Where are the coexisting parallel climates? Large ensemble climate projections from the point of view of chaos theory.

We review the recent results of large ensemble climate projections considering them to be the simulations of chaotic systems. The quick spread of an initially localized ensemble in the first weeks after initialization is an appearance of the butterfly effect, illustrating the unpredictability of the dynamics. We show that the growth rate of uncertainty (an analog of the Lyapunov exponent) can be determined right after initialization. The next phase corresponds to a convergence of the no longer localized ensemble to the time-dependent climate attractor and requires a much longer time. After convergence takes place, the ensemble faithfully represents the climate dynamics. Concerning a credible simulation, the observed signal should then wander within the spread of the converged ensemble all the time, i.e., to behave just as any of the ensemble members. As a manifestation of the chaotic-like climate dynamics, one can imagine that beyond the single, observed time-dependent climate, a plethora of parallel climate realizations exists. Converged climate ensembles also define the probability distribution by which the physical quantities of the different climate realizations occur. Large ensemble simulations were shown earlier to be credible in the sense formulated. Here, in addition, an extended credibility condition is given, which requires the ensemble to be a converged ensemble, valid also for low-dimensional models. Interestingly, to the best of our knowledge, no low-order physical or engineering systems subjected to time-dependent forcings are known for which a comparison between simulation and experiment would be available. As illustrative examples, the CESM1-LE climate model and a chaotic pendulum are taken.

Bioinspired gelatin/bioceramic composites loaded with bone morphogenetic protein-2 (BMP-2) promote osteoporotic bone repair.

There are currently several commercialized products approved by the Food and Drug Administration and the European Medicines Agency based on the use of recombinant human BMP-2 for the treatment of non-unions long fractures and spinal fusion. However, the adverse effects recorded with the use of BMPs suggest the need for drug delivery carriers that allow reducing the required doses and improve their cost-effectiveness. Herein, we have developed a new osteoconductive scaffold that reduces the required doses of BMP-2 for promoting bone regeneration in an osteoporotic defect model. The composite is, in brief, a gelatin-based 3D scaffold reinforced with either calcium sulfate or hydroxyapatite as an inorganic osteoconductive biomaterial. To this end, the organic/inorganic composite systems showed high hydration capacity and good in vitro degradability. The incorporation of 7.5% (m/v) ceramic compounds resulted in scaffolds with stiffer Young modulus (179 and 75 kPa for CaSO4_7 and HA_7, respectively) than bare gelatin hydrogels (48 kPa). Studies with human bone-marrow derived mesenchymal stem cells (hBM-MSCs) revealed that the 3D scaffolds promote cell adhesion and proliferation along with osteogenic differentiation capabilities. Specifically, downregulation of stemness (Nanog, Oct4) genes and upregulation of osteogenic markers (ALP, Col1a1, Fmod) by two fold were observed over 10 days under basal culture conditions. Promisingly, the sustained in vitro release of BMP-2 observed from the porous reinforced scaffolds allowed us to address the critical-sized osteoporotic mice calvarial defects with a relatively low growth factor doses (600 ng BMP-2/scaffold) compared to conventional doses at 2-15 micrograms. Overall, this study demonstrates the promising potential of osteoconductive gelatin/calcium bioceramics composites as osteogenic growth factors delivery carriers for bone-regeneration via ultra-low growth factor doses.

Possible metabolic conversion of pinene to ionone.

The unintended consequence of the ingestion of certain foods to alter the scent or color of urine is well known. Less awareness exists regarding the practice of ingestion of natural products or drugs with the intended purpose of conferring urine the scent of violets. The resin of the terebinth tree and the derived turpentine were widely used in antiquity in wine-making, both as taste enhancer and conserving agent, so the effect on urine was possibly noticed due to the presence in wines. It is also possible that turpentine's effect on urine was noticed subsequent to its use as medicine, as a component of various remedies popular in those days. The scent altering effect requires metabolic conversion of pinene, the main turpentine component to ionone, the molecule mainly responsible for the scent of violets. The metabolic pathway (in humans or otherwise) was (to our knowledge) not yet described. We here propose a possible metabolic pathway for the conversion of pinene to ionone, explaining the scent altering effect of turpentine. We also provide calculated pharmacokinetic (pK) data for the mentioned substances.

