We report a numerical study of van der Waals adsorption and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distribution of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to cros...

The article deals with the minimum-time running problem. The time of covering a given distance is minimized. The Hill-Keller model of running employed is based on Newton's second law and the equation of power balance. The problem is formulated in optimal control. The unknown function is the runner's velocity that varies with the distance. The problem is solved applying the direct Chebyshev's ps...

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental solution of the the Jacobi-Hill equation ü = −K(u)u....

The force-velocity characteristics of the primary pulvinus of Mimosa pudica have been determined using a new polytonic measurement technique. The contractile characteristics were determined from a modified form of Hill's equation (Hill, A. V. 1938. Proc. Roy. Soc. London B126: 136-195) describing the physiological contractile behavior of animal muscle. The values of the resulting Hill's constan...

Abstract The description of gel swelling by Flory and Rehner using the original Flory–Huggins interaction parameter for polymer–solvent cannot be applied to most smart microgels. Here, we compare descriptions curves such microgels series expansions $$\chi$$ ? with results Hill-like equation . We study N -isop...

Dose-response (or 'concentration-effect') relationships commonly occur in biological and pharmacological systems and are well characterised by Hill curves. These curves are described by an equation with two parameters: the inhibitory concentration 50% (IC50); and the Hill coefficient. Typically just the 'best fit' parameter values are reported in the literature. Here we introduce a Python-based...

Solutions of the Bethe ansatz equations associated to the XXX model of a simple Lie algebra g come in families called the populations. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra g . The proof is based on the correspondence between the solutions of the Bethe ansatz equations and special difference operators which we call the discrete Miura oper...

Critical points of a master function associated to a simple Lie algebra g come in families called the populations [MV1]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra g . The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a pop...

The paper is devoted to studying the behavior of solutions Cauchy problem for large values time—more precisely, obtaining an asymptotic expansion characterizing solution a one-dimensional second-order hyperbolic equation with periodic coefficients time parameter t. To obtain this as t→∞, methods spectral theory differential operators are used, well properties spectrum non-positive Hill operator...

Many scholars have used experimental research methods to conduct extensive on the impact energy release behavior of Polytetrafluoroethylene(PTFE)/Al reactive materials. However, in numerical simulation, PTFE/Al still lacks calculation parameters behavior. In order obtain simulation ignition, Hill mixture law was calculate material (mass ratio 73.5/26.5), and according Hugoniot curve γ state equ...