Determination of the source parameter in a heat equation with a non-local boundary condition

AbstractIn this article we consider the inverse problem of identifying a time dependent unknown coefficient in a parabolic problem subject to initial and non-local boundary conditions along with an overspecified condition defined at a specific point in the spatial domain. Due to the non-local boundary condition, the system of linear equations resulting from the backward Euler approximation have a coefficient matrix that is a quasi-tridiagonal matrix. We consider an efficient method for solving the linear system and the predictor–corrector method for calculating the solution and updating the estimate of the unknown coefficient. Two model problems are solved to demonstrate the performance of the methods

Quantum Hall Effect on the Flag Manifold F_2

The Landau problem on the flag manifold ${\bf F}_2 = SU(3)/U(1)\times U(1)$ is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) abelian connections. In quantizing the theory, we show that the wavefunctions, of a non-relativistic particle living on ${\bf F}_2$, are the SU(3) Wigner ${\cal D}$-functions satisfying two constraints. Using the ${\bf F}_2$ algebraic and geometrical structures, we derive the Landau Hamiltonian as well as its energy levels. The Lowest Landau level (LLL) wavefunctions coincide with the coherent states for the mixed SU(3) representations. We discuss the quantum Hall effect for a filling factor $\nu =1$. where the obtained particle density is constant and finite for a strong magnetic field. In this limit, we also show that the system behaves like an incompressible fluid. We study the semi-classical properties of the system confined in LLL. These will be used to discuss the edge excitations and construct the corresponding Wess-Zumino-Witten action.Comment: 23 pages, two sections and references added, misprints corrected, version to appear in IJMP

A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schr\"odinger cat states

A recursive approach to determine the Hilbert-Schmidt measure of pairwise quantum discord in a special class of symmetric states of $k$ qubits is presented. We especially focus on the reduced states of $k$ qubits obtained from a balanced superposition of symmetric $n$-qubit states (multiqubit Schr\"odinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots ,n-1)$. Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the party grouping $(k-1)$ qubits is explicitly derived. This uses recursive relations between the Fano-Bloch correlation matrices associated with subsystems comprising $k$, $k-1$, $\cdots$ and $2$ particles. A detailed analysis is given for two, three and four qubit systems. In the second scheme, the subsystem comprising the $(k-1)$ qubits is mapped into a system of two logical qubits. We show that these two bipartition schemes are equivalents in evaluating the pairwise correlation in multi-qubits systems. The explicit expressions of classical states presenting zero discord are derived.Comment: 26 page

On the solution of non linear systems.

SIGLEAvailable from British Library Document Supply Centre- DSC:D37560/81 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Incommensurate magnetic ordering in Cu2Te2O5X2Cu_2 Te_2 O_5 X_2 (X=Cl,Br) studied by neutron diffraction

We present the results of the first neutron powder and single crystal diffraction studies of the coupled spin tetrahedra systems {\CuTeX} (X=Cl, Br). Incommensurate antiferromagnetic order with the propagation vectors {\bf{k}_{Cl}}\approx[0.150,0.422,\half], {\bf{k}_{Br}}\approx[0.158,0.354,\half] sets in below $T_{N}$=18 K for X=Cl and 11 K for X=Br. No simple collinear antiferromagnetic or ferromagnetic arrangements of moments within Cu${}^{2+}$ tetrahedra fit these observations. Fitting the diffraction data to more complex but physically reasonable models with multiple helices leads to a moment of 0.67(1)$\mu_B$/Cu${}^{2+}$ at 1.5 K for the Cl-compound. The reason for such a complex ground state may be geometrical frustration of the spins due to the intra- and inter-tetrahedral couplings having similar strengths. The magnetic moment in the Br- compound, calculated assuming it has the same magnetic structure as the Cl compound, is only 0.51(5)$\mu_B$/Cu${}^{2+}$ at 1.5 K. In neither compound has any evidence for a structural transition accompanying the magnetic ordering been found

Scaling theory of DNA confined in nanochannels and nanoslits

A scaling analysis is presented of the statistics of long DNA confined in nanochannels and nanoslits. It is argued that there are several regimes in between the de Gennes and Odijk limits introduced long ago. The DNA chain folds back on itself giving rise to a global persistence length which may be very large owing to entropic deflection. Moreover, there is an orientational excluded-volume effect between the DNA segments imposed solely by the nanoconfinement. These two effects cause the chain statistics to be intricate leading to nontrivial power laws for the chain extension in the intermediate regimes. It is stressed that DNA confinement within nanochannels differs from that in nanoslits because the respective orientational excluded-volume effects are not the same.Comment: 5 pages, 1 figure Several corrections, some minor changes in the text and replacement of one referenc