Αρχεία: Tooltips

Fractal interpolation functions (FIFs) are a powerful mathematical tool used to model complicated patterns that arise in natural phenomena. By leveraging fractal geometry, FIFs create continuous, piecewise smooth curves or surfaces that retain the intricate details of the data they interpolate. These functions extend classical interpolation techniques by incorporating fractal concepts, allowing for the generation of curves with highly irregular yet predictable structures. In this talk, we will explore the foundational principles of fractal interpolation, its applications in various fields such as image processing, computer graphics, and signal analysis, and demonstrate the advantages of using FIFs over traditional interpolation methods. Additionally, we will discuss the theoretical underpinnings and practical implementation of these functions to better understand their potential and versatility in data representation.

The question of whether features and behaviors that are characteristic to completely integrable systems persist in the transition to non-integrable settings is a central one in the study of nonlinear evolution equations. This issue is closely related to the broader problem of the stability of evolution equations. Another fundamental question concerns the lifespan of solutions: whether it is infinite or finite distinguishes between global-in-time existence and instability phenomena, the latter manifested as blow-up in finite time. We examine these questions in the context of the Nonlinear Schrödinger Equation (NLS) and NLS-type lattices, supplemented with nonzero boundary conditions at infinity. Numerical investigations, based on high-accuracy schemes, highlight the relevance of the accompanying mathematical analysis and yield numerical results in excellent agreement with theoretical predictions.

After an introduction to the structure of nucleic acids DNA and RNA, we will focus on periodic and aperiodic (quasi periodic, fractal and random) nucleotide sequences. We will give some attention to genetically determined sequences. We discern charge transfer from charge transport. We give prominence to the role of trimers or codons. We discern coherent processes (quantum transmission) from incoherent or thermal processes (hopping). We will describe our methods, i.e., tight binding (TB) variants (coarse grained or at the atomic level) and based on density functional theory (DFT). Next, we will present results [1, 2, 3, 4] concerning charge transfer and transport in periodic and aperiodic nucleotide sequences. Finally, we will give an overview.

Στην ομιλία αυτή θα εστιάσουμε στις βασικές έννοιες του κλάδου που ονομάζεται Επιστήμη της Πολυπλοκότητας και θα αναφερθούμε σε θεμελιώδεις της αρχές για την κατανόηση της Φύσης, από άποψη στατικής αλλά και δυναμικής συμπεριφοράς. Πρώτα θα περιγράψουμε εφαρμογές της Πολυπλοκότητας σε γεωμετρικές μορφές φύλλων και δένδρων, και θα ανακαλύψουμε ότι οδηγούν σε σχήματα με μη ακέραιες διαστάσεις που ονομάζονται φράκταλ. Κατόπιν θα μιλήσουμε για ομαδικές κινήσεις πουλιών ή ψαριών και τη λειτουργία του εγκεφάλου.  Για να γίνουν καλύτερα αντιληπτές οι ως άνω έννοιες, τις παρουσιάζω εδώ μέσω απλών παραδειγμάτων στα οποία έχω και εγώ εργαστεί. Κατά τη διάρκεια του 31^ου Σχολείου, θα έχουμε την ευκαιρία να τις αναλύσουμε περαιτέρω και να αντιληφθούμε την μεγάλη προσφορά της Επιστήμης της Πολυπλοκότητας σε πάμπολλα θέματα φυσικών αλλά και βιολογικών επιστημών.

Since their discovery in the early 1960s, Josephson junctions (JJs) remain at the forefront of advancing technology in superconducting electronics, sensing, high-frequency devices, and quantum science. An important JJ-based device is the superconducting quantum interference device (SQUID), a highly sensitive magnetometer that uses JJs to measure extremely small magnetic fields. From a dynamical point of view, the SQUID is a highly nonlinear system exhibiting extreme multistablity and chaos. In the first part of my presentation, I will talk about the complex dynamics of SQUID oligomers and metamaterials, i. e. artificially structured media of periodically arranged, weakly coupled elements, which show extraordinary electromagnetic properties and tunability. Another fascinating application of JJs involves their exploration for the design of superconducting neuromorphic computing systems. When combined in circuits, coupled JJs can emulate sophisticated properties found in biological neurons. From a technological point of view, JJ-based neuromorphic systems are particularly appealing due to their capacity to operate in great speeds and with low energy. In the second part of my talk I will present recent work on such JJ-based systems and discuss the mechanisms underlying the exhibited dynamical properties relevant for neurocomputation.

Στην ομιλία αυτή θα συζητήσουμε εφαρμογές της μορφοκλασματικής γεωμετρίας στην μικροηλεκτρονική και της πολυπλοκότητας στη νανοτεχνολογία. Και στις δύο περιπτώσεις το σημείο επαφής θα είναι η τραχύτητα των επιφανειών στη νανοκλίμακα. Στην περίπτωση της μικροηλεκτρονικής θα εστιάσουμε στην τραχύτητα των επιφανειών της δομής των τρανζίστορ στο πρώτο στάδιο της λιθογραφικής σχηματοποίησής τους, ενώ στη νανοτεχνολογία θα εισάγουμε την έννοια της πολυπλοκότητας επιφανειών και θα διερευνήσουμε τη σύνδεσή της με τις ιδιότητες των επιφανειών (κυρίως οπτικές και διαβροχής) και τις άλλες μεθόδους περιγραφής της μορφολογίας τους. Θα τονίσουμε την κρίσιμη σημασία της τραχύτητας και της στοχαστικότητας στη σύγχρονη βιομηχανία των ημιαγωγών και τη σύνδεσή τους με τη μετάβαση από την αρχιτεκτονική von Neumman στις νευρομορφικές προσεγγίσεις. Τέλος, θα επιστρέψουμε σε ποιους θεωρητικούς προβληματισμούς και θα συζητήσουμε κατά πόσο μπορούμε να ορίσουμε την πολυπλοκότητα μιας επιφάνειας ως την αντίστασή της στην ομογενοποίησή της.

To be added soon…

Today’s world is full of instances of hyper-exponential growth (HEG). Clear examples of HEG have been identified, including the increase of the human population, the world economy and many aspects of technology. While hyper-exponential growth appears less often in natural sciences than exponential growth, it is especially important to understand of much that is happening today. Models of HEG have been developed to understand biological phenomena such as cancer growth and the dynamics of epidemics such as SARS-CoV-2. In this talk I will develop an epidemic model with evolution of transmission rates to show how HEG emerges naturally in a complex biological system. Solving the equations of growth, I show how many of the phenomena associated with HEG, such as asymptotic increase in finite time, can be understood. Finally, I apply these insights to the wider issues of importance, such as what is the nature of the collapse of hyper-exponential growth if it happens.

We present the theory of chaos. We give the definition of chaos and some examles and counterexamples. We concentrate on the chaotic set of the smale horseshoe and we prove that it is chaotic through its topological conjugacy with sympolic dynamics i.e. the Bernoulli shift on the doubly infinite series of symbols. Finally we present the Melnikov theorem that proves chaos through the tranverse intersection of the stable and unstable manifolds of a saddle point in a Poincare map of a one and a half degrees of freedom periodic system of differential equations.

The earthquake generation process is a complex phenomenon, manifested in the nonlinear dynamics and in the wide range of spatial and temporal scales that are incorporated in the process. Despite the complexity of the earthquake generation process and our limited knowledge on the physical processes that lead to the initiation and propagation of a seismic rupture giving rise to earthquakes, the collective properties of many earthquakes present patterns that seem universally valid. The most prominent is scale-invariance, which is manifested in the size of faults, the frequency of earthquake sizes and the spatial and temporal scales of seismicity….