171,192 research outputs found
Existence of Bounded Trajectories Via Upper and Lower Solutions
No full textThe paper deals with the boundary value problem (on the whole line) u''-f(u,u')+g(u)=0, u(-∞)=0, u(+∞)=1, where g is a continuous non-negative function with support [0, 1], and f is a continuous function. By means of a new approach, based on a combination of lower and upper-solutions methods and phase-plane techniques, we prove an existence result for the problem when f is superlinear in u'; by a similar technique, we also get a non-existence one. As an application, we investigate the attractivity of the singular point (0,0) in the phase-plane (u, u'). Applications of these results in the field of front-type solutions for reaction diffusion equations can be found in L. Malaguti, C. Marcelli, Math. Nachr. 242 (2002), 148—16
The Role of Three-Body Interactions on the Equilibrium and Non-Equilibrium Properties of Fluids from Molecular Simulation
No full textThe aim of this work is to use molecular simulation to investigate the role of
three-body interatomic potentials in noble gas systems for two distinct
phenomena: phase equilibria and shear flow. In particular we studied the
vapour-liquid coexisting phase for pure systems (argon, krypton and x enon) and
for an argon-krypton mixture, utilizing the technique called Monte Carlo Gibbs
ensemble. We also studied the dependence of the shear viscosity, pressure and
energy with the strain rate in planar Couette flow, using a non-equilibrium
molecular simulation (NEMD) technique.
The results we present in this work demonstrate that three-body interactions
play an important role in the overall interatomic interactions of noble gases. This
is demonstrated by the good agreement between our simulation results and the
experimental data for both equilibrium and non-equilibrium systems.
The good results for vapour-liquid coexisting phases encourage performing
further computer simulations with realistic potentials. This may improve the
prediction of quantities like critical temperature and density, in particular of
substances for which these properties are difficult to obtain from experiment.
We have demonstrated that use of accurate two- and three-body potentials for
shearing liquid argon and xenon displays significant departure from the
expected strain rate dependencies of the pressure, energy and shear viscosity.
For the first time, the pressure is convincingly observed to vary linearly with an
apparent analytic g&2 dependence, in contrast to the predicted g&3/ 2 dependence
of mode -coupling theory. Our best extrapolation of the zero -shear viscosity for
argon gives excellent agreement (within 1%) with the known experimental data.
To the best of our knowledge, this the first time that such accuracy has been
achieved with NEMD simulations. This encourages performing simulations with
accurate potentials for transport properties
Existence and multiplicity of heteroclinic solutions for a non-autonomous boundary eigenvalue problem
No full textIn this paper we investigate the boundary eigenvalue problem x''-b(c,t,x)x'+g(t,x)=0, x(-∞)=0, x(+∞)=1 depending on the real parameter c. We take the function b continuous and positive and assume that g is bounded and becomes active and positive only when it exceeds a threshold value theta in (0,1). At the point theta we allow g to have a jump. Additional monotonicity properties are required, when needed. Our main discussion deals with the non-autonomous case. In this context we prove the existence of a continuum of values for which this problem is solvable and we estimate the interval of such admissible values. In the autonomous case, we show its solvability for at most one c*. In the special case when b=c+h(x) with h continuous, we also give a non-existence result, for any real c. Our methods combine comparison-type arguments, both for first and second order dynamics, with a shooting technique. Some applications of the obtained results are included.In this paper we investigate the boundary eigenvalue problem (equation presented) depending on the real parameter c. We take β continuous and positive and assume that g is bounded and becomes active and positive only when x exceeds a threshold value θ ∈]0,1[. At the point θ we allow g(t, · ) to have a jump. Additional monotonicity properties are required, when needed. Our main discussion deals with the non-autonomous case. In this context we prove the existence of a continuum of values c for which this problem is solvable and we estimate the interval of such admissible values. In the autonomous case, we show its solvability for at most one c*. In the special case when β reduces to c + h(x) with h continuous, we also give a non-existence result, for any real c. Our methods combine comparison-type arguments, both for first and second order dynamics, with a shooting technique. Some applications of the obtained results are included
Sharp profiles in degenerate and doubly-degenerate Fisher-KPP equations
No full textThis paper investigates the effects of a degenerate diffusion term in reaction-diffusion models ut=[D(u)ux]x + g(u) with Fisher-KPP type g. Both in the case when D(0) = 0 and when D(0) = D(l) = 0, with D(u) > 0 elsewhere, we obtain a continuum of travelling wave solutions having wave speed c greater than a threshold value c* and we show the appearance of a sharp-type profile when c = c*. These results solve recent conjectures formulated by Sanchez-Garduno and Maini (J. Differential Equations 117 (1995) 281) and Satnoianu et al. (Discrete Continuous Dyn. Systems (Series B) 1 (2000) 339)
