Number of Spin II States of Identical Particles

In this paper we study the enumeration of number (denoted as ${D_I}$) of spin $I$ states for fermions in a single-$j$ shell and bosons with spin $l$. We show that $D_I$ can be enumerated by the reduction from SU$(n+1)$ to SO(3). New regularities of $D_I$ are discerned.Comment: 3 pages, no figures. to be publishe

Companion problems in quasispin and isospin

We note that the same mathematical results apply to problems involving quasispin and isospin, but the problems per se are different. In the quasispin case, one deals with a system of identical fermions (e.g. neutrons) and address the problem of how many seniority conserving interactions there are. In the isospin case, one deals with a system of both neutrons and protons and the problem in question is the number of neutron-proton pairs with a given total angular momentum. Other companion problems are also discussed.Comment: 12 pages, Latex; some additions in section II and a brief summary at the en

JJ-pairing interaction, number of states, and nine-jj sum rules of four identical particles

In this paper we study $J$-pairing Hamiltonian and find that the sum of eigenvalues of spin $I$ states equals sum of norm matrix elements within the pair basis for four identical particles such as four fermions in a single-$j$ shell or four bosons with spin $l$. We relate number of states to sum rules of nine-$j$ coefficients. We obtained sum rules for nine-$j$ coefficients $$and$$ summing over (1) even $J$ and $K$, (2) even $J$ and odd $K$, (3) odd $J$ and odd $K$, and (4) both even and odd $J,K$, where $j$ is a half integer and $l$ is an integer.Comment: 6 pages, no figure, updated version, to be published. Physical Review C, in pres

Seniority conservation and seniority violation in the g_{9/2} shell

The g_{9/2} shell of identical particles is the first one for which one can have seniority-mixing effects. We consider three interactions: a delta interaction that conserves seniority, a quadrupole-quadrupole (QQ) interaction that does not, and a third one consisting of two-body matrix elements taken from experiment (98Cd) that also leads to some seniority mixing. We deal with proton holes relative to a Z=50,N=50 core. One surprising result is that, for a four-particle system with total angular momentum I=4, there is one state with seniority v=4 that is an eigenstate of any two-body interaction--seniority conserving or not. The other two states are mixtures of v=2 and v=4 for the seniority-mixing interactions. The same thing holds true for I=6. Another point of interest is that the splittings E(I_{max})-E(I_{min}) are the same for three and five particles with a seniority conserving interaction (a well known result), but are equal and opposite for a QQ interaction. We also fit the spectra with a combination of the delta and QQ interactions. The Z=40,N=40 core plus g_{9/2} neutrons (Zr isotopes) is also considered, although it is recognized that the core is deformed.Comment: 19 pages, 9 figures; RevTeX4. We have corrected the SDI values in Table1 and Fig.1; in Sect.VII we have included an explanation of Fig.3 through triaxiality; we have added comments of Figs.10-12 in Sect.IX; we have removed Figs.7-

Number of states with fixed angular momentum for identical fermions and bosons

We present in this paper empirical formulas for the number of angular momentum I states for three and four identical fermions or bosons. In the cases with large I we prove that the number of states with the same ${\cal M}$ and n but different J is identical if $I \ge (n-2)J - {1/2} (n-1)(n-2)$ for fermions and $I \ge (n-2)J$ for bosons, and that the number of states is also identical for the same ${\cal M}$ but different n and J if ${\cal M} \le$min(n, 2J+1 - n) for fermions and for ${\cal M} \le$min(n, 2J) for bosons. Here ${\cal M} =I_{max}-I$, n is the particle number, and J refers to the angular momentum of a single-particle orbit for fermions, or the spin L carried by bosons.Comment: 9 pages, no figure

Nature-Inspired Interconnects for Self-Assembled Large-Scale Network-on-Chip Designs

