Spectral properties and stability of perturbed Cartesian product

Let \({\mathcal {A}}\) and \({\mathcal {B}}\) be commutative Banach algebras, and let \(T:{\mathcal {B}} \rightarrow {\mathcal {A}}\) be an algebra homomorphism with \({\Vert T\Vert }\le 1\). Then T induces a Banach algebra product \(\times _T\) perturbing the coordinatewise product on the Cartesian product space \({\mathcal {A}} \times {\mathcal {B}}\). We show that the spectral properties like spectral extension property, unique uniform norm property, regularity, weak regularity as well as Ditkin’s condition are stable with respect to this product.     

Chebyshev model arithmetic for factorable functions

This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden.     

Finite element analysis and approximation of Burgers’‐Fisher equation

In this article, the authors present finite element analysis and approximation of Burgers’‐Fisher equation. Existence and uniqueness of weak solution is proved by Galerkin's finite element method for non‐smooth initial data. Next, a priori error estimates of semi‐discrete solution in norm, are derived and the convergence of semi‐discrete solution is established. Then, fully discretization of the problem is done with the help of Euler's backward method. The nonlinearity is removed by lagging it to previous known level. The scheme is found to be convergent. Positivity of fully discrete solution is discussed, and bounds on time step are discovered for which the solution preserves its positivity. Finally, numerical experiments are performed on some examples to demonstrate the effectiveness of the scheme. The proposed scheme found to be fast, easy and accurate.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1652–1677, 2017     

Optimal solenoidal interpolation of turbulent vector fields: application to PTV and super-resolution PIV

A new approach for the interpolation of a filtered turbulence velocity field given random point samples of unfiltered turbulence velocity data is described. In this optimal interpolation method, the best possible value of the interpolated filtered field is obtained as a stochastic estimate of a conditional average, which minimizes the mean square error between the interpolated filtered velocity field and the true filtered velocity field. Besides its origins in approximation theory, the optimal interpolation method also has other advantages over more commonly used ad hoc interpolation methods (like the adaptive Gaussian window). The optimal estimate of the filtered velocity field can be guaranteed to preserve the solenoidal nature of the filtered velocity field and also the underlying correlation structure of both the filtered and the unfiltered velocity fields. The a posteriori performance of the optimal interpolation method is evaluated using data obtained from high-resolution direct numerical simulation of isotropic turbulence. Our results show that for a given sample data density, there exists an optimal choice of the characteristic width of cut-off filter that gives the least possible relative mean square error between the true filtered velocity and the interpolated filtered velocity. The width of this optimal filter and the corresponding minimum relative error appear to decrease with increase in sample data density. Errors due to the optimal interpolation method are observed to be quite low for appropriate choices of the data density and the characteristic width of the filter. The optimal interpolation method is also seen to outperform the adaptive Gaussian window, in representing the interpolated field given the data at random sample locations. The overall a posteriori performance of the optimal interpolation method was found to be quite good and hence makes a potential candidate for use in interpolation of PTV and super-resolution PIV data.     

A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder

Forced convection heat transfer from an unconfined circular cylinder in the steady cross-flow regime has been studied using a finite volume method (FVM) implemented on a Cartesian grid system in the range as 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. The numerical results are used to develop simple correlations for Nusselt number as a function of the pertinent dimensionless variables. In addition to average Nusselt number, the effects of Re, Pr and thermal boundary conditions on the temperature field near the cylinder and on the local Nusselt number distributions have also been presented to provide further physical insights into the nature of the flow. The rate of heat transfer increases with an increase in the Reynolds and/or Prandtl numbers. The uniform heat flux condition always shows higher value of heat transfer coefficient than the constant wall temperature at the surface of the cylinder for the same Reynolds and Prandtl numbers. The maximum difference between the two values is around 15–20%.     

The Cancer Genetics Network: recruitment results and pilot studies

OBJECTIVE: The National Cancer Institute established the Cancer Genetics Network (CGN) to support collaborative investigations into the genetic basis of cancer susceptibility, explore mechanisms to integrate this new knowledge into medical practice, and identify ways of addressing the associated psychosocial, ethical, legal, and public health issues. SUBJECTS AND METHODS: The CGN has developed the complex infrastructure required to support the projects, including the establishment of guidelines and policies, uniform methods, standard questionnaires to be used by all of the centers, and a standard format for submission of data to the Informatics Center. Cancer patients and their family members have been invited to enroll and be included in a pool of potential study participants. The Information Technology Group is responsible for support of the design, implementation, and maintenance of the multicenter Network-wide research protocols. RESULTS: As of January 2004, the CGN contained data on 23,995 probands (participants) and 425,798 family members. As a resource for cancer genetic studies, the CGN has a large number of probands and first-degree relatives with and without cancer and with multiple ethnicities. Different study designs can be used including case-control, case-case, and family studies. CONCLUSIONS: The unique resources of the CGN are available for studies on cancer genetic susceptibility, translational research, and behavioral research. The CGN is now at a point where approved collaborators may have access to enrolled patients and their families for special studies, as well as to the clinical, environmental and family cancer history data banked in the Informatics Center.     

