Multimodal therapy for complete regression of malignant melanoma using constrained nonlinear optimal dynamic inversion

Using a realistic nonlinear mathematical model for melanoma dynamics and the technique of optimal dynamic inversion (exact feedback linearization with static optimization), a multimodal automatic drug dosage strategy is proposed in this paper for complete regression of melanoma cancer in humans. The proposed strategy computes different drug dosages and gives a nonlinear state feedback solution for driving the number of cancer cells to zero. However, it is observed that when tumor is regressed to certain value, then there is no need of external drug dosages as immune system and other therapeutic states are able to regress tumor at a sufficiently fast rate which is more than exponential rate. As model has three different drug dosages, after applying dynamic inversion philosophy, drug dosages can be selected in optimized manner without crossing their toxicity limits. The combination of drug dosages is decided by appropriately selecting the control design parameter values based on physical constraints. The process is automated for all possible combinations of the chemotherapy and immunotherapy drug dosages with preferential emphasis of having maximum possible variety of drug inputs at any given point of time. Simulation study with a standard patient model shows that tumor cells are regressed from 2 x 107 to order of 105 cells because of external drug dosages in 36.93 days. After this no external drug dosages are required as immune system and other therapeutic states are able to regress tumor at greater than exponential rate and hence, tumor goes to zero (less than 0.01) in 48.77 days and healthy immune system of the patient is restored. Study with different chemotherapy drug resistance value is also carried out. (C) 2014 Elsevier Ltd. All rights reserved.

Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows

Single fluid schemes that rely on an interface function for phase identification in multicomponent compressible flows are widely used to study hydrodynamic flow phenomena in several diverse applications. Simulations based on standard numerical implementation of these schemes suffer from an artificial increase in the width of the interface function owing to the numerical dissipation introduced by an upwind discretization of the governing equations. In addition, monotonicity requirements which ensure that the sharp interface function remains bounded at all times necessitate use of low-order accurate discretization strategies. This results in a significant reduction in accuracy along with a loss of intricate flow features. In this paper we develop a nonlinear transformation based interface capturing method which achieves superior accuracy without compromising the simplicity, computational efficiency and robustness of the original flow solver. A nonlinear map from the signed distance function to the sigmoid type interface function is used to effectively couple a standard single fluid shock and interface capturing scheme with a high-order accurate constrained level set reinitialization method in a way that allows for oscillation-free transport of the sharp material interface. Imposition of a maximum principle, which ensures that the multidimensional preconditioned interface capturing method does not produce new maxima or minima even in the extreme events of interface merger or breakup, allows for an explicit determination of the interface thickness in terms of the grid spacing. A narrow band method is formulated in order to localize computations pertinent to the preconditioned interface capturing method. Numerical tests in one dimension reveal a significant improvement in accuracy and convergence; in stark contrast to the conventional scheme, the proposed method retains its accuracy and convergence characteristics in a shifted reference frame. Results from the test cases in two dimensions show that the nonlinear transformation based interface capturing method outperforms both the conventional method and an interface capturing method without nonlinear transformation in resolving intricate flow features such as sheet jetting in the shock-induced cavity collapse. The ability of the proposed method in accounting for the gravitational and surface tension forces besides compressibility is demonstrated through a model fully three-dimensional problem concerning droplet splash and formation of a crownlike feature. (C) 2014 Elsevier Inc. All rights reserved.

Nonlinear analysis of a thin pre-twisted and delaminated anisotropic strip

The present work is aimed at the development of an efficient mathematical model to assess the degradation in the stiffness properties of an anisotropic strip due to delamination. In particular, the motive is to capture those nonlinear effects in a strip that arise due to the geometry of the structure, in the presence of delamination. The variational asymptotic method (VAM) is used as a mathematical tool to simplify the original 3D problem to a 1D problem. Further simplification is achieved by modeling the delaminated structure by a sublaminate approach. By VAM, a 2D nonlinear sectional analysis is carried out to determine compact expression for the stiffness terms. The stiffness terms, both linear and nonlinear, are derived as functions of delamination length and location in closed form. In general, the results from the analysis include fully coupled nonlinear 1D stiffness coefficients, 3D strain field, 3D stress field, and in-plane and warping fields. In this work, the utility of the model is demonstrated for a static case, and its capability to capture the trapeze effect in the presence of delamination is investigated and compared with results available in the literature.

Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations

The periodic 3D Navier-Stokes equations are analyzed in terms of dimensionless, scaled, L-2m-norms of vorticity D-m (1 <= m <= infinity). The first in this hierarchy, D-1, is the global enstrophy. Three regimes naturally occur in the D-1-D-m plane. Solutions in the first regime, which lie between two concave curves, are shown to be regular, owing to strong nonlinear depletion. Moreover, numerical experiments have suggested, so far, that all dynamics lie in this heavily depleted regime 1]; new numerical evidence for this is presented. Estimates for the dimension of a global attractor and a corresponding inertial range are given for this regime. However, two more regimes can theoretically exist. In the second, which lies between the upper concave curve and a line, the depletion is insufficient to regularize solutions, so no more than Leray's weak solutions exist. In the third, which lies above this line, solutions are regular, but correspond to extreme initial conditions. The paper ends with a discussion on the possibility of transition between these regimes.

Field dependent and disorder-induced nonlinear charge transport in electrochemically doped polypyrrole devices

Electric field activated charge transport is studied in the metal/polymer/metal device structure of electropolymerized polypyrrole down to 10 K with varying carrier density and disorder. Disorder induced nonlinear behaviour is observed in polypyrrole devices grown at room temperature which is correlated to delocalization of states. The slope parameter of currentvoltage characteristics (in log-log scale) increases as the temperature decreases, which indicates the onset of stronger field dependence. The field dependence of mobility becomes dominant as the carrier density decreases. The sharp dip in differential conductance indicates the localization of carriers at low temperatures which reduces the effective number of carriers involved in the transport.

Formation Flying with Nonlinear Partial Integrated Guidance and Control

Using the dynamic inversion philosophy, a nonlinear partial integrated guidance and control approach is presented in this paper for formation flying. It is based on the evolving philosophy of integrated guidance and control. However, it also retains the advantages of the conventional guidance then control philosophy by retaining the timescale separation between translational and rotational dynamics explicitly. Simulation studies demonstrate that the proposed technique is effective in bringing the vehicles into formation quickly and maintaining the formation.

Optimal control of grinding mill circuit using model predictive static programming: A new nonlinear MPC paradigm

The recently developed reference-command tracking version of model predictive static programming (MPSP) is successfully applied to a single-stage closed grinding mill circuit. MPSP is an innovative optimal control technique that combines the philosophies of model predictive control (MPC) and approximate dynamic programming. The performance of the proposed MPSP control technique, which can be viewed as a `new paradigm' under the nonlinear MPC philosophy, is compared to the performance of a standard nonlinear MPC technique applied to the same plant for the same conditions. Results show that the MPSP control technique is more than capable of tracking the desired set-point in the presence of model-plant mismatch, disturbances and measurement noise. The performance of MPSP and nonlinear MPC compare very well, with definite advantages offered by MPSP. The computational speed of MPSP is increased through a sequence of innovations such as the conversion of the dynamic optimization problem to a low-dimensional static optimization problem, the recursive computation of sensitivity matrices and using a closed form expression to update the control. To alleviate the burden on the optimization procedure in standard MPC, the control horizon is normally restricted. However, in the MPSP technique the control horizon is extended to the prediction horizon with a minor increase in the computational time. Furthermore, the MPSP technique generally takes only a couple of iterations to converge, even when input constraints are applied. Therefore, MPSP can be regarded as a potential candidate for online applications of the nonlinear MPC philosophy to real-world industrial process plants. (C) 2014 Elsevier Ltd. All rights reserved.

