground state energies for the confined hydrogen atom in N dimensional impenetrable spherical cavity have been computed.The obtained results show their dependence on the size of the cavity and the space dimension N.

The pressure exerted on the wall of the cavity due to enclosing the H-atom inside a cavity of radius S was discussed.

We found that the pressure depends on N and S, and for a given N, the pressure increases with decreasing the radius of the cavity up to a maximum value Pmax and then starts to decrease. The value of this Pmax increases with increasing N, and the value of the radius of the cavity at which the pressure is maximum increases as N increases also.

Production and regulation of erythrocytes (red blood cells) is performed through complex processes. Cells are produced in the bone marrow (and the spleen, in mice), where hematopoietic stem cells, that have abilities of self-renewal and differentiation in all blood cell types, allow the appearance of erythroid cells. Throughout successive diviffsions, erythroid progenitors (immature red cells) acquire maturity (via cell markers) to ultimately become mature red blood cells (erythrocytes) that enter the bloodstream in order to carry oxygen to organs and tissues.
This continuous production of erythroid cells is permanently controlled in order to adapt very quickly to changes in or needs of the organism. One of the main feedback controls, discovered in the early 1990's by Koury and Bondurant [3] deals with cell death. Erythroid progenitors die by apoptosis, a programmed cell death (contrary to necrosis). Koury and Bondurant showed that, during an anemia (lack of red blood cells), a growth factor named erythropoietin (Epo) was released by the kidneys and inhibited progenitor apoptosis, allowing a fast production of numerous erythrocytes to get a correct level of red blood cells in blood.
Others controls occur at early stages of erythropoiesis, for instance differentiation of hematopoietic stem cells in cells committed to the red blood cell lineage is partly controlled by Epo. In the presence of Epo, hematopoietic stem cells will preferentially differentiate in red blood cells rather than in white blood cells or platelets.

The talk offers an overview about recent developments in the the field of Molecular Electronics. The focus will be on correlation effects introduced by the Coulomb interaction that the charge carriers feel when they flow through the molecule. Specifially, we will describe and discuss a scanning tunneling microscopy (STM) experiment [1] performed with an H2-phtalocyanine molecule (H2Pc). The measurement shows that the current-voltage curve is sensitive to the mutual alignment of the magnetization direction (paralell vs anti-parallel) of tip and substrate. The surprising aspect of the measurement is that in the absense of the molecule the magnetization effect is 5% only while in its presence we have 50% -- even though H2Pc is not magnetic. A theoretical analysis based on electronic structure calculations gives a quantitative explanation for this effect. At the end of the talk an outlook on other even more subtle magnetic correlation phenomena will be given [2].

Charge state distributions in violent ion-atom collisions have been investigated using a novel combination of experimental techniques that is termed Coincident Rutherford Backscattering Spectrometry (CRBS). The CRBS combines the traditional Rutherford backscattering spectrometry (RBS) with the time-of flight (TOF) coincidence and position-imaging techniques, in order to simultaneously determine the final charge states of both backscattered and recoil ions under single collision conditions. The use of coincidence technique can greatly enhance the information gained from the traditional RBS, and the novel CRBS measurements may shed light on the microscopic phenomena that dictate specific excitation processes, which, in turn, may lead to a better understanding of the macroscopic phenomena of energy loss and charge state evolution of ions traversing gaseous targets. To the best of our knowledge, this is the first attempt to perform such CRBS measurements.

The standard contact structure of has a vector-field defining a Hopf fibration in its kernel. Legendre transform w.r.t can be performed. Symmetric Hamiltonian problems are thereby transformed into their Lagrangian counterparts. It was believed that the existence of such a was special to this framework. This belief turns out to be wrong. V. Martino has produced a vector-field in the kernel of the first contact form by J.Gonzalo and F.Varela such that is also a contact form with the same orientation than α. This provides a new textbook example in Contact Form Geometry. We will describe in our talk the first contact form of J.Gonzalo and F.Varela and the vector-field in its kernel by V.Martino; we will study the related dynamics and the related Reeb vector-fields periodic orbit problems at the light of the homology for contact forms/structures that we have defined in our work.

Atomic force microscopy (AFM) is used to image biological samples with sub-nanometre resolution, and measure inter-molecular forces with picoNewton sensitivity. The tip, functionalized with a molecular probe, maps the epitope and allows bond energies to be measured. In mucins terminal sugars of oligosaccharide chains are often binding sites for bacteria, viruses and cells of the immune system. We used AFM to map the distribution of sialic acids (Neu5Ac) in isolated ocular mucins and mucus gels.
Tips were functionalised with the lectins Maackia amurensis (MAA) and Sambucus nigra (SNA). Spatially-correlated topographic and force-spectroscopy data were obtained in HEPES buffer. The localization, number, rupture forces and distances, and koff rates were calculated for all recognition events. Median rupture forces were conserved, irrespective of sample origin, and were 172 pN ± 4 pN for MAA- α-2, 3 Neu5Ac and 121 pN ± 8 pN for SNA- α-2, 6 Neu5Ac bonds, with koff rates of 156.6s-1 and 148.7 s-1, respectively. Blocking sugars injected in situ caused a 61% decrease in the frequency of interactions: washing reversed this effect. Force volume maps show 55% more α-2, 6 than α-2, 3-Neu5Ac in ocular impressions. MAA interactions occurred in larger clusters than SNA on single molecules, and the converse in gels. The observed clustering of sialic acids is expected when probing a highly glycosylated region of the mucin molecule. Not all α-2, 3 Neu5Ac are available to the probing lectin when mucins are part of a gel, as reflected in the smaller cluster size.
To conduct CRBS experiments, a special experimental setup has been designed, fabricated, and installed at the end-station of the RBS-beamline at the University of Jordan Van de Graaff accelerator (JUVAC). Different inert gases can be used as targets, and energetic ions of different charge states and energies as projectiles.

