Problem of nonlinear filtering

Stochastic filtering theory studies the problem of estimating an unobservable `signal' process X given the information obtained by observing an associated process Y (a `noisy' observation) within a certain time window [0; t]. It is possible to explicitly describe the distribution of X given Y in the setting of linear/gaussian systems. Outside the realm of the linear theory, it is known that only a few very exceptional examples have explicitly described posterior distributions. We present in detail a class of nonlinear filters (Benes filters) which allow explicit formulae. Using the explicit expression of the Laplace transform of a functional of Brownian motion we give a direct computation of the unnormalized conditional density of the signal for the Benes filter and obtain the formula for the normalized conditional density of X for two particular filters. In the case in which the signal X is a diffusion process and Y is given by the equation dY t = h(s; X s )ds+dW t ; where W is a Brownian moti..

Fractional-Order Models for Biochemical Processes

Biochemical processes present complex mechanisms and can be described by various computational models. Complex systems present a variety of problems, especially the loss of intuitive understanding. The present work uses fractional-order calculus to obtain mathematical models for erythritol and mannitol synthesis. The obtained models are useful for both prediction and process optimization. The models present the complex behavior of the process due to the fractional order, without losing the physical meaning of gain and time constants. To validate each obtained model, the simulation results were compared with experimental data. In order to highlight the advantages of fractional-order models, comparisons with the corresponding integer-order models are presented

Remarkable Magnetic Properties in a Mn_73.6Ga_26.4 Alloy Produced via Out-of-Equilibrium Method

Rare-earth-free permanent magnets with the L10 phase are actively researched for their potential as a future class of magnetic materials, capable of operating at higher temperatures and in challenging corrosion environments such as renewable energy applications. Among these classes, MnGa shows potential, being cost effective and having interesting magnetic properties. A MnGa magnetic alloy, with composition Mn73.6Ga26.4 in atomic percent, was produced via the out-of-equilibrium method, and its structural and magnetic properties were assessed using X-ray diffraction (XRD), transmission electron microscopy (TEM), selected area electron diffraction (SAED) and extended magnetic characterization. We show that the MnGa alloy submitted to thermal annealing in optimal conditions exhibits a two-phase microstructure, where small nanocrystals of tetragonal L10/D022 magnetic phase are embedded within a D019 MnGa matrix of a non-collinear antiferromagnetic nature. These co-existing, magnetically different phases produce an optimal set of promising magnetic properties, larger than the values reported in the literature for single-phase MnGa alloys and thin films. Such large values are explained by the exchange coupling between competing non-collinear magnetic sublattices of the D019 MnGa with the net moment of the small magnetic nanocrystals of tetragonal symmetry

Temperature-Dependent Phase Evolution in FePt-Based Nanocomposite Multiple-Phased Magnetic Alloys

A quaternary Fe–Pt–Nb–B alloy has been fabricated by the melt spinning method with the purpose of the formation of crystallographically coherent multiple magnetic phases, emerging from the same metastable precursor, as well as to investigate the phase interactions and the influence of their coupling on magnetic performances. For this purpose, extended structural and magnetic investigations were undertaken by making use of X-ray diffraction, transmission electron microscopy, and 57Fe Mössbauer spectroscopy, as well as magnetic measurements using SQUID magnetometry. It was documented that intermediate metastable phases formed during primary crystallization, in intermediate stages of annealing, and a growth-dominated mode was encountered for the secondary crystallization stage upon annealing at 700 °C and 800 °C where fcc Fe3Pt and fct Fe2B polycrystalline were formed. The Mössbauer investigations have documented rigorously the hyperfine parameters of each of the observed phases. The fcc A1 FePt phase was shown to exhibit a peculiar ferromagnetic transition, and this transition has been proven to occur gradually between 300 K and 77 K. The magnetic measurements allowed us to identify the annealing at 700 °C as optimal for obtaining good magnetic features. Coercive field dependence shows similarities to the random anisotropy model for samples annealed at 500 °C to 700 °C which are nanocrystalline. These results show good perspectives for use in applications where different magnetic states are required at different operating temperatures

Thermal Stability, Blocking Regime and Superparamagnetic Behavior in Mn-Al-C Melt Spun Ribbons

Alloys possessing nominal compositions Mn53Al45C2 and Mn52Al46C2 were prepared by the melt spinning method and were subjected to complex structural, morphological and magnetic investigations. As these alloys can exhibit tetragonal L10-type and τ phase, they have good potential as rare earth (RE)—free magnets. It is, therefore, important to monitor the ε–τ phase transformation and the stability and the magnetic features of the tetragonal phase in an entire temperature interval. By using synchrotron X-ray diffraction, it has been proven that the ε–τ phase transformation occurs gradually, with the τ phase becoming predominant only after 450 °C. Moreover, this phase has been proven to be quite stable without any grain growth even at the highest temperature investigated at 800 °C. Low temperature behavior was thoroughly investigated by using a complex combination of major and minor hysteresis loops combined with the zero field cooled-field cooled magnetization protocols (ZFC-FC). Two different regimes, blocking and superparamagnetic, were documented. A spin reorientation transition was proven to occur at 55 K while a maximum magnetization observed in ZFC-FC curves proved that at about 75 K, a transition from ferro to superparamagnetic state occurs. The existence of a blocking regime below 55 K that is characteristic to nanogranular systems with superparamagnetic behavior has shown further development towards obtaining RE-free magnets

