Related papers: Energy landscape properties studied by symbolic se…
We study the lattice N=1 Wess-Zumino model in two dimensions and we construct a sequence $\rho^{(L)}$ of exact lower bounds on its ground state energy density $\rho$, converging to $\rho$ in the limit $L\to\infty$. The bounds $\rho^{(L)}$…
The redistribution of energy levels between energy bands is studied for a family of simple effective Hamiltonians depending on one control parameter and possessing axial symmetry and energy-reflection symmetry. Further study is made on the…
We study the energy-landscape network of Lennard-Jones clusters as a model of a glass forming system. We find the stable basins and the first order saddles connecting them, and identify them with the network nodes and links, respectively.…
A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
The analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or…
A wide variety of intricate dynamics may be created at border-collision bifurcations of piecewise-smooth maps, where a fixed point collides with a surface at which the map is nonsmooth. For the border-collision normal form in two…
A compact analytical scheme is presented for describing ultra-dense hadronic matter, which combines a multicomponent van der Waals (vdW)-type description with temperature-dependent effective degrees of freedom. Although the vdW formalism…
The topology of isoenergetic surfaces in reciprocal space for simple (sc), body-centered (bcc), and face-centered (fcc) cubic lattices is investigated in detail in the tight-binding approximation, taking into account the transfer integrals…
In this lecture we outline the main results of our investigations of certain field-theoretic systems which have V-shaped field potential. After presenting physical examples of such systems, we show that in static problems the exact ground…
In this paper we continue our studies of the phase space geometry and dynamics associated with index k saddles (k > 1) of the potential energy surface. Using normal form theory, we give an explicit formula for a "dividing surface" in phase…
Motivated by the famous Waddington's epigenetic landscape metaphor in developmental biology, biophysicists and applied mathematicians made different proposals to realize this metaphor in a rationalized way. We adopt comprehensive…
We apply the method of Lagrangian Descriptors (LDs) to a symmetric Caldera-type potential energy surface which has three index-1 saddles surrounding a relatively flat region that contains no minimum. Using this method we show the phase…
Landscape is one of the key notions in literature on biological processes and physics of complex systems with both deterministic and stochastic dynamics. The large deviation theory (LDT) provides a possible mathematical basis for the…
We study fermion pairing in a population-imbalanced mixture of $^{6}$Li atomic gas loaded in a three-dimensional lattice at very low temperatures. Using the number equation for each population, the gap equation and the equation for the…
We investigate the fragmentation dynamics of an atomic chain under tensile stress. We have classified the location, stability type (indices) and energy of all equilibria for the general $n$-particle chain, and have highlighted the…
A novel method for glassy landscape exploration is presented which utilizes a time series of energy values collected during an isothermal relaxation after a thermal quench. A sub-series of increasingly rare events, or quakes, which are…
Energetic correlations due to polymeric constraints and the locality of interactions, in conjunction with the apriori specification of the existence of a particularly low energy state, provides a method of introducing the aspect of minimal…
The excess power, energy and intensity of a random electromagnetic field above a high threshold level are characterized based on a Slepian--Kac model for upcrossings. For quasi-static fields, the probability distribution of the excess…
In this paper we study an asymmetric valley-ridge inflection point (VRI) potential, whose energy surface (PES) features two sequential index-1 saddles (the upper and the lower), with one saddle having higher energy than the other and two…