131 research outputs found
Non-convex-valued differential inclusions in Banach spaces
Digitalitzat per Artypla
Estimating long term behavior of flows without trajectory integration: the infinitesimal generator approach
The long-term distributions of trajectories of a flow are described by
invariant densities, i.e. fixed points of an associated transfer operator. In
addition, global slowly mixing structures, such as almost-invariant sets, which
partition phase space into regions that are almost dynamically disconnected,
can also be identified by certain eigenfunctions of this operator. Indeed,
these structures are often hard to obtain by brute-force trajectory-based
analyses. In a wide variety of applications, transfer operators have proven to
be very efficient tools for an analysis of the global behavior of a dynamical
system.
The computationally most expensive step in the construction of an approximate
transfer operator is the numerical integration of many short term trajectories.
In this paper, we propose to directly work with the infinitesimal generator
instead of the operator, completely avoiding trajectory integration. We propose
two different discretization schemes; a cell based discretization and a
spectral collocation approach. Convergence can be shown in certain
circumstances. We demonstrate numerically that our approach is much more
efficient than the operator approach, sometimes by several orders of magnitude
Comparison of averages of flows and maps
It is shown that in transient chaos there is no direct relation between
averages in a continuos time dynamical system (flow) and averages using the
analogous discrete system defined by the corresponding Poincare map. In
contrast to permanent chaos, results obtained from the Poincare map can even be
qualitatively incorrect. The reason is that the return time between
intersections on the Poincare surface becomes relevant. However, after
introducing a true-time Poincare map, quantities known from the usual Poincare
map, such as conditionally invariant measure and natural measure, can be
generalized to this case. Escape rates and averages, e.g. Liapunov exponents
and drifts can be determined correctly using these novel measures. Significant
differences become evident when we compare with results obtained from the usual
Poincare map.Comment: 4 pages in Revtex with 2 included postscript figures, submitted to
Phys. Rev.
Diffusion in normal and critical transient chaos
In this paper we investigate deterministic diffusion in systems which are
spatially extended in certain directions but are restricted in size and open in
other directions, consequently particles can escape. We introduce besides the
diffusion coefficient D on the chaotic repeller a coefficient which
measures the broadening of the distribution of trajectories during the
transient chaotic motion. Both coefficients are explicitly computed for
one-dimensional models, and they are found to be different in most cases. We
show furthermore that a jump develops in both of the coefficients for most of
the initial distributions when we approach the critical borderline where the
escape rate equals the Liapunov exponent of a periodic orbit.Comment: 4 pages Revtex file in twocolumn format with 2 included postscript
figure
Bursts in the Chaotic Trajectory Lifetimes Preceding the Controlled Periodic Motion
The average lifetime () it takes for a randomly started trajectory
to land in a small region () on a chaotic attractor is studied. is
an important issue for controlling chaos. We point out that if the region
is visited by a short periodic orbit, the lifetime strongly deviates
from the inverse of the naturally invariant measure contained within that
region (). We introduce the formula that relates
to the expanding eigenvalue of the short periodic orbit
visiting .Comment: Accepted for publication in Phys. Rev. E, 3 PS figure
marker tracking for local strain measurement in mechanical testing of biomedical materials
Local strain measurement is one of the key aspects in tensile tests of biomedical materials and biological tissues, especially if aimed at developing appropriate constitutive formulations to describe mechanical behavior. The measurement of strain as the ratio between the current and the initial length of the sample can be coupled with markers recognition via non-contact video extensometer for characterizing the local mechanical behavior. A crucial point in video extensometer measurement is the selection of the most appropriate markers and technique of their application on the sample surface. This work promotes understanding the effect of markers on material mechanical response. Different solutions were taken into account, as paint markers, namely a commercial lacquer and an acrylic paint, or physical markers attached with the use of adhesives, i.e. cyanoacrylate or medical spray band. Tensile tests revealed that markers can modify the mechanical response of the tested materials, inducing a local stiffening of the samples. The use of cyanoacrylate, as marker adhesive, affects not only the local but also the overall mechanical response, at least for the sample size considered in this work. These effects are more pronounced with higher material compliance. Based on these results, caution is recommended with the use of cyanoacrylate for attaching markers on biomedical polymers
Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems
For a fixed initial reference measure, we study the dependence of the escape
rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we
prove the existence and Holder continuity of the escape rate for systems with
small holes admitting Young towers. Then we consider general holes for Anosov
diffeomorphisms, without size or Markovian restrictions. We prove bounds on the
upper and lower escape rates using the notion of pressure on the survivor set
and show that a variational principle holds under generic conditions. However,
we also show that the escape rate function forms a devil's staircase with jumps
along sequences of regular holes and present examples to elucidate some of the
difficulties involved in formulating a general theory.Comment: 21 pages. v2 differs from v1 only by additions to the acknowledgment
Spectral degeneracy and escape dynamics for intermittent maps with a hole
We study intermittent maps from the point of view of metastability. Small
neighbourhoods of an intermittent fixed point and their complements form pairs
of almost-invariant sets. Treating the small neighbourhood as a hole, we first
show that the absolutely continuous conditional invariant measures (ACCIMs)
converge to the ACIM as the length of the small neighbourhood shrinks to zero.