When is high-dimensional scattering chaos essentially two dimensional? Measuring the product structure of singularities.

We demonstrate how the area of the enveloping surface of the scattering singularities in a three-degrees-of-freedom (3-dof) system depends on a perturbation parameter controlling the distance from a reducible case. This dependence is monotonic and approximately linear. Therefore it serves as a measure for this distance, which can be extracted from an investigation of the fractal structure. These features are a consequence of the dynamics being governed by normally hyperbolic invariant manifolds. We conclude that typical n-dof chaotic scattering exhibits either structures developing out of a stack of chaotic structures of 2-dof type or hardly any chaotic effects.

Synthesis of a new series of heterocyclic scaffolds for medicinal purposes.

A new series of substituted 8-fluro-4H-pyrimido[2,1-b] [1,3]benzothiazole-4-ones () substituted 7-methyl-4H-isoxazolo[2,3-a]pyrimidin-4-ones, and substituted 2-methyl-5,6,7,8-tetrahydro-9H-isoxazolo[2,3-a]pyridopyrimidin-9-ones, compounds I-VII, have been prepared via condensation of beta-keto esters with 2-aminopyridine derivatives, in the presence of polyphosphoric acid. The same technique has also been used to prepare diazepine compounds, VIII-X, by condensation of a gamma-keto ester with 2-aminopyridine derivatives. Details of synthetic procedures are shown. The new compounds have been characterized by elemental analysis, GC-MS, FT-IR and NMR spectrometry. Antibacterial, antifungal and anticancer (cytotoxic) activities, for three of these compounds, have been investigated and are presented.

Coexistence of inertial competitors in chaotic flows.

We investigate the dynamics of inertial particles immersed in open chaotic flows. We consider the generic problem of competition between different species, e.g., phytoplankton populations in oceans. The strong influence from inertial effects is shown to result in the persistence of different species even in cases when the passively advected species cannot coexist. Multispecies coexistence in the ocean can be explained by the fact that the unstable manifold is different for each advected competitor of different size.

Selective sensitivity of open chaotic flows on inertial tracer advection: catching particles with a stick.

We investigate the effects of finite size and inertia of a small spherical particle immersed in an open unsteady flow which, for ideal tracers, generates transiently chaotic trajectories. The inertia effects may strongly modify the chaotic motion to the point that attractors may appear in the configuration space. These studies are performed in a model of the two-dimensional flow past a cylindrical obstacle. The relevance to modeling efforts of biological pathogen transport in large-scale flows is discussed. Since the tracer dynamics is sensitive to the particle inertia and size, simple geometric setups in such flows could be used as a particle mixture segregator separating and trapping particles.

Multibaker map for shear flow and viscous heating.

A consistent description of shear flow and the accompanying viscous heating as well as the associated entropy balance is given in the framework of a deterministic dynamical system. The laminar shear flow is modeled by a Hamiltonian multibaker map which drives velocity and temperature fields. In the appropriate macroscopic limit one recovers the Navier-Stokes and heat conduction equations along with the associated entropy balance. This indicates that results of nonequilibrium thermodynamics can be described by means of an abstract, sufficiently chaotic, and mixing dynamics. A thermostating algorithm can also be incorporated into this framework.

Multifractal structure of chaotically advected chemical fields

The structure of the concentration field of a decaying substance produced by chemical sources and advected by a smooth incompressible two-dimensional flow is investigated. We focus our attention on the nonuniformities of the Holder exponent of the resulting filamental chemical field. They appear most evidently in the case of open flows where irregularities of the field exhibit strong spatial intermittency as they are restricted to a fractal manifold. Nonuniformities of the Holder exponent of the chemical field in closed flows appears as a consequence of the nonuniform stretching of the fluid elements. We study how this affects the scaling exponents of the structure functions, displaying anomalous scaling, and relate the scaling exponents to the distribution of local Lyapunov exponents of the advection dynamics. Theoretical predictions are compared with numerical experiments.

