Influence of Co amount on the efficiency of energy absorption of Fe-Co ferrite nanoparticles

We present the chemical synthesis, structural characterization and efficiency of AC field energy absorption of Fe-Co ferrite particles sized between 35 and 100 nm and containing different cobalt amounts up to 3 wt%. Dynamic magnetic measurements in an AC field with frequency of 430 Hz and amplitude of up to 1200 Oe were performed for both solid and liquid dispersions of obtained particles. The energy absorption per one field cycle in function of the field amplitude and Co content was always bigger in liquid systems, under the same conditions, than in solid systems. The obtained results are of significance for the technology of low-frequency ferromagnetic hyperthermia of tumors.     

Inverse Problems for Differential Forms on Riemannian Manifolds with Boundary

Consider a real-analytic orientable connected complete Riemannian manifold M with boundary of dimension n ≥ 2 and let k be an integer 1 ≤ k ≤ n. In the case when M is compact of dimension n ≥ 3, we show that the manifold and the metric on it can be reconstructed, up to an isometry, from the set of the Cauchy data for harmonic k-forms, given on an open subset of the boundary. This extends a result of [14 Lassas , M. , Uhlmann , G. ( 2001 ). On determining a Riemannian manifold from the Dirichlet-to-Neumann map . Ann. Sci. École Norm. 34 : 771 – 787 .[Web of Science ®] , [Google Scholar]] when k = 0. In the two-dimensional case, the same conclusion is obtained when considering the set of the Cauchy data for harmonic 1-forms. Under additional assumptions on the curvature of the manifold, we carry out the same program when M is complete non-compact. In the case n ≥ 3, this generalizes the results of [13 Lassas , M. , Taylor , M. , Uhlmann , G. ( 2003 ). The Dirichlet-to-Neumann map for complete Riemannian manifolds with boundary . Comm. Anal. Geom. 11 : 207 – 221 .[Crossref], [Web of Science ®] , [Google Scholar]] when k = 0. In the two-dimensional case, we are able to reconstruct the manifold from the set of the Cauchy data for harmonic 1-forms.     

Effect of anodic oxygen evolution on cell morphology of sulfuric acid anodic alumina films

Journal of Solid State Electrochemistry - The purpose of this work was to study and analyze the effect of electrolyte temperature and anodization voltage on cell morphology of thin films of...     

Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential

We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in ${\mathbb{R}^n}$ , ${n \geq 3}$ , for the magnetic Schrödinger operator with L ^∞ magnetic and electric potentials, determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schrödinger operator with a gain of two derivatives.     

The Calderón Problem with Partial Data for Conductivities with 3/2 Derivatives

We study a chain of four interacting rotors (rotators) connected at both ends to stochastic heat baths at different temperatures. We show that for non-degenerate interaction potentials the system relaxes, at a stretched exponential rate, to a non-equilibrium steady state (NESS). Rotors with high energy tend to decouple from their neighbors due to fast oscillation of the forces. Because of this, the energy of the central two rotors, which interact with the heat baths only through the external rotors, can take a very long time to dissipate. By appropriately averaging the oscillatory forces, we estimate the dissipation rate and construct a Lyapunov function. Compared to the chain of length three (considered previously by C. Poquet and the current authors), the new difficulty with four rotors is the appearance of resonances when both central rotors are fast. We deal with these resonances using the rapid thermalization of the two external rotors.     

Inverse Problems With Partial Data for a Magnetic Schrödinger Operator in an Infinite Slab and on a Bounded Domain

In this paper we study inverse boundary value problems with partial data for the magnetic Schrödinger operator. In the case of an infinite slab in \({\mathbb{R}^n}\) , n ≥ 3, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of Li and Uhlmann (Inverse Probl Imaging 4(3):449–462, 2010), obtained for the Schrödinger operator without magnetic potentials.In the case of a bounded domain in \({\mathbb{R}^n}\) , n ≥ 3, extending the results of Ammari and Uhlmann (Indiana Univ Math J 53(1):169–183, 2004), we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of Isakov (Inverse Probl Imaging 1(1):95–105, 2007), we also obtain uniqueness results for the magnetic Schrödinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane.     

On L p Resolvent Estimates for Elliptic Operators on Compact Manifolds

We prove uniform L^p estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding result of [3 Dos Santos Ferreira, D., Kenig, C., and Salo, M., 2014. On L^p resolvent estimates for Laplace-Beltrami operators on compact manifolds, Forum Math. 26 (2014), pp. 815–849.[Crossref], [Web of Science ®] , [Google Scholar]] in the case of Laplace-Beltrami operators on Riemannian manifolds. In doing so, we follow the methods, developed in [1 Bourgain, J., Shao, P., Sogge, C., and Yao, X., On L^p-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds, Comm. Math. Phys., to appear.[Web of Science ®] , [Google Scholar]] very closely. We also show that spectral regions in our L^p resolvent estimates are optimal.     

Study of cobalt ferrite nanosuspensions for low-frequency ferromagnetic hyperthermia

High-coercive cobalt ferrite nanoparticles were synthesized and studied for magnetic hyperthermia by direct injection of their suspension into a tumor and application of a strong audio-frequency magnetic field for heating.Physical (dynamic magnetic hysteresis and heat generation in both liquid and solid dispersions),biological (toxicity and penetration of particles in therapeutic quantities into mouse tumor tissue) as well as other properties of the particles were studied.A model was developed to describe the magnetodynamics in suspensions of magnetic nanoclusters with an account for both Brownian and regular rotations,to provide understanding of observed phenomena.The experimental and theoretical techniques developed have formed a basis for controllable synthesis of the magnetic nanoparticles for low-frequency heat generation in medical and other applications.     

Elliptic quasicomplexes in Boutet de Monvel algebra

We consider quasicomplexes of Boutet de Monvel operators in Sobolev spaces on a smooth compact manifold with boundary. To each quasicomplex we associate two complexes of symbols. One complex is defined on the cotangent bundle of the manifold and the other on that of the boundary. The quasicomplex is elliptic if these symbol complexes are exact away from the zero sections. We prove that elliptic quasicomplexes are Fredholm. As a consequence of this result we deduce that a compatibility complex for an overdetermined elliptic boundary problem operator is also Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes of Boutet de Monvel operators.