Dynamic shearing resistance of molten metal films under high pressures and extremely high shearing rates

In the present study plate-impact pressureshear experiments have been conducted to study the dynamic shearing resistance of molten metal films at shearing rates of approximately 10⁷ s⁻¹. These molten films are generated by pressure-shear impact of relatively low melt-point metals such as 7075-T6 Al alloy with high hardness and high flow-strength tool-steel plates. By employing high impact speeds and relatively smooth impacting surfaces, normal interfacial pressures ranging from 1–3 GPa and slip speeds of over 100 m/s are generated during the pressure-shear loading. The resulting friction stress (∼100 to 400 MPa) combined with the high slip speeds generate conditions conductive to interfacial temperatures approaching the fully melt temperature regime of the lower melt-point metal (7075-T6 aluminum alloy) comprising the tribo-pair. During pressure-shear loading, laser interferometry is employed to measure normal and transverse motion at the rear surface of the target plate. The normal component of the particle velocity provides the interfacial normal traction while the transverse component provides the shearing resistance of the interface as it passes through melt. In order to extract the critical interfacial parameters, such as the interfacial slip-speed and interfacial temperatures, a Lagrangian finiteelement code is developed. The computational procedure accounts for dynamic effects, heat conduction, contact with friction, and full thermo-mechanical coupling. At temperatures below melt the flyer and target materials are described as an isotropic thermally softening elastic-viscoplastic solid. For material elements with temperatures in excess of the melt point, a purely Newtonian fluid constitutive model is employed. The results of this hybrid experimental-computational study provide insights into the dynamic shearing resistance of molten metal films at high pressures and extremely high shearing rates.     

Direct electrochemistry of glucose oxidase and sensing glucose using a screen-printed carbon electrode modified with graphite nanosheets and zinc oxide nanoparticles

We have studied the direct electrochemistry of glucose oxidase (GOx) immobilized on electrochemically fabricated graphite nanosheets (GNs) and zinc oxide nanoparticles (ZnO) that were deposited on a screen printed carbon electrode (SPCE). The GNs/ZnO composite was characterized by using scanning electron microscopy and elemental analysis. The GOx immobilized on the modified electrode shows a well-defined redox couple at a formal potential of −0.4 V. The enhanced direct electrochemistry of GOx (compared to electrodes without ZnO or without GNs) indicates a fast electron transfer at this kind of electrode, with a heterogeneous electron transfer rate constant (K_s) of 3.75 s⁻¹. The fast electron transfer is attributed to the high conductivity and large edge plane defects of GNs and good conductivity of ZnO-NPs. The modified electrode displays a linear response to glucose in concentrations from 0.3 to 4.5 mM, and the sensitivity is 30.07 μA mM⁻¹ cm⁻². The sensor exhibits a high selectivity, good repeatability and reproducibility, and long term stability.

Graphical representation for the fabrication of GNs/ZnO composite modified SPCE and the immobilization of GOx

     

Study of transfer of trace elements from soil to medicinal plants in the environment of Mangalore

The concentration of five trace elements Cr, As, Pb, Rb and Sr in seven medicinal plants Garcinia indica, Ficus benghalensis, Flacartia Montana, Nyctanthes arbor-tristis, Morinda citrifolia, Ficus recemosa, Barringtonia acutangula and associated soils were analyzed using ICP-MS. In plant the elemental concentrations of Cr, Pb, Rb and Sr vary widely and in soil the elemental concentrations of Cr, As and Sr showed wide variation. Selective enrichment of elements Rb and Sr was observed in some plants. The soil to plant transfer ratio was significant for Sr. The results of these systematic investigations are presented and discussed in this paper.     

Copper oxide nanoparticles catalyzed synthesis of aryl sulfides via cascade reaction of aryl halides with thiourea

Recyclable copper oxide nanoparticles catalyzed simple and highly efficient protocol for the synthesis of symmetrical aryl sulfides was developed by the cross-coupling of aromatic halides with inexpensive and commercially available thiourea which was used as an effective sulfur surrogate. The present cross-coupling protocol of thiourea, via cascade reaction with various substituted aryl halides, producing desired aryl sulfides, has an added advantage of avoiding foul-smelling thiols.