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The evaporation of multiple sessile droplets is both scientifically interesting and practically important, occurring in many natural and industrial applications. Although there are simple analytic expressions to predict evaporation rates of single droplets, there are no such frameworks for general configurations of droplets of arbitrary size, contact angle or spacing. However, a recent theoretical contribution by Masoud, Howell & Stone (J. Fluid Mech., vol. 927, 2021, R4) shows how considerable insight can be gained into the evaporation of arbitrary configurations of droplets without having either to obtain the solution for the concentration of vapour in the atmosphere or to perform direct numerical simulations of the full problem. The theoretical predictions show excellent agreement with simulations for all configurations, only deviating by 25 % for the most confined droplets.

Induction of humoral responses to HIV at mucosal compartments without inflammation is important for vaccine design. We developed charged wax nanoparticles that efficiently adsorb protein antigens and are internalized by DC in the absence of inflammation. HIV-gp140-adsorbed nanoparticles induced stronger in vitro T-cell proliferation responses than antigen alone. Such responses were greatly enhanced when antigen was co-adsorbed with TLR ligands. Immunogenicity studies in mice showed that intradermal vaccination with HIV-gp140 antigen-adsorbed nanoparticles induced high levels of specific IgG. Importantly, intranasal immunization with HIV-gp140-adsorbed nanoparticles greatly enhanced serum and vaginal IgG and IgA responses. Our results show that HIV-gp140-carrying wax nanoparticles can induce strong cellular/humoral immune responses without inflammation and may be of potential use as effective mucosal adjuvants for HIV vaccine candidates.

We consider the problem of how to recover the state and parameter values of typical model neurons, such as Hindmarsh-Rose, FitzHugh-Nagumo, Morris-Lecar, from in-vitro measurements of membrane potentials. In control theory, in terms of observer design, model neurons qualify as locally observable. However, unlike most models traditionally addressed in control theory, no parameter-independent diffeomorphism exists, such that the original model equations can be transformed into adaptive canonic observer form. For a large class of model neurons, however, state and parameter reconstruction is possible nevertheless. We propose a method which, subject to mild conditions on the richness of the measured signal, allows model parameters and state variables to be reconstructed up to an equivalence class. © 2010 World Scientific Publishing Company.

We consider the problem of state and parameter estimation for a class of nonlinear oscillators defined as a system of coupled nonlinear ordinary differential equations. Observable variables are limited to a few components of state vector and an input signal. This class of systems describes a set of canonic models governing the dynamics of evoked potential in neural membranes, including Hodgkin-Huxley, Hindmarsh-Rose, FitzHugh-Nagumo, and Morris-Lecar models. We consider the problem of state and parameter reconstruction for these models within the classical framework of observer design. This framework offers computationally-efficient solutions to the problem of state and parameter reconstruction of a system of nonlinear differential equations, provided that these equations are in the so-called adaptive observer canonic form. We show that despite typical neural oscillators being locally observable they are not in the adaptive canonic observer form. Furthermore, we show that no parameter-independent diffeomorphism exists such that the original equations of these models can be transformed into the adaptive canonic observer form. We demonstrate, however, that for the class of Hindmarsh-Rose and FitzHugh-Nagumo models, parameter-dependent coordinate transformations can be used to render these systems into the adaptive observer canonical form. This allows reconstruction, at least partially and up to a (bi)linear transformation, of unknown state and parameter values with exponential rate of convergence. In order to avoid the problem of only partial reconstruction and at the same time to be able to deal with more general nonlinear models in which the unknown parameters enter the system nonlinearly, we present a new method for state and parameter reconstruction for these systems. The method combines advantages of standard Lyapunov-based design with more flexible design and analysis techniques based on the notions of positive invariance and small-gain theorems. We show that this flexibility allows to overcome ill-conditioning and non-uniqueness issues arising in this problem. Effectiveness of our method is illustrated with simple numerical examples.