Quasiconformal maps, analytic capacity, and non linear potentials

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The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Multiple-scale hydrological and geophysical data integration through non-linear Bayesian sequential simulation

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the scale of a field site represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed downscaling procedure based on a non-linear Bayesian sequential simulation approach. The main objective of this algorithm is to estimate the value of the sparsely sampled hydraulic conductivity at non-sampled locations based on its relation to the electrical conductivity logged at collocated wells and surface resistivity measurements, which are available throughout the studied site. The in situ relationship between the hydraulic and electrical conductivities is described through a non-parametric multivariatekernel density function. Then a stochastic integration of low-resolution, large-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities is applied. The overall viability of this downscaling approach is tested and validated by comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure allows obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Modelling of non-linear viscoelastic tissues with bar elements

In this work we develop a viscoelastic bar element that can handle multiple rheo- logical laws with non-linear elastic and non-linear viscous material models. The bar element is built by joining in series an elastic and viscous bar, constraining the middle node position to the bar axis with a reduction method, and stati- cally condensing the internal degrees of freedom. We apply the methodology to the modelling of reversible softening with sti ness recovery both in 2D and 3D, a phenomenology also experimentally observed during stretching cycles on epithelial lung cell monolayers.

A test of the predictive validity of non-linear QALY models using time trade-off utilities

This paper presents a test of the predictive validity of various classes ofQALY models (i.e., linear, power and exponential models). We first estimatedTTO utilities for 43 EQ-5D chronic health states and next these states wereembedded in health profiles. The chronic TTO utilities were then used topredict the responses to TTO questions with health profiles. We find that thepower QALY model clearly outperforms linear and exponential QALY models.Optimal power coefficient is 0.65. Our results suggest that TTO-based QALYcalculations may be biased. This bias can be avoided using a power QALY model.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Non-Linear and Non-Conventional Speech Processing: Alternative Techniques

This special issue aims to cover some problems related to non-linear and nonconventional speech processing. The origin of this volume is in the ISCA Tutorial and Research Workshop on Non-Linear Speech Processing, NOLISP’09, held at the Universitat de Vic (Catalonia, Spain) on June 25–27, 2009. The series of NOLISP workshops started in 2003 has become a biannual event whose aim is to discuss alternative techniques for speech processing that, in a sense, do not fit into mainstream approaches. A selected choice of papers based on the presentations delivered at NOLISP’09 has given rise to this issue of Cognitive Computation.

A non-linear Bayesian approach for upscaling local-scale hydraulic conductivity measurements based on local- and regional-scale geophysical data

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed an upscaling procedure based on a Bayesian sequential simulation approach. This method is then applied to the stochastic integration of low-resolution, regional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this upscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Non-Linear Journal Bearing Model for Analysis of Superharmonic Vibrations of Rotor Systems

A rotating machine usually consists of a rotor and bearings that supports it. The nonidealities in these components may excite vibration of the rotating system. The uncontrolled vibrations may lead to excessive wearing of the components of the rotating machine or reduce the process quality. Vibrations may be harmful even when amplitudes are seemingly low, as is usually the case in superharmonic vibration that takes place below the first critical speed of the rotating machine. Superharmonic vibration is excited when the rotational velocity of the machine is a fraction of the natural frequency of the system. In such a situation, a part of the machine’s rotational energy is transformed into vibration energy. The amount of vibration energy should be minimised in the design of rotating machines. The superharmonic vibration phenomena can be studied by analysing the coupled rotor-bearing system employing a multibody simulation approach. This research is focused on the modelling of hydrodynamic journal bearings and rotorbearing systems supported by journal bearings. In particular, the non-idealities affecting the rotor-bearing system and their effect on the superharmonic vibration of the rotating system are analysed. A comparison of computationally efficient journal bearing models is carried out in order to validate one model for further development. The selected bearing model is improved in order to take the waviness of the shaft journal into account. The improved model is implemented and analyzed in a multibody simulation code. A rotor-bearing system that consists of a flexible tube roll, two journal bearings and a supporting structure is analysed employing the multibody simulation technique. The modelled non-idealities are the shell thickness variation in the tube roll and the waviness of the shaft journal in the bearing assembly. Both modelled non-idealities may cause subharmonic resonance in the system. In multibody simulation, the coupled effect of the non-idealities can be captured in the analysis. Additionally one non-ideality is presented that does not excite the vibrations itself but affects the response of the rotorbearing system, namely the waviness of the bearing bushing which is the non-rotating part of the bearing system. The modelled system is verified with measurements performed on a test rig. In the measurements the waviness of bearing bushing was not measured and therefore it’s affect on the response was not verified. In conclusion, the selected modelling approach is an appropriate method when analysing the response of the rotor-bearing system. When comparing the simulated results to the measured ones, the overall agreement between the results is concluded to be good.

BEM/FEM non-linear model applied to transient analysis with viscous damping

In this article a two-dimensional transient boundary element formulation based on the mass matrix approach is discussed. The implicit formulation of the method to deal with elastoplastic analysis is considered, as well as the way to deal with viscous damping effects. The time integration processes are based on the Newmark rhoand Houbolt methods, while the domain integrals for mass, elastoplastic and damping effects are carried out by the well known cell approximation technique. The boundary element algebraic relations are also coupled with finite element frame relations to solve stiffened domains. Some examples to illustrate the accuracy and efficiency of the proposed formulation are also presented.

Non-linear analysis of laminated metal matrix composites by an integrated micro/macro-mechanical model

The present paper describes an integrated micro/macro mechanical study of the elastic-viscoplastic behavior of unidirectional metal matrix composites (MMC). The micromechanical analysis of the elastic moduli is based on the Composites Cylinder Assemblage model (CCA) with comparisons also draw with a Representative Unit Cell (RUC) technique. These "homogenization" techniques are later incorporated into the Vanishing Fiber Diameter (VFD) model and a new formulation is proposed. The concept of a smeared element procedure is employed in conjunction with two different versions of the Bodner and Partom elastic-viscoplastic constitutive model for the associated macroscopic analysis. The formulations developed are also compared against experimental and analytical results available in the literature.

Non-Linear Unsteady Aerodynamic Response Approximation Using Multi-Layer Functionals

Non-linear functional representation of the aerodynamic response provides a convenient mathematical model for motion-induced unsteady transonic aerodynamic loads response, that accounts for both complex non-linearities and time-history effects. A recent development, based on functional approximation theory, has established a novel functional form; namely, the multi-layer functional. For a large class of non-linear dynamic systems, such multi-layer functional representations can be realised via finite impulse response (FIR) neural networks. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process in which a limited sample of system input-output data sets is presented to the temporal neural network. The present work describes a procedure for the systematic identification of parameterised neural network models of motion-induced unsteady transonic aerodynamic loads response. The training process is based on a conventional genetic algorithm to optimise the network architecture, combined with a simplified random search algorithm to update weight and bias values. Application of the scheme to representative transonic aerodynamic loads response data for a bidimensional airfoil executing finite-amplitude motion in transonic flow is used to demonstrate the feasibility of the approach. The approach is shown to furnish a satisfactory generalisation property to different motion histories over a range of Mach numbers in the transonic regime.