Thermodynamic cross effects from dynamical systems

We give a thermodynamically consistent description of simultaneous heat and particle transport, as well as of the associated cross effects, in the framework of a chaotic dynamical system, a generalized multibaker map. Besides the density, a second field with appropriate source terms is included in order to mimic, after coarse graining, a spatial temperature distribution and its time evolution. An expression is derived for the irreversible entropy production in a steady state, as the average of the growth rate of the relative density, a unique combination of the two fields.

Multibaker map for thermodynamic cross effects in dynamical systems

A consistent description of simultaneous heat and particle transport, including cross effects, and the associated entropy balance is given in the framework of a deterministic dynamical system. This is achieved by a multibaker map where, in addition to the phase-space density of the multibaker, a second field with appropriate source terms is included in order to mimic a spatial temperature distribution and its time evolution. Conditions are given to ensure consistency in an appropriately defined continuum limit with the thermodynamic entropy balance. They leave as the only free parameter of the model the entropy flux let directly into the surroundings. If it vanishes in the bulk, the transport properties of the model are described by the thermodynamic transport equations. Another choice leads to a uniform temperature distribution. It represents transport problems treated by means of a thermostating algorithm, similar to the one considered in nonequilibrium molecular dynamics.

Chaotic flow: the physics of species coexistence.

Hydrodynamical phenomena play a keystone role in the population dynamics of passively advected species such as phytoplankton and replicating macromolecules. Recent developments in the field of chaotic advection in hydrodynamical flows encourage us to revisit the population dynamics of species competing for the same resource in an open aquatic system. If this aquatic environment is homogeneous and well-mixed then classical studies predict competitive exclusion of all but the most perfectly adapted species. In fact, this homogeneity is very rare, and the species of the community (at least on an ecological observation time scale) are in nonequilibrium coexistence. We argue that a peculiar small-scale, spatial heterogeneity generated by chaotic advection can lead to coexistence. In open flows this imperfect mixing lets the populations accumulate along fractal filaments, where competition is governed by an "advantage of rarity" principle. The possibility of this generic coexistence sheds light on the enrichment of phytoplankton and the information integration in early macromolecule evolution.

Fluctuation theorems for entropy production in open systems

We derive a fluctuation theorem to describe entropy fluctuations in steady states of systems with density gradients due to open boundaries. The fluctuations are related to the growth rate of the phase-space density, instead of the phase-space contraction rate. Explicit derivations are presented for a multibaker map, but the arguments are rather general, and should hold for a much wider class of dynamical systems. A comparison with recent results for stochastic systems is also given.

Topological scaling and gap filling at crisis

Scaling laws associated with an interior crisis of chaotic dynamical systems are studied. We argue that open gaps of the chaotic set become densely filled at the crisis due to the sudden appearance of unstable periodic orbits with extremely long periods. We formulate a scaling theory for the associated growth of the topological entropy.

Chemical or biological activity in open chaotic flows.

We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B-->2B and A+B-->2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von Kármán vortex street, a time-periodic two-dimensional flow of a viscous fluid around a cylinder. We show that a fractal unstable manifold acts as a catalyst for the process, and the products cover fattened-up copies of this manifold. This may account for the observed filamental intensification of activity in environmental flows. The reaction equations valid in the wake are derived either in the form of dissipative maps or differential equations depending on the regime under consideration. They contain terms that are not present in the traditional reaction equations of the same active process: the decay of the products is slower while the productivity is much faster than in homogeneous flows. Both effects appear as a consequence of underlying fractal structures. In the long time limit, the system locks itself in a dynamic equilibrium state synchronized to the flow for both types of reactions. For particles of finite size an emptying transition might also occur leading to no products left in the wake.