MNat lines

I. Mathematical Foundation, Models, and Methods in Nature

Kinetic Theory and hydrodynamic limits. Stochastic processes. Evolution PDEs. Fluid Mechanics and Rheology. Non-linear diffusion: applications to tumor dynamics. Singularities in kinetic and fluid dynamics equations. From nano and microscopic dynamics to hydrodynamic models. BioMechanics. Classical mechanics, low dimensional topology and algebraic topology. Dynamical Systems in the transmission of signals and cellular communication. Nonlinear dynamics of many-body systems. Emerging collective properties in ecology and cellular populations. Calculus of Variations. Geometry to models of cerebral cortex vision and reconstruction of images.

Photo by J. Soler


II. Modeling Cell Communications and Tumor Dynamics

Quorum sensing and biopolymer dynamics in aquatic environments. Pathways and cell signalling and mechanotransduction. Activation of target genes. Big Data cell signalling. Wave-cell interaction. Tumor stem cells and microenvironment. Exosomes. Liquid Biopsy. Ultrasonic tumour signalling. Mathematical models in tumour growth. Modeling glioma and neuronal fibres interactions and motility. Targeted gene therapy. Targeted compounds. Smart nano drug delivery systems. Theranostic nanoparticles. Medical devices.

Images by E. López Ruiz & M. Perán.


III. Modeling Bio-Nanotechnology. New Materials and Bio-Engineering.

Nanomedicine. Nanomaterials for the release of drugs and genes. Directed nano-drugs. Applications to regenerative biomedicine. Biosensors. Mechanical biomarkers. Applications to tumour dynamics. Composite materials. Nanostructured materials and devices, graphene. Films and surfaces. Nanotechnology of polymers. Bio-nano materials. Nanofluids. Biopolymers and Nanoparticles. Bio-ink and bio-printer. Bioreactors.

Images by J. de Vicente, K. Shahrivar, J.R. Morillas


IV. Modeling complex and dynamic adaptive systems at multiple scales. Computational Biology

Evolutionary Biology. Complex networks. Eco-evolutionary dynamics in complex scenarios. Ecological genetics. Epigenetics. Molecular ecology. Dispersal processes in space and time. From micro to macro scales. Ecology and evolution of biotic interactions: the continuum between mutualism, competition, and antagonism. Emerging collective processes. Biomathematics in ecology. Cancer as an ecological and evolutionary process. Dynamics of dissolved polymers, colloids and particulate organic matter in aquatic ecosystems: self-assembling and fragmentation. Microorganisms in the atmosphere. Bioaerosols and climate.



Photo by the SeaWiFS Project, NASA/Goddard Space Flight Center, and ORBIMAGE



Image by Javier Valverde