We then quantify how the escape dynamics from these almost-invariant sets are
connected with the second eigenfunctions of Perron-Frobenius (transfer)
operators when a small perturbation is applied near the intermittent fixed
point. In particular, we describe precisely the scaling of the second
eigenvalue with the perturbation size, provide upper and lower bounds, and
demonstrate convergence of the positive part of the second eigenfunction
to the ACIM as the perturbation goes to zero. This perturbation and associated
eigenvalue scalings and convergence results are all compatible with Ulam's
method and provide a formal explanation for the numerical behaviour of Ulam's
method in this nonuniformly hyperbolic setting. The main results of the paper
are illustrated with numerical computations.Comment: 34 page
Evaluation of a microbiological screening and acceptance procedure for cryopreserved skin allografts based on 14Â day cultures
Viable donor skin is still considered the gold standard for the temporary covering of burns. Since 1985, the Brussels military skin bank supplies cryopreserved viable cadaveric skin for therapeutic use. Unfortunately, viable skin can not be sterilised, which increases the risk of disease transmission. On the other hand, every effort should be made to ensure that the largest possible part of the donated skin is processed into high-performance grafts. Cryopreserved skin allografts that fail bacterial or fungal screening are reworked into âsterileâ non-viable glycerolised skin allografts. The transposition of the European Human Cell and Tissue Directives into Belgian Law has prompted us to install a pragmatic microbiological screening and acceptance procedure, which is based on 14Â day enrichment broth cultures of finished product samples and treats the complex issues of âacceptable bioburdenâ and âabsence of objectionable organismsâ. In this paper we evaluate this procedure applied on 148 skin donations. An incubation time of 14Â days allowed for the detection of an additional 16.9% (25/148) of contaminated skin compared to our classic 3Â day incubation protocol and consequently increased the share of non-viable glycerolised skin with 8.4%. Importantly, 24% of these slow-growing microorganisms were considered to be potentially pathogenic. In addition, we raise the issue of ârepresentative samplingâ of heterogeneously contaminated skin. In summary, we feel that our present microbiological testing and acceptance procedure assures adequate patient safety and skin availability. The question remains, however, whether the supposed increased safety of our skin grafts outweighs the reduced overall clinical performance and the increase in work load and costs
Open Mushrooms: Stickiness revisited
We investigate mushroom billiards, a class of dynamical systems with sharply
divided phase space. For typical values of the control parameter of the system
, an infinite number of marginally unstable periodic orbits (MUPOs) exist
making the system sticky in the sense that unstable orbits approach regular
regions in phase space and thus exhibit regular behaviour for long periods of
time. The problem of finding these MUPOs is expressed as the well known problem
of finding optimal rational approximations of a real number, subject to some
system-specific constraints. By introducing a generalized mushroom and using
properties of continued fractions, we describe a zero measure set of control
parameter values for which all MUPOs are destroyed and therefore
the system is less sticky. The open mushroom (billiard with a hole) is then
considered in order to quantify the stickiness exhibited and exact leading
order expressions for the algebraic decay of the survival probability function
are calculated for mushrooms with triangular and rectangular stems.Comment: 21 pages, 11 figures. Includes discussion of a three-dimensional
mushroo
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