Numerical investigation of fluid structure interaction between unsteady flow and vibrating liner in a combustion chamber

Numerical investigations of fluid structure interaction between unsteady flow\ud and vibrating liner in a combustion chamber are undertaken. The computational study consist of two approaches. Firstly, a partioned procedure consists of coupling the LES code AVBP for combustion modelling with the FEM code CaluliX for structural dynamic analysis. The CFD code CFX together with the FEM Ansys package are then used.\ud Results of unsteady fluid structure interaction applied to combustion system are presented and compare well with experimental results

A Quantum Mechanical Model of Spherical Supermembranes

We present a quantum mechanical model of spherical supermembranes. Using superfields to represent the cartesian coordinates of the membrane, we are able to exactly determine its supersymmetric vacua. We find there are two classical vacua, one corresponding to an extended membrane and one corresponding to a point-like membrane. For the ${\mathcal N} = 2$ case, instanton effects then lift these vacua to massive states. For the ${\mathcal N} = 4$ case, there is no instanton tunneling, and the vacua remain massless. Similarities to spherical supermembranes as giant gravitons and in Matrix theory on pp-waves is discussed.Comment: 9 page

Field trialling of a pulse airtightness tester in a range of UK homes

A new low pressure ‘quasi-steady’ pulse technique for determining the airtightness of buildings has been developed further and compared with the standard blower-door technique for field-testing a range of typical UK homes. The reported low pressure air pulse unit (APU) has gone through several development stages related to optimizing the algorithm, pressure reference and system construction. The technique, which is compact, portable and easy to use, has been tested alongside the standard blower-door technique to measure the airtightness of a range of typical UK home types. Representative of the UK housing stock, the homes mostly have low levels of airtightness, resulting in poor energy performance, poor indoor air quality and poor thermal comfort. Some of these homes have been targeted for retrofitting and a quick, low cost and simple method for accurately determining their airtightness has clear advantages for correctly predicting the benefits of any improvements. A comparison between the results given by the two techniques is presented and the field trials indicate that the latest version of the pulse technique is reliable for determining building leakage at low pressure. Repeatability of multiple APU tests in the same house is found to be within +/-5% of the mean. A test where the leakage is increased by a known amount shows the APU is able to measure the change more accurately than the blower-door test. The APU also gives convenience in practical applications, due to being more compact and portable, plus it doesn’t need to penetrate the building envelope. The field trials demonstrate the pulse test has the potential to be a feasible alternative to the standard blower-door test

The effects of grain shape and frustration in a granular column near jamming

We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below it. The resulting four dynamical regimes (ballistic, logarithmic, activated and glassy) are characterised by means of the jamming time of zero-temperature dynamics, and of the statistics of attractors reached by the latter. Shape effects are most pronounced in the cases of strong and weak frustration, and essentially disappear around a mean-field point.Comment: 17 pages, 19 figure

On a graph related to permutability in finite groups

This paper has been published in Annali di Matematica Pura ed Applicata. Series IV, 189(4):567-570 (2010). Copyright 2010 by Springer-Verlag. The final publication is available at www.springerlink.com. http://link.springer.com/article/10.1007%2Fs10231-009-0124-7 http://dx.doi.org/10.1007/s10231-009-0124-7For a finite group G we define the graph $\Gamma(G)$ to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes $\{\mathcal {A}, \mathcal {B}\}$ are joined by an edge if for some $\{A \in \mathcal {A},\, B \in \mathcal {B}\, A\}$ and B permute. We characterise those groups G for which $\Gamma(G)$ is complete.This paper has been suported by the research grants MTM2007-68010-C03-02 from MEC (Spain) and FEDER (European Union) and GV/2007/243 from Generalitat (Valencian Community).http://dx.doi.org/10.1007/s10231-009-0124-7Ballester Bolinches, A.; Cossey, J.; Esteban Romero, R. (2010). On a graph related to permutability in finite groups. Annali di Matematica Pura ed Applicata. 4(189). doi:10.1007/s10231-009-0124-74189Abe S., Iiyori N.: A generalization of prime graphs of finite groups. Hokkaido Math. J. 29(2), 391–407 (2000)Agrawal R.K.: Finite groups whose subnormal subgroups permute with all Sylow subgroups. Proc. Am. Math. Soc. 47(1), 77–83 (1975)Alejandre M.J., Ballester-Bolinches A., Pedraza-Aguilera M.C.: Finite soluble groups with permutable subnormal subgroups. J. Algebra 240(2), 705–722 (2001)Ballester-Bolinches A., Esteban-Romero R.: Sylow permutable subnormal subgroups of finite groups. J. Algebra 251(2), 727–738 (2002)Cooper C.D.H.: Power automorphisms of a group. Math. Z. 107, 335–356 (1968)Herzog M., Longobardi P., Maj M.: On a commuting graph on conjugacy classes of groups. Commun. Algebra 37(10), 3369–3387 (2009)Huppert B.: Endliche Gruppen I, vol. 134 of Grund. Math. Wiss. Springer, Berlin (1967)Longobardi P.: Gruppi finite a fattoriali modulari. Note Math. II, 73–100 (1982)Neumann B.: A problem of Paul Erdős on groups. J. Austral. Math. Soc. Ser. A 21, 467–472 (1976)Ore O.: Contributions to the theory of groups of finite order. Duke Math. J. 5, 431–460 (1939)Schmidt R.: Subgroup lattices of groups. De Gruyter Expositions in Mathematics, vol. 14. Walter de Gruyter, Berlin (1994)Zacher G.: I gruppi risolubli finiti in cui i sottogruppi di composizione coincidono con i sottogrupi quasi-normali. Atti Accad. Naz. Lincei Rend. cl. Sci. Fis. Mat. Natur. 37(8), 150–154 (1964