Magnetism and ε-τ Phase Transformation in MnAl-Based Nanocomposite Magnets

Melt spun ribbons of Mn53Al45C2 and Mn52Al46C2 have been synthesized by rapid quenching of the melt with the purpose of monitoring the ε-τ phase transformation to show technologically feasible ways to increase magnetic parameters and to illustrate the viability of these alloys as the next generation of rare earth (RE)-free magnets. By differential scanning calorimetry (DSC), activation energies and temperatures of onset of the ε-τ phase transformation were obtained. Structural analysis was performed using X-ray diffraction (XRD) and the resulting XRD patterns were quantitatively assessed using full profile Rietveld-type analysis. Appropriate annealing was performed in order to enable the ε-τ phase transformation. While hcp ε-phase was found to be predominant in the as-cast samples, after appropriate annealing, the tetragonal τ-phase, the one that furnishes the relevant magnetic response, was found to be predominant with an abundance of about 90%. The data suggested a mechanism of hcp ε-phase decomposition controlled by the segregation towards the interfacial regions, having the rate of transformation governed by antiphase boundary diffusion processes. Magnetic measurements of annealed sample Mn53Al45C2, consisting of predominant tetragonal τ-phase, showed high values of magnetization and increased coercivity, consistent with an energy product of about 10 MGOe, similar with previously reported magnetization measurements, providing further insight into the realization of future class of RE-free low-cost permanent magnets

Mn-Induced Thermal Stability of L10 Phase in Fept Magnetic Nanoscale Ribbons

Magnetic nanoscale materials exhibiting the L10 tetragonal phase such as FePt or ternary alloys derived from FePt show most promising magnetic properties as a novel class of rare earth free permanent magnets with high operating temperature. A granular alloy derived from binary FePt with low Pt content and the addition of Mn with the nominal composition Fe57Mn8Pt35 has been synthesized in the shape of melt-spun ribbons and subsequently annealed at 600 °C and 700 °C for promoting the formation of single phase, L10 tetragonal, hard magnetic phase. Proton-induced X-ray emission spectroscopy PIXE has been utilized for checking the compositional effect of Mn addition. Structural properties were analyzed using X-ray diffraction and diffractograms were analyzed using full profile Rietveld-type analysis with MAUD (Materials Analysis Using Diffraction) software. By using temperature-dependent synchrotron X-ray diffraction, the disorder–order phase transformation and the stability of the hard magnetic L10 phase were monitored over a large temperature range (50–800 °C). A large interval of structural stability of the L10 phase was observed and this stability was interpreted in terms of higher ordering of the L10 phase promoted by the Mn addition. It was moreover found that both crystal growth and unit cell expansion are inhibited, up to the highest temperature investigated (800 °C), proving thus that the Mn addition stabilizes the formed L10 structure further. Magnetic hysteresis loops confirmed structural data, revealing a strong coercive field for a sample wherein single phase, hard, magnetic tetragonal L10 exists. These findings open good perspectives for use as nanocomposite, rare earth free magnets, working in extreme operation conditions

Annealing-Induced High Ordering and Coercivity in Novel L10 CoPt-Based Nanocomposite Magnets

A novel class of quaternary intermetallic alloys based on CoPt is investigated in view of their interesting magnetic properties induced by the presence of hard magnetic L10 phase. A Co48Pt28Ag6B18 alloy has been prepared by rapid solidification from the melt and subjected to various isothermal annealing procedures. The structure and magnetism of both as-cast and annealed samples as well as the phase evolution with temperature are investigated by means of thermal analysis, X-ray, and selected area electron diffraction, scanning and high-resolution electron microscopy, and magnetic measurements. The X-ray diffraction (XRD) analysis shows that both the as-cast alloy and the sample annealed at 400 °C (673 K) have a nanocrystalline structure where fcc CoPt phase predominates. Annealing at 473 °C promotes the formation of L10 phase triggered by the disorder-order phase transformation as documented in the differential scanning calorimetry results. The sample annealed at 670 °C (943 K) shows full formation of L10 CoPt as revealed by XRD. Magnetic measurements showed coercivity values ten times increased compared to the as-cast state. This confirms the full formation of L10 CoPt in the annealed samples. Moreover, detailed atomic resolution HREM images and SAED patterns show the occurrence of the rarely seen (003) superlattice peaks, which translated into a high ordering of the L10 CoPt superlattice. Such results spur more interest in finding novel classes of nanocomposite magnets based on L10 phase