Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Graphene-based nanostructures: Plasmonics in the THz range

The properties of surface plasmon-polaritons (SPPs) in graphene are discussed and several possible ways of coupling electromagnetic radiation in the terahertz (THz) spectral range to this type of surface waves are described: (i) the attenuated total reflection (ATR) method employing a prism, (ii) graphene-based gratings or graphene monolayers with modulated conductivity, (iii) a metal stripe on top of the graphene layer, and (iv) a nanoparticle located above it. Potentially interesting for applications SPP effects, such as switching, modulation and polarization of THz radiation, as well as its enhanced absorption in graphene, are considered. The discussion also concerns the impact of the nonlinear properties of graphene, such as optical bistability.

On the temperature dependence of the absorption cross section for black holes in string theory

We study the low frequency absorption cross section of spherically symmetric nonextremal d-dimensional black holes. In the presence of α′ corrections, this quantity must have an explicit dependence on the Hawking temperature of the form 1/TH. This property of the low frequency absorption cross section is shared by the D1-D5 system from type IIB superstring theory already at the classical level, without α′ corrections. We apply our formula to the simplest example, the classical d-dimensional Reissner-Nordstr¨om solution, checking that the obtained formula for the cross section has a smooth extremal limit. We also apply it for a d-dimensional Tangherlini-like solution with α′3 corrections.

Absorption of scalars by nonextremal charged black holes in string theory

We analyze the low frequency absorption cross section of minimally coupled massless scalar fields by different kinds of charged static black holes in string theory, namely the D1–D5 system in d=5 and a four dimensional dyonic four-charged black hole. In each case we show that this cross section always has the form of some parameter of the solution divided by the black hole Hawking temperature. We also verify in each case that, despite its explicit temperature dependence, such quotient is finite in the extremal limit, giving a well defined cross section. We show that this precise explicit temperature dependence also arises in the same cross section for black holes with string \alpha' corrections: it is actually induced by them.

Nonlinear behavior of gelatin networks reveals a hierarchical structure

We investigate the strain hardening behavior of various gelatin networks-namely physical gelatin gel, chemically cross-linked gelatin gel, and a hybrid gel made of a combination of the former two-under large shear deformations using the pre-stress, strain ramp, and large amplitude oscillations shear protocols. Further, the internal structures of physical gelatin gels and chemically cross-linked gelatin gels were characterized by small angle neutron scattering (SANS) to enable their internal structures to be correlated with their nonlinear rheology. The Kratky plots of SANS data demonstrate the presence of small cross-linked aggregates within the chemically cross-linked network whereas, in the physical gelatin gels, a relatively homogeneous structure is observed. Through model fitting to the scattering data, we were able to obtain structural parameters, such as the correlation length (ξ), the cross-sectional polymer chain radius (Rc) and the fractal dimension (df) of the gel networks. The fractal dimension df obtained from the SANS data of the physical and chemically cross-linked gels is 1.31 and 1.53, respectively. These values are in excellent agreement with the ones obtained from a generalized nonlinear elastic theory that has been used to fit the stress-strain curves. The chemical cross-linking that generates coils and aggregates hinders the free stretching of the triple helix bundles in the physical gels.

Nonlinear analysis and control of PEM fuel cells

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2010

Beitrag zur Absorption in flüssigkeitsbedüsten Wirbelschichten

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2003

Approximations of the Fisher information for the construction of efficient experimental designs in nonlinear mixed effects models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

equivalence of almost bent and almost perfect nonlinear functions and their generalizations

Vectorial Boolean function, almost bent, almost perfect nonlinear, affine equivalence, CCZ-equivalence

Theory and application of nonlinear wave propagation phenomena in combined reaction/separation processes

Reaction separation processes, reactive distillation, chromatographic reactor, equilibrium theory, nonlinear waves, process control, observer design, asymptoticaly exact input/output-linearization

Sparse nonlinear discriminants

Kernel-Functions, Machine Learning, Least Squares, Speech Recognition, Classification, Regression

Analysis of the potential of nonlinear solvent gradients in preparative chromatography

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2010

Nonlinear frequency response analysis for the diagnosis of polymer electrolyte membrane fuel cells

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2012

Nonlinear dynamics of Poly(hydroxyalkanoate) production in Ralstonia eutropha and Rhodospirillum rubrum

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015

Absorption and nutrient concentration in apple (Pyrus mains L.)

In order to obtain the following informations: a) dry matter production and extraction of nutrients by the fruits at different ages; b) dry matter production and extraction of nutrient by the leaves and "trunk + branches" collected at the flowering stage; c) dry matter production and export of nutrients by pruning (leaves and branches) at the begining dormant stage; A trial was conducted on Latossolo Vermelho Escuro Orto group (Orthox) at Buri, São Paulo State, Brazil. The material was collected from 'Ohio Beauty' and 'Brazil' apples grafted on 'Doucin' 1-2; 3-4; 4-5 and 6-7 years old. The main conclusions were as follows: a) differences were observed on dry matter production by two varieties at the different stages of growth; b) differences were also observed between the two varieties on the matter production in the leaves and "trunk + branches" at the flowering stage, as well as by the leaves and branches pruned at the begining of dormant stages; c) differences were observed betwen the two varieties concerning to nutrient concentration (on dry matter basis) on the fruits collected at different stages of growth. Same results were observed on leaves and "trunk + branches" collected at flowering period; d) differences were observed on the exportation of the nutrients referring to growth period of fruit; e) at the flowering and dormant period, differences were observed on the contents of nutrients in the leaves, 'trunk + branches', on the two varieties; f) the nutrient exportation by the fruits obyed the following order: K>N>P>S>Ca>Mg>Fe>B > Cu > Mn > Zn > Mo; g) the nutrient extration by the aerial part the apple trees obyed the following order: N > K > Ca > Mg > P > S > Fe > B > Cu = Mn = Zn.