Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice

We investigate the connection between local and global dynamics in the Fermi -- Pasta -- Ulam (FPU) $\beta$ -- model from the point of view of stability of its simplest periodic orbits (SPOs). In particular, we show that there is a relatively high $q$ mode $(q=2(N+1)/{3})$ of the linear lattice, having one particle fixed every two oppositely moving ones (called SPO2 here), which can be exactly continued to the nonlinear case for $N=5+3m, m=0,1,2,...$ and whose first destabilization, $E_{2u}$, as the energy (or $\beta$) increases for {\it any} fixed $N$, practically {\it coincides} with the onset of a ``weak'' form of chaos preceding the break down of FPU recurrences, as predicted recently in a similar study of the continuation of a very low ($q=3$) mode of the corresponding linear chain. This energy threshold per particle behaves like $\frac{E_{2u}}{N}\propto N^{-2}$. We also follow exactly the properties of another SPO (with $q=(N+1)/{2}$) in which fixed and moving particles are interchanged (called SPO1 here) and which destabilizes at higher energies than SPO2, since $\frac{E_{1u}}{N}\propto N^{-1}$. We find that, immediately after their first destabilization, these SPOs have different (positive) Lyapunov spectra in their vicinity. However, as the energy increases further (at fixed $N$), these spectra converge to {\it the same} exponentially decreasing function, thus providing strong evidence that the chaotic regions around SPO1 and SPO2 have ``merged'' and large scale chaos has spread throughout the lattice.Comment: Physical Review E, 18 pages, 6 figure

Anatomical variation of a trifid (trifurcation) lateral root origin of the median nerve

Anatomic variations of the brachial plexus are common. Awareness of these variations is of paramount importance in clinical practice mainly in achieving best results in minimal invasive or surgical procedures. The aim of our study was to depict a case of a trifid lateral root origin of the medial nerve. This anatomical variation in the brachial plexus was encountered after dissection in upper extremities in a 90-year-old male cadaver

Site-specific characterisation of SARS-CoV-2 spike glycoprotein receptor binding domain

The novel coronavirus SARS-CoV-2, the infective agent causing COVID-19, is having a global impact both in terms of human disease as well as socially and economically. Its heavily glycosylated spike glycoprotein is fundamental for the infection process, via its receptor binding domains interaction with the glycoprotein angiotensin converting enzyme 2 on human cell surfaces. We therefore utilized an integrated glycomic and glycoproteomic analytical strategy to characterise both N- and O- glycan site specific glycosylation within the receptor binding domain. We demonstrate the presence of complex type N-glycans with unusual fucosylated LacdiNAc at both sites N331 and N343 and a single site of O-glycosylation on T323

Scaling similarities of multiple fracturing of solid materials

It has recently reported that electromagnetic flashes of low-energy <IMG WIDTH='12' HEIGHT='29' ALIGN='MIDDLE' BORDER='0' src='http://www.nonlin-processes-geophys.net/11/137/2004/npg-11-137-img1.gif' ALT='$gamma$'>-rays emitted during multi-fracturing on a neutron star, and electromagnetic pulses emitted in the laboratory by a disordered material subjected to an increasing external load, share distinctive statistical properties with earthquakes, such as power-law energy distributions (Cheng et al., 1996; Kossobokov et al., 2000; Rabinovitch et al., 2001; Sornette and Helmstetter, 2002). The neutron starquakes may release strain energies up to <IMG WIDTH='32' HEIGHT='16' ALIGN='BOTTOM' BORDER='0' src='http://www.nonlin-processes-geophys.net/11/137/2004/npg-11-137-img2.gif' ALT='$10^{46}$'>erg, while, the fractures in laboratory samples release strain energies approximately a fraction of an erg. An earthquake fault region can build up strain energy up to approximately <IMG WIDTH='32' HEIGHT='16' ALIGN='BOTTOM' BORDER='0' src='http://www.nonlin-processes-geophys.net/11/137/2004/npg-11-137-img3.gif' ALT='$10^{26}$'>erg for the strongest earthquakes. Clear sequences of kilohertz-megahertz electromagnetic avalanches have been detected from a few days up to a few hours prior to recent destructive earthquakes in Greece. A question that arises effortlessly is if the pre-seismic electromagnetic fluctuations also share the same statistical properties. Our study justifies a positive answer. Our analysis also reveals 'symptoms' of a transition to the main rupture common with earthquake sequences and acoustic emission pulses observed during laboratory experiments (Maes et al., 1998)