Future nano-scale electronics built up from an Avogadro number of components needs efficient, highly scalable, and robust means of communication in order to be competitive with traditional silicon approaches. In recent years, the Networks-on-Chip (NoC) paradigm emerged as a promising solution to interconnect challenges in silicon-based electronics. Current NoC architectures are either highly regular or fully customized, both of which represent implausible assumptions for emerging bottom-up self-assembled molecular electronics that are generally assumed to have a high degree of irregularity and imperfection. Here, we pragmatically and experimentally investigate important design trade-offs and properties of an irregular, abstract, yet physically plausible 3D small-world interconnect fabric that is inspired by modern network-on-chip paradigms. We vary the framework's key parameters, such as the connectivity, the number of switch nodes, the distribution of long- versus short-range connections, and measure the network's relevant communication characteristics. We further explore the robustness against link failures and the ability and efficiency to solve a simple toy problem, the synchronization task. The results confirm that (1) computation in irregular assemblies is a promising and disruptive computing paradigm for self-assembled nano-scale electronics and (2) that 3D small-world interconnect fabrics with a power-law decaying distribution of shortcut lengths are physically plausible and have major advantages over local 2D and 3D regular topologies

Classical and Quantum-like approaches to Charged-Particle Fluids in a Quadrupole

A classical description of the dynamics of a dissipative charged-particle fluid in a quadrupole-like device is developed. It is shown that the set of the classical fluid equations contains the same information as a complex function satisfying a Schrodinger-like equation in which Planck's constant is replaced by the time-varying emittance, which is related to the time-varying temperature of the fluid. The squared modulus and the gradient of the phase of this complex function are proportional to the fluid density and to the current velocity, respectively. Within this framework, the dynamics of an electron bunch in a storage ring in the presence of radiation damping and quantum-excitation is recovered. Furthermore, both standard and generalized (including dissipation) coherent states that may be associated with the classical particle fluids are fully described in terms of the above formalism.Comment: LaTex, to appear in Physica Script

VLTI observations of the dust geometry around R Coronae Borealis stars

We are investigating the formation and evolution of dust around the hydrogen-deficient supergiants known as R Coronae Borealis (RCB) stars. We aim to determine the connection between the probable merger past of these stars and their current dust-production activities. We carried out high-angular resolution interferometric observations of three RCB stars, namely RY Sgr, V CrA, and V854 Cen with the mid-IR interferometer, MIDI on the VLTI, using two telescope pairs. The baselines ranged from 30 to 60 m, allowing us to probe the dusty environment at very small spatial scales (~ 50 mas or 400 stellar radii). The observations of the RCB star dust environments were interpreted using both geometrical models and one-dimensional radiative transfer codes. From our analysis we find that asymmetric circumstellar material is apparent in RY Sgr, may also exist in V CrA, and is possible for V854 Cen. Overall, we find that our observations are consistent with dust forming in clumps ejected randomly around the RCB star so that over time they create a spherically symmetric distribution of dust. However, we conclude that the determination of whether there is a preferred plane of dust ejection must wait until a time series of observations are obtained.Comment: Accepted for publication in MNRAS; 14 pages, 10 figures, 6 table

Screening families of patients with premature coronary heart disease to identify avoidable cardiovascular risk: a cross-sectional study of family members and a general population comparison group

<b>Background:</b> Primary prevention should be targeted at individuals with high global cardiovascular risk, but research is lacking on how best to identify such individuals in the general population. Family history is a good proxy measure of global risk and may provide an efficient mechanism for identifying high risk individuals. The aim was to test the feasibility of using patients with premature cardiovascular disease to recruit family members as a means of identifying and screening high-risk individuals. <b>Findings:</b> We recruited family members of 50 patients attending a cardiology clinic for premature coronary heart disease (CHD). We compared their cardiovascular risk with a general population control group, and determined their perception of their risk and current level of screening. 103 (36%) family members attended screening (27 siblings, 48 adult offspring and 28 partners). Five (5%) had prevalent CHD. A significantly higher percentage had an ASSIGN risk score >20% compared with the general population (13% versus 2%, p < 0.001). Only 37% of family members were aware they were at increased risk and only 50% had had their blood pressure and serum cholesterol level checked in the previous three years. <b>Conclusions:</b> Patients attending hospital for premature CHD provide a mechanism to contact family members and this can identify individuals with a high global risk who are not currently screened

Dirac operator on κ\kappa-Minkowski space bicovariant differential calculus and deformed U(1) gauge theory

Derivation of $\kappa$-Poincare bicovariant commutation relations between coordinates and 1-forms on $\kappa$-Minkowski space is given using Dirac operator and Allain Connes formula. The deformed U(1) gauge theory and appearance of an additional spin 0 gauge field is discussed