A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

/pdf/pattern-formation-outside-of-equilibrium-1601b9znum.pdf

Pattern formation outside of equilibrium

Sasidharan Swarnalatha Lucky,†,§ Khee Chee Soo,‡ and Yong Zhang*,†,§,∥ †NUS Graduate School for Integrative Sciences & Engineering (NGS), National University of Singapore, Singapore, Singapore 117456 ‡Division of Medical Sciences, National Cancer Centre Singapore, Singapore, Singapore 169610 Department of Biomedical Engineering, Faculty of Engineering, National University of Singapore, Singapore, Singapore 117576 College of Chemistry and Life Sciences, Zhejiang Normal University, Zhejiang, P. R. China 321004

Nanoparticles in photodynamic therapy.

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Art of electronics

Photodynamic therapy - mechanisms, photosensitizers and combinations.

Graphene exhibits unique 2-D structure and exceptional phyiscal and chemical properties that lead to many potential applications. Among various applications, biomedical applications of graphene have attracted ever-increasing interests over the last three years. In this review, we present an overview of current advances in applications of graphene in biomedicine with focus on drug delivery, cancer therapy and biological imaging, together with a brief discussion on the challenges and perspectives for future research in this field.

/pdf/biomedical-applications-of-graphene-pjfwy21mqr.pdf

Biomedical applications of graphene.

Photodynamic therapy (PDT) involves the administration of photosensitizer followed by local illumination with visible light of specific wavelength(s). In the presence of oxygen molecules, the light illumination of photosensitizer can lead to a series of photochemical reactions and consequently the generation of cytotoxic species. The quantity and location of PDT-induced cytotoxic species determine the nature and consequence of PDT. Much progress has been seen in both basic research and clinical application in recent years. Although the majority of approved PDT clinical protocols have primarily been used for the treatment of superficial lesions of both malignant and non-malignant diseases, interstitial PDT for the ablation of deep-seated solid tumors are now being investigated worldwide. The complexity of the geometry and non-homogeneity of solid tumor pose a great challenge on the implementation of minimally invasive interstitial PDT and the estimation of PDT dosimetry. This review will discuss the recent progress and technical challenges of various forms of interstitial PDT for the treatment of parenchymal and/or stromal tissues of solid tumors.

https://journals.sagepub.com/doi/pdf/10.1177/153303460800700405

Photodynamic Therapy for Treatment of Solid Tumors — Potential and Technical Challenges

The primary instabilities and bicritical curves for flow between counter‐rotating cylinders have been computed numerically from the Navier–Stokes equations assuming axial periodicity. The computations provide values of the Reynolds numbers, wavenumbers, and wave speeds at the primary transition from Couette flow for radius ratios from 0.40–0.98. Particular attention has been focused on the bicritical curves that separate (as the magnitude of counter‐rotation is increased) the transitions from Couette flow to flows with different azimuthal wavenumbers m and m+1. This lays the foundation for further analysis of nonlinear mode interactions and pattern formation occurring along the bicritical curves and serves as a benchmark for experimental studies. Preliminary experimental measurements of transition Reynolds numbers and wave speeds presented here agree well with the computations from the mathematical model.

Primary instabilities and bicriticality in flow between counter-rotating cylinders

We have controlled chaos in a pendulum with vertically driven pivot over a range of drive frequencies and damping levels. Using two variations on the OGY method [Ott, Grebogi, and Yorke, Phys. Rev. Lett. 64, 1196 (1990)], and with eddy-current damping as a control parameter, we have stabilized the motion of the pendulum about several of its unstable period-1, -2, and -4 limit cycles. Sampling the angular position at a correct choice of phase within the drive cycle simplified the OGY control rule. A time-proportioning rule was also found to provide robust control.

Control of a chaotic parametrically driven pendulum.

Recent studies have brought into question the view that at sufficiently high Reynolds number turbulence is an asymptotic state. We present direct observation of the decay of turbulent states in Taylor-Couette flow with lifetimes spanning five orders of magnitude. We also show that there is a regime where Taylor-Couette flow shares many of the decay characteristics observed in other shear flows, including Poisson statistics and the coexistence of laminar and turbulent patches. Our data suggest that for a range of Reynolds numbers characteristic decay times increase superexponentially with increasing Reynolds number but remain bounded in agreement with the most recent data from pipe flow. Our data are also consistent with recent theoretical predictions of lifetime scaling in transitional flows.

Transient turbulence in Taylor-Couette flow.

A nonlinear stability analysis by Demay and Iooss of flow between concentric rotating cylinders (the Couette-Taylor system) predicted a transition from the basic flow to a state with ribbons, which are traveling waves in the azimuthal direction but standing waves in the axial direction. We have observed the transition to ribbons in laboratory experiments and numerical simulations, and the measured wave speeds are in accord with those obtained numerically.

http://cfd.me.berkeley.edu/wp-content/uploads/2011/07/Nonlinear-Standing-Waves-in-Taylor-Couette-Flow.pdf

Randall Tagg

Papers

Photodynamic Therapy for Treatment of Solid Tumors — Potential and Technical Challenges

Primary instabilities and bicriticality in flow between counter-rotating cylinders

Control of a chaotic parametrically driven pendulum.

Transient turbulence in Taylor-Couette flow.

Nonlinear standing waves in Couette-Taylor flow.