On the magnetism of Ln{2/3}Cu{3}Ti{4}O{12} (Ln = lanthanide)

The magnetic and thermodynamic properties of the complete Ln$_{2/3}$Cu$_3$Ti$_4$O$_{12}$ series were investigated. Here $Ln$ stands for the lanthanides La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb. %Most of the compounds were prepared as single phase polycrystalline powder %without any traces of impurities. Marginal amounts of %impurities $(< 2$ were detected $Ln=$ Gd, Er, and Tm. %Significant amounts of impurity phases were found for $Ln=$ Ce and Yb. All the samples investigated crystallize in the space group $Im\bar{3}$ with lattice constants that follow the lanthanide contraction. The lattice constant of the Ce compound reveals the presence of Ce$^{4+}$ leading to the composition Ce$_{1/2}$Cu$_3$Ti$_4$O$_{12}$. From magnetic susceptibility and electron-spin resonance experiments it can be concluded that the copper ions always carry a spin $S=1/2$ and order antiferromagnetically close to 25\,K. The Curie-Weiss temperatures can approximately be calculated assuming a two-sublattice model corresponding to the copper and lanthanide ions, respectively. It seems that the magnetic moments of the heavy rare earths are weakly coupled to the copper spins, while for the light lanthanides no such coupling was found. The $4f$ moments remain paramagnetic down to the lowest temperatures, with the exception of the Tm compound, which indicates enhanced Van-Vleck magnetism due to a non-magnetic singlet ground state of the crystal-field split $4f$ manifold. From specific-heat measurements we accurately determined the antiferromagnetic ordering temperature and obtained information on the crystal-field states of the rare-earth ions. The heat-capacity results also revealed the presence of a small fraction of Ce$^{3+}$ in a magnetic $4f^1$ state.Comment: 10 pages, 10 figure

Compton scattering beyond the impulse approximation

We treat the non-relativistic Compton scattering process in which an incoming photon scatters from an N-electron many-body state to yield an outgoing photon and a recoil electron, without invoking the commonly used frameworks of either the impulse approximation (IA) or the independent particle model (IPM). An expression for the associated triple differential scattering cross section is obtained in terms of Dyson orbitals, which give the overlap amplitudes between the N-electron initial state and the (N-1) electron singly ionized quantum states of the target. We show how in the high energy transfer regime, one can recover from our general formalism the standard IA based formula for the cross section which involves the ground state electron momentum density (EMD) of the initial state. Our formalism will permit the analysis and interpretation of electronic transitions in correlated electron systems via inelastic x-ray scattering (IXS) spectroscopy beyond the constraints of the IA and the IPM.Comment: 7 pages, 1 figur

Thermodynamics of Dipolar Chain Systems

The thermodynamics of a quantum system of layers containing perpendicularly oriented dipolar molecules is studied within an oscillator approximation for both bosonic and fermionic species. The system is assumed to be built from chains with one molecule in each layer. We consider the effects of the intralayer repulsion and quantum statistical requirements in systems with more than one chain. Specifically, we consider the case of two chains and solve the problem analytically within the harmonic Hamiltonian approach which is accurate for large dipole moments. The case of three chains is calculated numerically. Our findings indicate that thermodynamic observables, such as the heat capacity, can be used to probe the signatures of the intralayer interaction between chains. This should be relevant for near future experiments on polar molecules with strong dipole moments.Comment: 15 pages, 5 figures, final versio