Adaptive Flight-Control Design Using Neural-Network-Aided Optimal Nonlinear Dynamic Inversion

A neural-network-aided nonlinear dynamic inversion-based hybrid technique of model reference adaptive control flight-control system design is presented in this paper. Here, the gains of the nonlinear dynamic inversion-based flight-control system are dynamically selected in such a manner that the resulting controller mimics a single network, adaptive control, optimal nonlinear controller for state regulation. Traditional model reference adaptive control methods use a linearized reference model, and the presented control design method employs a nonlinear reference model to compute the nonlinear dynamic inversion gains. This innovation of designing the gain elements after synthesizing the single network adaptive controller maintains the advantages that an optimal controller offers, yet it retains a simple closed-form control expression in state feedback form, which can easily be modified for tracking problems without demanding any a priori knowledge of the reference signals. The strength of the technique is demonstrated by considering the longitudinal motion of a nonlinear aircraft system. An extended single network adaptive control/nonlinear dynamic inversion adaptive control design architecture is also presented, which adapts online to three failure conditions, namely, a thrust failure, an elevator failure, and an inaccuracy in the estimation of C-M alpha. Simulation results demonstrate that the presented adaptive flight controller generates a near-optimal response when compared to a traditional nonlinear dynamic inversion controller.

Nonlinear constraints on gravity from entanglement

Using the positivity of relative entropy arising from the Ryu-Takayanagi formula for spherical entangling surfaces, we obtain constraints at the nonlinear level for the gravitational dual. We calculate the Green's function necessary to compute the first order correction to the entangling surface and use this to find the relative entropy for non-constant stress tensors in a derivative expansion. We show that the Einstein value satisfies the positivity condition, while the multidimensional parameter space away from it gets constrained.

Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system D(t)w - del.(z) over right arrow = g(x, t, x/epsilon) (0.1) w is an element of alpha(u, x/epsilon) (0.2) (z) over right arrow is an element of (gamma) over right arrow (del u, x/epsilon) (0.3) Here epsilon is a positive parameter; alpha and (gamma) over right arrow are maximal monotone with respect to the first variable and periodic with respect to the second one. The inclusions (0.2) and (0.3) are here formulated as null-minimization principles, via the theory of Fitzpatrick MR 1009594]. As epsilon -> 0, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved. (C) 2015 Elsevier Ltd. All rights reserved.

Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system D(t)w - del.(z) over right arrow = g(x, t, x/epsilon) (0.1) w is an element of alpha(u, x/epsilon) (0.2) (z) over right arrow is an element of (gamma) over right arrow (del u, x/epsilon) (0.3) Here epsilon is a positive parameter; alpha and (gamma) over right arrow are maximal monotone with respect to the first variable and periodic with respect to the second one. The inclusions (0.2) and (0.3) are here formulated as null-minimization principles, via the theory of Fitzpatrick MR 1009594]. As epsilon -> 0, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved. (C) 2015 Elsevier Ltd. All rights reserved.

VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.

Investigations on growth, structure, optical properties and laser damage threshold of organic nonlinear optical crystals of Guanidinium L-Ascorbate

Single crystals of Guanidinium L-Ascorbate (GuLA) were grown and crystal structure was determined by direct methods. GuLA crystallizes in orthorhombic, non-centrosymmetric space group P2(1)2(1)2(1). The UV-cutoff was determined as 325 nm. The morphology was generated and the interplanar angles estimated and compared with experimental values. Second harmonic generation conversion efficiency was measured and compared with other salts of L-Ascorbic acid. Surface laser damage threshold was calculated as 11.3GW/cm(2) for a single shot of laser of 1064 nm wavelength.

Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems

This paper deals with the adaptive mesh generation for singularly perturbed nonlinear parameterized problems with a comparative research study on them. We propose an a posteriori error estimate for singularly perturbed parameterized problems by moving mesh methods with fixed number of mesh points. The well known a priori meshes are compared with the proposed one. The comparison results show that the proposed numerical method is highly effective for the generation of layer adapted a posteriori meshes. A numerical experiment of the error behavior on different meshes is carried out to highlight the comparison of the approximated solutions. (C) 2015 Elsevier B.V. All rights reserved.