Nonclassical Potential Symmetry Generators of Differential Equations

We determine the nonclassical potential symmetries for a number ofequations that arise in the literature. A large number of these areobtained for some equations which only admit a single potential(classical) symmetry (e.g., the wave equation and the motion of wavesthrough some medium). However, we show that some of the exact solutionsinvariant under the nonclassical potential symmetries are equivalent toknown solutions but these solutions are not obtainable through theclassical point or potential symmetries. The Korteweg–deVries equation,it is shown, does not admit nonclassical potential symmetries – as inthe classical case.     

Group theoretic methods for approximate invariants and Lagrangians for some classes of y″+εF(t)y′+y=f(y,y′)

Some recent results on the Lie symmetry generators of equations with a small parameter and the relationship between symmetries and conservation laws for such equations are used to construct first integrals and Lagrangians for autonomous weakly non-linear systems, y″+εF(t)y′+y=f(y,y′). An adaptation of a theorem that provides the point symmetry generators that leave the invariant functional involving a Lagrangian for such equations is presented. A detailed example to illustrate the method is given (and other examples are discussed). The (approximate) symmetry generators, invariants and Lagrangians maintain the perturbation order of the ‘small parameter’ stipulated in the equation — first order in this case.     

On Entropy,Information, and Conservation of Information

The term entropy is used in different meanings in different contexts, sometimes in contradictory ways, resulting in misunderstandings and confusion. The root cause of the problem is the close resemblance of the defining mathematical expressions of entropy in statistical thermodynamics and information in the communications field, also called entropy, differing only by a constant factor with the unit ‘J/K’ in thermodynamics and ‘bits’ in the information theory. The thermodynamic property entropy is closely associated with the physical quantities of thermal energy and temperature, while the entropy used in the communications field is a mathematical abstraction based on probabilities of messages. The terms information and entropy are often used interchangeably in several branches of sciences. This practice gives rise to the phrase conservation of entropy in the sense of conservation of information, which is in contradiction to the fundamental increase of entropy principle in thermodynamics as an expression of the second law. The aim of this paper is to clarify matters and eliminate confusion by putting things into their rightful places within their domains. The notion of conservation of information is also put into a proper perspective.     

Unraveling the Nature of Sites Active toward Hydrogen Peroxide Reduction in Fe-N-C Catalysts

Fe-N-C catalysts with high O₂ reduction performance are crucial for displacing Pt in low-temperature fuel cells. However, insufficient understanding of which reaction steps are catalyzed by what sites limits their progress. The nature of sites were investigated that are active toward H₂O₂ reduction, a key intermediate during indirect O₂ reduction and a source of deactivation in fuel cells. Catalysts comprising different relative contents of FeN_xC_y moieties and Fe particles encapsulated in N-doped carbon layers (0–100 %) show that both types of sites are active, although moderately, toward H₂O₂ reduction. In contrast, N-doped carbons free of Fe and Fe particles exposed to the electrolyte are inactive. When catalyzing the ORR, FeN_xC_y moieties are more selective than Fe particles encapsulated in N-doped carbon. These novel insights offer rational approaches for more selective and therefore more durable Fe-N-C catalysts.     

Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains

On complete pseudoconvex Reinhardt domains in ?², we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in ?² that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite dimensional and the Hankel operator \({H_{{{\bar z}_1}{{\bar z}_2}}}\) is Hilbert-Schmidt.     

Dielectrophoretic characterization of macrophage phenotypes

Different macrophage phenotypes play important roles in diverse biological processes and diseases. In this study, we have characterized the dielectrophoretic responses of human monocytes and macrophage phenotypes: nonactivated (M0), pro-inflammatory (M1), and pro-healing (M2a). Dielectrophoretic responses of cells change as a function of frequency of the applied electric field. We measured the crossover frequency at which cells transition from negative to positive dielectrophoresis (DEP) or vice versa using interdigitated electrodes. For these characterization experiments, we also developed a new low-conductivity media formulation that retained 100% of the initial viability for 1 h. Human THP1 monocytes showed a distinguishable DEP response from mature macrophages. M1 macrophages also showed a distinct DEP response compared to M0 and M2a macrophages. No clear distinction could be drawn between M0 and M2a. The median values of the crossover frequencies of monocytes, M0, M1, and M2a were 38, 21, 11, and 23 kHz, respectively. Membrane capacitances of these cells were calculated consequently, and the values were 0.0111, 0.0128, 0.0244, and 0.0117 F/m² for monocytes, M0, M1, and M2a, respectively. These results show how bioelectric properties are influenced by changes in macrophage phenotype.     

Thermal Phase Transitions of IOTA Carrageenan in CaCl2 Solutions: A Fluorescence Study

The fluorescence technique was employed to study thermal phase transitions of iota (ι-) carrageenan (IC) in CaCl₂ solution. IC gels underwent coil to double helix (c-h) and double helix to dimer (h-d) transitions upon cooling. Upon heating IC gels presented dimer to double helix (d-h) and double helix to coil (h-c) transitions, showing hysteresis types of transition paths. Scattered light, I_sc and fluorescence intensity, I, were monitored against temperature to determine phase transitions. Transition temperatures were determined from the derivative of the transition paths. The critical gel fraction exponent, β, was measured and found to be in accord with the classic Flory–Stockmayer model.