Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Many biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

Performance Analysis of Guidance Laws Based on Timescale Gap

An analytical treatment of performance analysis of guidance laws is possible only in simplistic scenarios. As the complexity of the guidance system increases, a search for analytical solutions becomes quite impractical. In this paper, a new performance measure, based upon the notion of a timescale gap that can be computed through numerical simulations, is developed for performance analysis of guidance laws. Finite time Lyapunov exponents are used to define the timescale gap. It is shown that the timescale gap can be used for quantification of the rate of convergence of trajectories to the collision course. Comparisonbetween several guidance laws, based on the timescale gap, is presented. Realistic simulations to study the effect of aerodynamicsand atmospheric variations on the timescale gap of these guidance laws are also presented.

Design of first- and second-order sliding mode observers for induction motors using a stator-flux model

We extend current research in the area of 'sensorless' control of induction motors by presenting two observers based on first- and second-order sliding mode control theories for the simultaneous estimation of flux and speed. We base the observers on the stator-flux model of the motor instead of the usual rotor-flux model mainly because of the uncertain rotor resistance that plays a significant role in the latter. By designing the observers as if they are sliding mode controllers, we lend the properties of parameter insensitive closed-loop dynamics and finite time convergence to the stator flux and speed estimation schemes. We also present simulation and experimental results to validate the operation of the observers.

The Alfvén Wave Equation for Magnetospheric Plasmas

It is shown that besides the continuous spectrum which damps away as inverse power of time, the coupled Alfvén wave equation, which gives coupling between a shear Alfvén wave and a surface wave, can also admit a well behaved harmonic solution in the closed form for a set of initial conditions. This solution, though valid for finite time intervals, points out that the Alfvén surface waves can have a band of frequency (instead of a monochromatic frequency for a nonsheared magnetic field) within which the local field line resonance frequency can lie, and thus can excite magnetic pulsations with latitude-dependent frequency. By considering magnetic fields not only varying in magnitude but also in direction, it is shown that the time interval for the validity of the harmonic solution depend upon the angle between the magnetic field directions on either side of the magnetopause. For small values of the angle the time interval can become appreciably large.

Kohdennetut nanopartikkelit ja isotooppikuvantaminen syövän hoidossa

Syövän diagnostiikassa ja hoidossa nanopartikkelit voivat toimia kuljetinaineina lääke- ja diagnostisille aineille tai nukleiinihappojaksoille. Kantaja-aineeseen voidaan liittää kohdennusmolekyylejä partikkelien passiivista tai aktiivista kohdennusta varten tai radioleima kuvantamista tai radioterapiaa varten. Kantaja-aineiden avulla voidaan parantaa lääkeaineen fysikaalis-kemiallisia ominaisuuksia ja biologista hyötyosuutta, vähentää systeemisiä sivuvaikutuksia, pidentää lääkeaineen puoliintumisaikaa ja siten harventaa annosteluväliä, sekä parantaa lääkeaineen pääsyä kohdekudokseen. Näin voidaan parantaa kemo- ja radioterapian tehoa ja hoidon onnistumisen todennäköisyyttä. Kirjallisuuskatsauksessa perehdytään nanokantajien rooliin syövän hoidossa. Vuosikymmeniä jatkuneesta tutkimuksesta huolimatta vain kaksi (Eurooppa) tai kolme (Yhdysvallat) nanopartikkeliformulaatiota on hyväksytty markkinoille syövän hoidossa. Ongelmina ovat riittämätön hakeutuminen kohdekudokseen, immunogeenisyys ja nanopartikkelien labiilius. Kokeellisessa osassa tutkitaan in vitro ja hiirillä in vivo 99mTc-leimattujen, PEG-verhoiltujen biotiiniliposomien kaksivaiheista kohdennusta ihmisen munasarjan adenokarsinoomasoluihin. Kohdentamiseen käytetään biotinyloitua setuksimabi-(Erbitux®) vasta-ainetta, joka sitoutuu solujen yli-ilmentämiin EGF-reseptoreihin. Kaksivaiheista kohdennusta verrataan suoraan ja/tai passiiviseen kohdennukseen. Tehokkaampien kuvantamismenetelmien kehitys on vauhdittanut kohdennettujen nanopartikkelien tutkimusta. Isotooppikuvantamista käyttäen pystytään seuraamaan radioleiman jakautumista elimistössä ja kuvantamaan solutasolla tapahtuvia ilmiöitä. Kirjallisuuskatsauksessa perehdytään SPECT- ja PET-kuvantamiseen syövän hoidossa, sekä niiden hyödyntämiseen lääkekehityksessä nanopartikkelien kuvantamisessa. Kyseiset kuvantamismenetelmät erottuvat muista menetelmistä korkean erotuskyvyn, herkkyyden ja helppokäyttöisyyden suhteen. Kokeellisessa osassa 99mTc-leimattujen liposomien distribuutiota hiirissä tutkittiin SPECT-CT-laitteen avulla. Aktiivisuus kasvaimessa, pernassa ja maksassa kvantifioitiin InVivoScope-ohjelman ja gammalaskijan avulla. Tuloksia verrattiin keskenään. In vitro-kokeessa saavutettiin kaksivaiheisella kohdennuksella 2,7- 3,5-kertainen (solulinjasta riippuen) hakeutuminen soluihin kontrolliliposomeihin verrattuna. Kuitenkin suora kohdennus toimi kaksivaiheista kohdennusta paremmin in vitro. In vivo –kokeissa liposomit jakautuivat kasvaimeen tehokkaammin i.p.-annosteltuna kuin i.v.-annosteltuna. Kaksivaiheisella kohdennuksella saavutettiin 1,24-kertainen jakautuminen kasvaimeen (% ID/g kudosta) passiivisesti kohdennettuihin liposomeihin verrattuna. %ID/elin oli kohdennetuilla liposomeilla 5,9 % ja passiivisesti kohdennetuilla 5,4%. Todellinen ero oli siis pieni. InVivoScope:n ja gammalaskijan tulokset eivät korreloineet keskenään. Lisätutkimuksia ja menetelmän optimointia vaaditaan liposomien kohdennuksessa kasvaimeen.

