12,162 research outputs found
Regularization of moving boundaries in a Laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results
The dynamics of ionization fronts that generate a conducting body, are in
simplest approximation equivalent to viscous fingering without regularization.
Going beyond this approximation, we suggest that ionization fronts can be
modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact
uniformly propagating solutions of this problem in 2D and construct a single
partial differential equation governing small perturbations of these solutions.
For some parameter value, this equation can be solved analytically which shows
that the uniformly propagating solution is linearly convectively stable.Comment: 4 pages, 1 figur
Nonlinear physics of electrical wave propagation in the heart: a review
The beating of the heart is a synchronized contraction of muscle cells
(myocytes) that are triggered by a periodic sequence of electrical waves (action
potentials) originating in the sino-atrial node and propagating over the atria and
the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF)
or ventricular tachycardia (VT) are caused by disruptions and instabilities of these
electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent
wave patterns (AF,VF). Numerous simulation and experimental studies during the
last 20 years have addressed these topics. In this review we focus on the nonlinear
dynamics of wave propagation in the heart with an emphasis on the theory of pulses,
spirals and scroll waves and their instabilities in excitable media and their application
to cardiac modeling. After an introduction into electrophysiological models for action
potential propagation, the modeling and analysis of spatiotemporal alternans, spiral
and scroll meandering, spiral breakup and scroll wave instabilities like negative line
tension and sproing are reviewed in depth and discussed with emphasis on their impact
in cardiac arrhythmias.Peer ReviewedPreprin
The complex life of hydrodynamic modes
We study analytic properties of the dispersion relations in classical
hydrodynamics by treating them as Puiseux series in complex momentum. The radii
of convergence of the series are determined by the critical points of the
associated complex spectral curves. For theories that admit a dual
gravitational description through holography, the critical points correspond to
level-crossings in the quasinormal spectrum of the dual black hole. We
illustrate these methods in supersymmetric Yang-Mills theory in
3+1 dimensions, in a holographic model with broken translation symmetry in 2+1
dimensions, and in conformal field theory in 1+1 dimensions. We comment on the
pole-skipping phenomenon in thermal correlation functions, and show that it is
not specific to energy density correlations.Comment: V3: 54 pages, 18 figures. Appendix added. Version to appear in JHE
Computational study of resting state network dynamics
Lo scopo di questa tesi è quello di mostrare, attraverso una simulazione con il software The Virtual Brain, le più importanti proprietà della dinamica cerebrale durante il resting state, ovvero quando non si è coinvolti in nessun compito preciso e non si è sottoposti a nessuno stimolo particolare. Si comincia con lo spiegare cos’è il resting state attraverso una breve revisione storica della sua scoperta, quindi si passano in rassegna alcuni metodi sperimentali utilizzati nell’analisi dell’attività cerebrale, per poi evidenziare la differenza tra connettività strutturale e funzionale. In seguito, si riassumono brevemente i concetti dei sistemi dinamici, teoria indispensabile per capire un sistema complesso come il cervello. Nel capitolo successivo, attraverso un approccio ‘bottom-up’, si illustrano sotto il profilo biologico le principali strutture del sistema nervoso, dal neurone alla corteccia cerebrale. Tutto ciò viene spiegato anche dal punto di vista dei sistemi dinamici, illustrando il pionieristico modello di Hodgkin-Huxley e poi il concetto di dinamica di popolazione. Dopo questa prima parte preliminare si entra nel dettaglio della simulazione. Prima di tutto si danno maggiori informazioni sul software The Virtual Brain, si definisce il modello di network del resting state utilizzato nella simulazione e si descrive il ‘connettoma’ adoperato. Successivamente vengono mostrati i risultati dell’analisi svolta sui dati ricavati, dai quali si mostra come la criticità e il rumore svolgano un ruolo chiave nell'emergenza di questa attività di fondo del cervello. Questi risultati vengono poi confrontati con le più importanti e recenti ricerche in questo ambito, le quali confermano i risultati del nostro lavoro. Infine, si riportano brevemente le conseguenze che porterebbe in campo medico e clinico una piena comprensione del fenomeno del resting state e la possibilità di virtualizzare l’attività cerebrale
In-Medium Spectral Functions of Vector- and Axial-Vector Mesons from the Functional Renormalization Group
In this work we present first results on vector and axial-vector meson
spectral functions as obtained by applying the non-perturbative functional
renormalization group approach to an effective low-energy theory motivated by
the gauged linear sigma model. By using a recently proposed analytic
continuation method, we study the in-medium behavior of the spectral functions
of the and mesons in different regimes of the phase diagram. In
particular, we demonstrate explicitly how these spectral functions degenerate
at high temperatures as well as at large chemical potentials, as a consequence
of the restoration of chiral symmetry. In addition, we also compute the
momentum dependence of the and spectral functions and discuss the
various time-like and space-like processes that can occur.Comment: 18 pages, 13 figures, 1 tabl
The renormalized and Renormalization-Group invariant Hartree-Fock approximation
We study the renormalization problem for the Hartree--Fock approximation of
the invariant model in the symmetric phase and show how to
systematically improve the corresponding diagrammatic resummation to achieve
the correct renormalization properties of the effective field equations,
including Renormalization--Group invariance with the one--loop beta function.
These new Hartree--Fock dynamics is still of mean field type but includes
memory effects which are generically nonlocal also in space.Comment: 32 pages, 13 figure
- …