Related papers: Towards a Nano Geometry? Geometry and Dynamics on …
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…
We present a framework to take new measurements in nematic systems that contain active elements such as molecular motors. Spatio-temporal fields of stress, traction, velocity, pressure, and forces are estimated jointly from microscopy…
On the basis of the relativistic kinetic theory the relativistic statistical systems with scalar interaction particles are investigated. The self-consistent system of the equations describing self-gravitating plasma with interpartial scalar…
During developmental processes such as embryogenesis, how a group of cells fold into specific structures, is a central question in biology that defines how living organisms form. Establishing tissue-level morphology critically relies on how…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
Mechanical properties of the cell are important biomarkers for probing its architectural changes caused by cellular processes and/or pathologies. The development of microfluidic technologies have enabled measuring cell mechanics at…
This paper studies a bulk-surface reaction-diffusion system for cell polarization in two-dimensional domains. The model describes the formation of localized patterns through the wave-pinning mechanism, while explicitly incorporating the…
Gaining access to the cell interior is fundamental for many applications, such as electrical recording, drug and biomolecular delivery. A very promising technique consists of culturing cells on nano/micro pillars. The tight adhesion and…
We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of…
Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph…
Synthetic biology is a recent area of biological engineering, whose aim is to provide cells with novel functionalities. A number of important results regarding the development of control circuits in synthetic biology have been achieved…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
The use of statistical methods to model gravitational systems is crucial to physics practice, but the extent to which thermodynamics and statistical mechanics genuinely apply to these systems is a contentious issue. This paper provides new…
Nanofluidics has emerged recently in the footsteps of microfluidics, following the quest of scale reduction inherent to nanotechnologies. By definition, nanofluidics explores transport phenomena of fluids at the nanometer scales. Why is the…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face is to find the discrete protoforms of…
Soft interfaces formed by lipid membranes are fundamental to living cells, synthetic cells, and membrane-based soft materials. However, a quantitative framework linking molecular organization with nonlinear interfacial mechanics remains…
Nowadays, multiscale modelling is recognized as the most suitable way to study biological processes. Indeed, almost every phenomenon in nature exhibits a multiscale behaviour, i.e., it is the outcome of interactions that occur at different…