Role of surface tension driven convection in pulsed - laser melting and solidification

Surface melting by a stationary, pulsed laser has been modelled by the finite element method. The role of the surface tension driven convection is investigated in detail. Numerical results are presented for a triangular laser pulse of durations 10, 50 and 200 ms. Though the magnitude of the velocity is high due to the surface tension forces, the present results indicate that a finite time is required for convection to affect the temperature distribution within the melt pool. The effect of convection is very significant for pulse durations longer than 10 ms.

``Clickable'', Trifunctional Magnetite Nanoparticles and Their Chemoselective Biofunctionalization

A multifunctional iron oxide based nanoformulation for combined cancer-targeted therapy and multimodal imaging has been meticulously designed and synthesized using a chemoselective ligation approach. Novel superparamagnetic magnetite nanoparticles simultaneously functionalized with amine, carboxyl, and azide groups were fabricated through a sequence of stoichiometrically controllable partial succinylation and Cu (II) catalyzed diazo transfer on the reactive amine termini of 2-aminoethylphosphonate grafted magnetite nanoparticles (MNPs). Functional moieties associated with MNP surface were chemoselectively conjugated with rhodamine B isothiocyanate (RITC), propargyl folate (FA), and paclitaxel (PTX) via tandem nucleophic addition of amine to isothithiocyanates, Cu (I) catalyzed azide-alkyne click chemistry and carbodiimide-promoted esterification. An extensive in vitro study established that the bioactives chemoselectively appended to the magnetite core bequeathed multifunctionality to the nanoparticles without any loss of activity of the functional molecules. Multifunctional nanoparticles, developed in the course of the study, could selectively target and induce apoptosis to folate-receptor (FR) overexpressing cancer cells with enhanced efficacy as compared to the free drug. In addition, the dual optical and magnetic properties of the synthesized nanoparticles aided in the real-time tracking of their intracellular pathways also as apoptotic events through dual fluorescence and MR-based imaging.

Survival of the fittest and zero sum games

Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The. dynamics of this selection is studied using a simple linear model. It has similarities to features of quantum computation, in particular conservation laws leading to destructive interference. Compared to an altruistic scenario, competition introduces instability and eliminates the weaker species in a finite time.

Sliding mode control-based algorithms for consensus in connected swarms

In this article, finite-time consensus algorithms for a swarm of self-propelling agents based on sliding mode control and graph algebraic theories are presented. Algorithms are developed for swarms that can be described by balanced graphs and that are comprised of agents with dynamics of the same order. Agents with first and higher order dynamics are considered. For consensus, the agents' inputs are chosen to enforce sliding mode on surfaces dependent on the graph Laplacian matrix. The algorithms allow for the tuning of the time taken by the swarm to reach a consensus as well as the consensus value. As an example, the case when a swarm of first-order agents is in cyclic pursuit is considered.