Heteroclinic Orbits in Plane Dynamical Systems
No full textWe consider general second order boundary value problems on the whole line of the type u''=h(t, u, u'), u(-∞)=0, u(+∞)=1, for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the (u, u') plane dynamical system
Traveling waves for highly degenerate and singular reaction-diffusion-advection equations with discontinuous coefficients
No full textSufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are furnished. Under an additional hypothesis on the convection term, the set of admissible wave speeds is characterized in terms of the minimum wave speed, which is estimated through a double-sided bound. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies
Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms
No full textThis paper deals with the appearance of monotone bounded travelling wave solutions for a parabolic reaction-diffusion equation which frequently meets both in chemical and biological systems. In particular, we prove the existence of monotone front type solutions for any wave speed c greater than or equal to c* and give an estimate for the threshold value c*. Our model takes into account both of a density dependent diffusion term and of a non-linear convection effect. Moreover, we do not require the main non-linearity g to be a regular C1 function; in particular we are able to treat both the case when g'(0) = 0, giving rise to a degenerate equilibrium point in the phase plane, and the singular case when g'(0) = +∞. Our results generalize previous ones due to ARONSON and WEINBERGER [Adv. Math. 30 (1978), pp. 33 - 76], GIBBS and MURRAY (see MURRAY [Mathematical Biology, Springer-Verlag, Berlin, 1993]) and MCCABE, LEACH and NEEDHAM [SIAM J. Appl. Math. 59 (1998), pp. 870-899]. Finally, we obtain our conclusions by means of a comparison-type technique which was introduced and developed in this framework in a recent paper by the same authors
Do handwriting difficulties of Parkinson's patients depend on their impaired ability to retain the motor plan? A pilot study
No full textPatients affected by Parkinson’s disease (PD) show deficits in learning novel motor behaviors and executing previously acquired ones. We investigated whether the two phenomena are related, evaluating the hypothesis that PD patients have difficulties in executing fine movements (such as handwriting) acquired before the onset of the disease since they perform the task as they are executing it for the first time. We asked healthy subjects to write a sequence of ‘l’ on a digitizer tablet by drawing the loop of the letter in counterclockwise fashion (as they are used to do) and clockwise fashion (i.e. using a novel motor plan). We compared the kinematic features of the samples produced by healthy subjects to those measured in samples produced by PD patients. We focused the analysis on the ink trace segmentation points, which represent the starting/ending points of the elementary handwriting movements. Our results suggests that deficits observed in PD patients in executing both novel tasks (reduced learning performance compared to controls) and previously acquired task (disrupted kinematic features compared to controls) could be due to the same underlying deficit, i.e. impaired ability of PD patients to retain the motor plan associated to the task
Remarks on growth conditions in calculus of variations
No full textWe discuss some classical growth assumptions for the integrands of the calculus of variations and compare them with a new local condition we are introducing in the present paper. Our existence result has great advantages with respect to applications, as examples show
Opinions regarding outcome differences in European and US haemodialysis patients
No full textStudy goal and design. The aim of this evaluation was to understand why outcomes seem to be different in different parts of the world. Ln an attempt to look at this question from a point of view other than that necessarily adopted by epidemiological studies, we decided to explore the personal opinion of a selected group of American (US and European (EU) experts by means of a simple questionnaire. A 13-item questionnaire was sent to 14 internationally recognized opinion leaders in the field of haemodialysis: all seven Europeans and five of the seven Americans responded. The answers to each question were stratified in order to highlight the key differences between the experts in the different continents. Results. Ten of the 12 respondents (six EU and four US) said that dialysis outcomes are better in Europe; nine (six EU and three US) confirmed their opinion after taking patient characteristics into account. When asked to suggest reasons for this difference, the highest score was given to the quality of procedures and medical training with no differences between EU and US physicians. This was followed by three other factors that received the same overall score (financial issues, doctor bedside time and quality of pre-dialysis care), but it is interesting to note that the Europeans attributed considerably greater importance to bedside time than their US counterparts. Conclusion. It seems that the reported difference in dialysis outcomes between Europe and the US is a widely accepted fact. Although directed towards few respondents, our questionnaire does suggest some differences in the approach towards dialysis and endstage renal disease patients
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