The effect of infrared laser of wavelength (λ = 1064nm), pulse energy of 40 mJ/pulse at a repetition rate of 10 Hz, on the activation energy of CR-39 solid state nuclear track detector has been investigated. Fifteen detectors were divided into three sets of equal numbers. The first set (post-exposed) was first exposed to alpha radiation with close contact to the 241Am source and then treated in air with laser at energy intensity 8 J/cm2. For the second set (pre-exposed), the process was reversed (laser + alpha) under the same conditions. The third set (unexposed to laser beam) was irradiated in close contact with the same alpha source (241Am). The activation energy of track etch (EV) for post-exposed, pre-exposed and unexposed was found equal to 0.887, 0.914 and 0.671 eV, respectively. The respective activation energies of bulk etch (EB) for post-exposed, pre-exposed and unexposed was found equal to 0.984, 0.912 and 0.926 eV.
From these measurements, it is concluded that the laser exposure led to the hardening of the material of the detector as evidenced from the values of activation energies for both bulk and track etch.

This study reports the association of noise pollution level with blood pressure (systolic and diastolic) and heart pulse rate in schools’ children. The test sample schools consist of six different schools chosen randomly in Jenin city. The measured sound pressure levels (SPL) in all tested schools were found to be above the standard international acceptable levels. Strong positive correlation (person correlation coefficient) was found between sound pressure levels in the sample schools from one side and blood pressures (R=0.285 for both systolic and diastolic) and heart pulse rate (R=0.273) from the other side. The average change rate of systolic and dyastolic blood pressures were found to be about 5 mm-Hg and 2.7 mm-Hg for every 75dB/hr change in SPL values, respectively. Also, the average rate of change of heart pulse rate was found to be about 5beats/min which reflects the strong correlation between changes of systolic blood pressure and heart pulse rate.

The structure of the electrical double layer (EDL) of a spherical macroion is studied by Monte Carlo simulation. Through the simulation two models have been used: uniform charge distribution (continuous) and discrete model. In the uniform model the total charge of -60 e is considered to be concentrated in the center of the spherical macroion, in the discrete one, elementary charges were movable and randomly distributed over the surface of the macroion. The radial profiles of local densities and electric potential in EDL, as well as the degree of counterion binding by the macroion, are calculated. It is concluded that the character of charge distribution affects the EDL structure near the macroion, whereas its effect is much weaker at larger distances.

Until very recently, many authors start using the so called post hoc power (also called a posteriori power, retrospective power, observed power or achieved power) in response to the demand of some scientific journals and editors especially when the outcome of the test is not significant or slightly significant. It is suggested as an estimator of the prospective power (also called a priori power or true power). This paper is raised at the time when misunderstandings and misconceptions abounded concerning retrospective power; it has been noticed that some authors disagree to calculate the post hoc power in the sense that it is unhelpful in the presence of the crude p-value and some others advocate the use of post hoc power in the sense that it has another interpretation than what we have from the crude p-value. This study tries to discover the nature of this concept, to summarize what is available in the literature and to dispel some confusion concerning this concept. Power function with new look within permutation approach (post hoc conditional power) is developed. Convergence of empirical post hoc conditional power to the empirical conditional power is investigated as well as the connection between them is studied. Real data application from the perspective of industry and simulation studies are considered.

In 1960 Overhauser [1] suggested that the ground state of nuclear matter may not be described by plane wave orbitals corresponding to a uniform density fluid phase but rather by orbitals that produce a periodically varying density. Such Overhauser orbitals were shown [2] to give an energy lower than that obtained from plane waves, but only at low densities. Such periodic densities correspond to α particle-like clusters arranged on a lattice and thus correspond to a solid phase. These results were subsequently extended to finite temperature [3] and a triple point of nuclear matter was found at a temperature of about 1.1 MeV. Recent experimental analyses of moderate-temperature nuclear gases produced in heavy ion reactions reveal a large degree of α particle clustering at low densities [4]. The thermodynamic properties and equation of state of low density nuclear matter, including cluster formation, will be examined.

The passage of light through apertures much smaller than the wavelength of the light has proved to be a surprisingly subtle phenomenon. This talk describes how modern developments in nanofabrication, coherent light sources and numerical vector field simulations have led to the upending of early predictions from scalar diffraction theory and classical electrodynamics. Optical response of real materials to incident coherent radiation at petahertz frequencies leads to unexpected consequences for transmission (and extinction) of light through sub wavelength aperture arrays.