Sliding-Mode Guidance and Control for All-Aspect Interceptors with Terminal Angle Constraints

In this paper, sliding-mode-control-based guidance laws to intercept stationary, constant-velocity, and maneuvering targets at a desired impact angle are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the missile's lateral acceleration to enforce terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. The conditions for capturability are also presented. In addition, by considering a three-degree-of-freedom linear-interceptor dynamic model and by following the procedure used to design a dynamic sliding-mode controller, the interceptor autopilot is designed as a simple static controller to track the lateral acceleration generated by the guidance law. Numerical simulation results are presented to validate the proposed guidance laws and the autopilot design for different initial engagement geometries and impact angles.

Proportional navigation with delayed line-of-sight rate

This brief discusses the convergence analysis of proportional navigation (PN) guidance law in the presence of delayed line-of-sight (LOS) rate information. The delay in the LOS rate is introduced by the missile guidance system that uses a low cost sensor to obtain LOS rate information by image processing techniques. A Lyapunov-like function is used to analyze the convergence of the delay differential equation (DDE) governing the evolution of the LOS rate. The time-to-go until which decreasing behaviour of the Lyapunov-like function can be guaranteed is obtained. Conditions on the delay for finite time convergence of the LOS rate are presented for the linearized engagement equation. It is observed that in the presence of line-of-sight rate delay, increasing the effective navigation constant of the PN guidance law deteriorates its performance. Numerical simulations are presented to validate the results.

Optimal incentive timing strategies for product marketing on social networks

We consider the problem of devising incentive strategies for viral marketing of a product. In particular, we assume that the seller can influence penetration of the product by offering two incentive programs: a) direct incentives to potential buyers (influence) and b) referral rewards for customers who influence potential buyers to make the purchase (exploit connections). The problem is to determine the optimal timing of these programs over a finite time horizon. In contrast to algorithmic perspective popular in the literature, we take a mean-field approach and formulate the problem as a continuous-time deterministic optimal control problem. We show that the optimal strategy for the seller has a simple structure and can take both forms, namely, influence-and-exploit and exploit-and-influence. We also show that in some cases it may optimal for the seller to deploy incentive programs mostly for low degree nodes. We support our theoretical results through numerical studies and provide practical insights by analyzing various scenarios.

Non-singular terminal sliding mode guidance and control with terminal angle constraints for non-maneuvering targets

In this paper guidance laws to intercept stationary and constant velocity targets at a desired impact angle, based on sliding mode control theory, are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight (LOS) angle, is achieved in finite time by selecting the missile's lateral acceleration (latax) to enforce non-singular terminal sliding mode on a switching surface designed using this desired LOS angle and based on non-linear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles.

Nonsingular Terminal Sliding Mode Guidance with Impact Angle Constraints

Guidance laws based on a conventional sliding mode ensures only asymptotic convergence. However, convergence to the desired impact angle within a finite time is important in most practical guidance applications. These finite time convergent guidance laws suffer from singularity leading to control saturation. In this paper, guidance laws to intercept targets at a desired impact angle, from any initial heading angle, without exhibiting any singularity, are presented. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the interceptor's lateral acceleration to enforce nonsingular terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles. Although the guidance laws are designed for constant speed interceptors, its robustness against the time-varying speed of interceptors is also evaluated through extensive simulation results.

Capturability Analysis of a 3-D Retro-PN Guidance Law for Higher Speed Nonmaneuvering Targets

This brief presents the capturability analysis of a 3-D Retro-proportional navigation (Retro-PN) guidance law, which uses a negative navigation constant (as against the usual positive one), for intercepting targets having higher speeds than interceptors. This modification makes it possible to achieve collision conditions that were inaccessible to the standard PN law. A modified polar coordinate system, that makes the model more compact, is used in this brief for capturability analysis. In addition to the ratio of the target to interceptor speeds, the directional cosines of the interceptor, and target velocity vectors play a crucial role in the capturability. The existence of nontrivial capture zone of the Retro-PN guidance law and necessary and sufficient conditions, for capturing the target in finite time, are presented. A sufficient condition on the navigation constant is derived to ensure finiteness of the line-of-sight turn rate. The results are more extensive than those available for 2-D engagements, which can be obtained as special cases of this brief. Simulation results are given to support the analytical results.