268 research outputs found
Optimal rates of decay for operator semigroups on Hilbert spaces
We investigate rates of decay for -semigroups on Hilbert spaces under
assumptions on the resolvent growth of the semigroup generator. Our main
results show that one obtains the best possible estimate on the rate of decay,
that is to say an upper bound which is also known to be a lower bound, under a
comparatively mild assumption on the growth behaviour. This extends several
statements obtained by Batty, Chill and Tomilov (J. Eur. Math. Soc., vol.
18(4), pp. 853-929, 2016). In fact, for a large class of semigroups our
condition is not only sufficient but also necessary for this optimal estimate
to hold. Even without this assumption we obtain a new quantified asymptotic
result which in many cases of interest gives a sharper estimate for the rate of
decay than was previously available, and for semigroups of normal operators we
are able to describe the asymptotic behaviour exactly. We illustrate the
strength of our theoretical results by using them to obtain sharp estimates on
the rate of energy decay for a wave equation subject to viscoelastic damping at
the boundary.Comment: 25 pages. To appear in Advances in Mathematic
Fluid Vesicles in Shear Flow
The shape dynamics of fluid vesicles is governed by the coupling of the flow
within the two-dimensional membrane to the hydrodynamics of the surrounding
bulk fluid. We present a numerical scheme which is capable of solving this flow
problem for arbitrarily shaped vesicles using the Oseen tensor formalism. For
the particular problem of simple shear flow, stationary shapes are found for a
large range of parameters. The dependence of the orientation of the vesicle and
the membrane velocity on shear rate and vesicle volume can be understood from a
simplified model.Comment: 10 pages, LaTeX2e, psfig, 5 eps figures included, to appear in Phys.
Rev. Lett., 199
Time resolved fission in metal clusters
We explore from a theoretical point of view pump and probe (P&P) analysis for
fission of metal clusters where probe pulses are generalized to allow for
scanning various frequencies. We show that it is possible to measure the time
the system needs to develop to scission. This is achieved by a proper choice of
both delay and frequency of the probe pulse. A more detailed analysis even
allows to access the various intermediate stages of the fission process.Comment: 4 pages, 4 figure
Wetting by critical layers
Interface depinning transitions such as wetting are described where the surface layer becomes critical as the interface unbinds from the wall. As a consequence, there are two different types of fluctuations, namely, capillary waves and critical fluctuations within the surface layer, which are shown to be governed by two different length scales
Adhesion of vesicles and membranes
In the presence of an attractive surface, a vesicle can undergo shape transformations between two different free states, between a free and a bound state, and between two different bound states. Adhesion can also lead to topological changes such as vesicle rupture and vesicle fusion. The interaction between the vesicle membrane and the surface is renormalized by thermally excited shape fluctuations. This renormalization leads to unbinding phenomena both for fluid and for polymerized (or solid-like) membranes
Adhesion of membranes : a theoretical perspective
We theoretically study (i) a large membrane segment and (ii) a closed membrane surface or vesicle that adhere to another surface. The membrane segment can undergo unbinding transitions as a result of thermally excited shape fluctuations. These transitions are studied by renormalization group methods and by Monte Carlo simulations. The shape of a bound vesicle is determined by the interplay of bending and adhesion energies. This interplay leads to adhesion transitions from a free to a bound vesicle state even in the absence of shape fluctuations. Our theory helps to clarify the notion of a contact angle for membranes
Adhesion of vesicles
A simple model for the adhesion of vesicles to interfaces and membranes is introduced and theoretically studied. It is shown that adhering (or bound) vesicles can exhibit a large variety of different shapes. The notion of a contact angle governed by tension is found to be applicable only for a restricted subset of these shapes. Furthermore, the vesicle undergoes a nontrivial adhesion transition from a free to a bound state. This transition is governed by the balance between the overall bending and adhesion energies, and occurs even in the absence of shape fluctuations
The Impact of National Culture on Mobile Commerce Adoption and Usage Intensity
The usage of mobile commerce increases around the world. However, little is known about why adoption and usage of mobile commerce services differ across countries. We address this question by analyzing the impact of national culture on mobile commerce adoption and usage intensity. Using a dataset that comprises individual consumer survey data from 43 countries across six continents and country-level data on Hofstedeâs six cultural dimensions, we study cross-cultural adoption and usage patterns pertaining three mobile commerce services, i.e. mobile banking, mobile shopping and mobile payment. Our results show that adoption and usage intensity are indeed affected by different cultural dimensions. Specifically, the adoption of mobile commerce services is negatively influenced by a countryâs level of uncertainty avoidance, while consumersâ usage intensity is driven by indulgence. This implies that providers of mobile commerce services need to tailor their market entry and market cultivation strategies accounting for each countryâs specific culture
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