Chaotic Dynamics of N-degree of Freedom Hamiltonian Systems

We investigate the connection between local and global dynamics of two N-degree of freedom Hamiltonian systems with different origins describing one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a discretized version of the nonlinear Schrodinger equation related to Bose-Einstein Condensation (BEC). We study solutions starting in the vicinity of simple periodic orbits (SPOs) representing in-phase (IPM) and out-of-phase motion (OPM), which are known in closed form and whose linear stability can be analyzed exactly. Our results verify that as the energy E increases for fixed N, beyond the destabilization threshold of these orbits, all positive Lyapunov exponents exhibit a transition between two power laws, occurring at the same value of E. The destabilization energy E_c per particle goes to zero as N goes to infinity following a simple power-law. However, using SALI, a very efficient indicator we have recently introduced for distinguishing order from chaos, we find that the two Hamiltonians have very different dynamics near their stable SPOs: For example, in the case of the FPU system, as the energy increases for fixed N, the islands of stability around the OPM decrease in size, the orbit destabilizes through period-doubling bifurcation and its eigenvalues move steadily away from -1, while for the BEC model the OPM has islands around it which grow in size before it bifurcates through symmetry breaking, while its real eigenvalues return to +1 at very high energies. Still, when calculating Lyapunov spectra, we find for the OPMs of both Hamiltonians that the Lyapunov exponents decrease following an exponential law and yield extensive Kolmogorov--Sinai entropies per particle, in the thermodynamic limit of fixed energy density E/N with E and N arbitrarily large.Comment: 29 pages, 10 figures, published at International Journal of Bifurcation and Chaos (IJBC

Glyco-engineered MDCK cells display preferred receptors of H3N2 influenza absent in eggs used for vaccines

Evolution of human H3N2 influenza viruses driven by immune selection has narrowed the receptor specificity of the hemagglutinin (HA) to a restricted subset of human-type (Neu5Acα2-6 Gal) glycan receptors that have extended poly-LacNAc (Galβ1-4GlcNAc) repeats. This altered specificity has presented challenges for hemagglutination assays, growth in laboratory hosts, and vaccine production in eggs. To assess the impact of extended glycan receptors on virus binding, infection, and growth, we have engineered N-glycan extended (NExt) cell lines by overexpressing β3-Ν-acetylglucosaminyltransferase 2 in MDCK, SIAT, and hCK cell lines. Of these, SIAT-NExt cells exhibit markedly increased binding of H3 HAs and susceptibility to infection by recent H3N2 virus strains, but without impacting final virus titers. Glycome analysis of these cell lines and allantoic and amniotic egg membranes provide insights into the importance of extended glycan receptors for growth of recent H3N2 viruses and relevance to their production for cell- and egg-based vaccines

Successful network inference from time-series data using Mutual Information Rate

This work uses an information-based methodology to infer the connectivity of complex systems from observed time-series data. We first derive analytically an expression for the Mutual Information Rate (MIR), namely, the amount of information exchanged per unit of time, that can be used to estimate the MIR between two finite-length low-resolution noisy time-series, and then apply it after a proper normalization for the identification of the connectivity structure of small networks of interacting dynamical systems. In particular, we show that our methodology successfully infers the connectivity for heterogeneous networks, different time-series lengths or coupling strengths, and even in the presence of additive noise. Finally, we show that our methodology based on MIR successfully infers the connectivity of networks composed of nodes with different time-scale dynamics, where inference based on Mutual Information fails

Weak chaos detection in the Fermi-Pasta-Ulam-α\alpha system using qq-Gaussian statistics

We study numerically statistical distributions of sums of orbit coordinates, viewed as independent random variables in the spirit of the Central Limit Theorem, in weakly chaotic regimes associated with the excitation of the first ($k=1$) and last ($k=N$) linear normal modes of the Fermi-Pasta-Ulam-$\alpha$ system under fixed boundary conditions. We show that at low energies ($E=0.19$), when the $k=1$ linear mode is excited, chaotic diffusion occurs characterized by distributions that are well approximated for long times ($t>10^9$) by a $q$-Gaussian Quasi-Stationary State (QSS) with $q\approx1.4$. On the other hand, when the $k=N$ mode is excited at the same energy, diffusive phenomena are \textit{absent} and the motion is quasi-periodic. In fact, as the energy increases to $E=0.3$, the distributions in the former case pass through \textit{shorter} $q$-Gaussian states and tend rapidly to a Gaussian (i.e. $q\rightarrow 1$) where equipartition sets in, while in the latter we need to reach to E=4 to see a \textit{sudden transition} to Gaussian statistics, without any passage through an intermediate QSS. This may be explained by different energy localization properties and recurrence phenomena in the two cases, supporting the view that when the energy is placed in the first mode weak chaos and "sticky" dynamics lead to a more gradual process of energy sharing, while strong chaos and equipartition appear abruptly when only the last mode is initially excited.Comment: 12 pages, 3 figures, submitted for publication to International Journal of Bifurcation and Chaos. In honor of Prof. Tassos Bountis' 60th birthda