Structure of wake of a sharp-edged bluff body in a shallow channel flow

The flow field downstream of a bluff body in a typical open channel flow was explored by two-dimensional particle image velocimetry. Measurements are obtained in horizontal planes at the near-bed, mid-depth and near-surface locations downstream of the body up to a streamwise distance of 10D, where D is the width of the body. The dimensionless streamwise defect velocity profile of the wake flow matches well with the data of a previous investigation and does not reflect any dependency on the distance from the bed. However, the nature of development of the recirculation region is found to be different at the three vertical locations. The time-averaged streamline pattern indicates the existence of a unique nodal pattern close to the bed. The variation of the half-width is also found to be affected by the presence of the bed and the free surface. The bed friction arrests the transverse growth of the shear layer, and the free-surface helps to redistribute the turbulent kinetic energy in the streamwise and transverse directions. Swirling strength analysis is carried out to compare the behavior and statistics of the vortex population in the vertical direction. The prevailing magnitude of the swirling strength is found to be different at the three vertical locations. Bed friction assists to dissipate vorticity rapidly, and therefore reduces the probability of appearance of strong vortices close to the bed.     

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

In this paper, an adaptive synchronization scheme is proposed for a class of nonlinear systems. The design utilizes an adaptive observer, which is quite useful in establishing a transmitter–receiver kind of synchronization scheme. The proposed approach is based on contraction theory and provides a very simple way of establishing exponential convergence of observer states to actual system states. The class of systems addressed here has uncertain parameters, associated with the part of system dynamics that is a function of measurable output only. The explicit conditions for the stability of the observer are derived in terms of gain selection of the observer. Initially, the case without uncertainty is considered and then the results are extended to the case with uncertainty in parameters of the system. An application of the proposed approach is presented to synchronize the family of N chaotic systems which are coupled through the output variable only. The numerical results are presented for designing an adaptive observer for the chaotic Chua system to verify the efficacy of the proposed approach. Explicit bounds on observer gains are derived by exploiting the properties of the chaotic attractor exhibited by Chua’s system. Convergence of uncertain parameters is also analyzed for this case and numerical simulations depict the convergence of parameter estimates to their true value.     

A combinatorial formula for Macdonald polynomials

In this paper we use the combinatorics of alcove walks to give uniform combinatorial formulas for Macdonald polynomials for all Lie types. These formulas resemble the formulas of Haglund, Haiman and Loehr for Macdonald polynomials of type GLn. At q=0 these formulas specialize to the formula of Schwer for the Macdonald spherical function in terms of positively folded alcove walks and at q=t=0 these formulas specialize to the formula for the Weyl character in terms of the Littelmann path model (in the positively folded gallery form of Gaussent and Littelmann).     

On mock theta functions and weight-attached Frobenius partitions

The Ramanujan Journal - In this paper, we provide the combinatorial interpretations of many mock theta functions and some generalizations using Frobenius partitions with attached weights. We...     

Forward–Backward–Half Forward Dynamical Systems for Monotone Inclusion Problems with Application to v-GNE

Journal of Optimization Theory and Applications - In this paper, the first-order forward–backward–half forward dynamical systems associated with the inclusion problem consisting of...     

Hamming weight distributions of multi-twisted codes over finite fields

Designs, Codes and Cryptography - Let $${\mathbb {F}}_q$$ denote the finite field of order q,  and let $$n = m_1+m_2+\cdots +m_\ell ,$$ where $$m_1,m_2,\ldots ,m_\ell $$ are arbitrary...     

Strain field due to point defects in Ni dilute alloys

We report the results for strain field due to substitutional transition metal impurities in Ni. The Kanzaki lattice static method has been used to calculate the strain field, the effective ion-ion interaction potential due to Wills and Harrison is used to calculate dynamical matrix with first nearest neighbour and the impurity-induced force with second nearest neighbour. The results for 3d, 4d and 5d impurities (Fe, Co, Cu, Nb, Mo, Pd, Pt and Au) are compared with the experimental data, which are found in agreement.     

EPR of Cu2+-doped tris-sarcosine calcium chloride

The EPR study of the Cu²⁺-doped tris-sarcosine calcium chloride (TSCC) at room temperature is reported. Two magnetically inequivalent sites for Cu²⁺ were observed. The rhombic spin Hamiltonian parameters are determined by fitting the EPR spectra for two centres: Cu²⁺(I) g₁ = 2.0276, g₂ = 2.0517, g₃ = 2.4019, A₁ = 82, A₂ = 128, A₃ = 152 [G] and Cu²⁺(II) g₁ = 2.0231, g₂ = 2.0368, g₃ = 2.5294, A₁ = 76, A₂ = 92, A₃ = 156 [G]. The ground state wave function is also determined. The g-anisotropy is evaluated and compared with the experimental value. Further, the optical study of the crystal at room temperature is carried out and the nature of bonding in the complex is discussed.     

Spin-polarised DFT study of cobalt-doped gallium clusters

The structural, electronic and magnetic properties of small gallium clusters doped with Cobalt have been studied using spin-polarised density functional theory. The binding energy per atom, second-order differences of total energies and fragmentation energies of equilibrium geometries of the host Ga_n+1 and doped Ga_nCo (n = 1–12) clusters are computed. Doped clusters are found to be more stable than pure Ga clusters; Ga₃Co, Ga₅Co and Ga₈Co clusters are exceptionally stable. Doping with Co changes the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) gap, and also affects the magnetic moments of clusters.     

Coupled tapering/uptapering of soliton pairs in nonlinear media

Phenomenon of coupled tapering/uptapring of two mutually incoherent beams coaxially co-propagating in a nonlinear medium with small gain or loss has been investigated in this paper using standard parabolic equation approach (PEA) and the results are compared with the results obtained by Beam Propagation Method (BPM), i.e., by direct simulations of the underlying Nonlinear Schrödinger Equation (NLSE). The PEA results are shown to be in excellent agreement with the BPM results. It is seen that both beams of the pair induce uptapering in each other in presence of losses and tapering in presence of gain. When the medium offers gain to the first beam and losses to the other, both beams taper. When the medium offers gain/absorption to only one of the two beams, the beam undergoes self-tapering/self-uptapering and induces a taperd/uptaperd waveguide. The other beam (for which the medium is lossless) uptapers/tapers due to the taperd/uptaperd waveguide created by the first beam.