Directional persistence and the optimality of run-and-tumble chemotaxis

E. coli does chemotaxis by performing a biased random walk composed of alternating periods of swimming (runs) and reorientations (tumbles). Tumbles are typically modelled as complete directional randomisations but it is known that in wild type E. coli, successive run directions are actually weakly correlated, with a mean directional difference of ∼63°. We recently presented a model of the evolution of chemotactic swimming strategies in bacteria which is able to quantitatively reproduce the emergence of this correlation. The agreement between model and experiments suggests that directional persistence may serve some function, a hypothesis supported by the results of an earlier model. Here we investigate the effect of persistence on chemotactic efficiency, using a spatial Monte Carlo model of bacterial swimming in a gradient, combined with simulations of natural selection based on chemotactic efficiency. A direct search of the parameter space reveals two attractant gradient regimes, (a) a low-gradient regime, in which efficiency is unaffected by directional persistence and (b) a high-gradient regime, in which persistence can improve chemotactic efficiency. The value of the persistence parameter that maximises this effect corresponds very closely with the value observed experimentally. This result is matched by independent simulations of the evolution of directional memory in a population of model bacteria, which also predict the emergence of persistence in high-gradient conditions. The relationship between optimality and persistence in different environments may reflect a universal property of random-walk foraging algorithms, which must strike a compromise between two competing aims: exploration and exploitation. We also present a new graphical way to generally illustrate the evolution of a particular trait in a population, in terms of variations in an evolvable parameter.

Revisiting borehole stresses in anisotropic elastic media : comparison of analytical versus numerical solutions

We present a rigorous validation of the analyticalAmadei solution for the stress concentration around arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients β11 and β55 are not equal. It is shown from theoretical considerations and published experimental data that the β11 and β55 are not equal for realistic rocks. Second, we develop a 3D finite-element elastic model within a hybrid analyticalnumerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic and transverse isotropic symmetries. It is concluded that the analytical Amadei solution is valid with no restrictions on the borehole orientation or elastic anisotropy symmetry.

Numerical investigation of case hardening of plant tissue during dying and its influence on the cellular level shrinkage

Dried plant food materials are one of the major contributors to the global food industry. Widening the fundamental understanding on different mechanisms of food material alterations during drying assists the development of novel dried food products and processing techniques. In this regard, case hardening is an important phenomenon, commonly observed during the drying processes of plant food materials, which significantly influences the product quality and process performance. In this work, a recent meshfree-based numerical model of the authors is further improved and used to simulate the influence of case hardening on shrinkage characteristics of plant tissues during drying. In order to model fluid and wall mechanisms in each cell, Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM) are used. The model is fundamentally more capable of simulating large deformation of multiphase materials, when compared with conventional grid-based modelling techniques such as Finite Element Methods (FEM) or Finite Difference Methods (FDM). Case hardening is implemented by maintaining distinct moisture levels in the different cell layers of a given tissue. In order to compare and investigate different factors influencing tissue deformations under case hardening, four different plant tissue varieties (apple, potato, carrot and grape) are studied. The simulation results indicate that the inner cells of any given tissue undergo limited shrinkage and cell wall wrinkling compared to the case hardened outer cell layers of the tissues. When comparing unique deformation characteristics of the different tissues, irrespective of the normalised moisture content, the cell size, cell fluid turgor pressure and cell wall characteristics influence the tissue response to case hardening.

Directional synthesis of tin oxide@graphene nanocomposites via a one-step up-scalable wet-mechanochemical route for lithium ion batteries

Directional synthesis of SnO2@graphene nanocomposites via a one-step, low-cost, and up-scalable wetmechanochemical method is achieved using graphene oxide and SnCl2 as precursors. The graphene oxides are reduced to graphene while the SnCl2 is oxidized to SnO2 nanoparticles that are in situ anchored onto the graphene sheets evenly and densely, resulting in uniform SnO2@graphene nanocomposites. The prepared nanocomposites possess excellent electrochemical performance and outstanding cycling in Li-ion batteries.

Evolution of multivariant microstructures with anisotropic misfit: A phase field study

We study, in two dimensions, the effect of misfit anisotropy on microstructural evolution during precipitation of an ordered beta phase from a disordered alpha matrix; these phases have, respectively, 2- and 6-fold rotation symmetries. Thus, precipitation produces three orientational variants of beta phase particles, and they have an anisotropic (and crystallographically equivalent) misfit strain with the matrix. The anisotropy in misfit is characterized using a parameter t = epsilon(yy)/epsilon(xx), where epsilon(xx) and epsilon(yy) are the principal components of the misfit strain tensor. Our phase field, simulations show that the morphology of beta phase particles is significantly influenced by 1, the level of misfit anisotropy. Particles are circular in systems with dilatational misfit (t = 1), elongated along the direction of lower principal misfit when 0 < t < 1 and elongated along the invariant direction when - 1 <= t <= 0. In the special case of a pure shear misfit strain (t = - 1), the microstructure exhibits star, wedge and checkerboard patterns; these microstructural features are in agreement with those in Ti-Al-Nb alloys.

Addendum to ``Reconciling grand unification with strings by anisotropic compactifications''

In this brief addendum, we clarify a point which we left unaddressed in a previous publication [Phys. Rev. D 78, 066006 (2008)]. In particular, we show that a specific vacuum configuration constructed in one of our models satisfies the condition D=0. In the previous publication, we only showed F=0. Both D=0 and F=0 are necessary to ensure that supersymmetry survives to the weak scale.

An experimental study on anisotropic mechanical properties of porcine thoracic aorta

Objective: To study the anisotropic mechanical properties of the thoracic aorta in porcine. Methods: Twenty-one porcine thoracic aortas were collected and categorized into three groups. The aortas were then cut through in their axial directions and expanded into two-dimensional planes. Then, by setting the length direction of the planar aortas (i.e., axial directions of the aortas) as 0°, each planar aorta was counterclockwisely cut into 8 samples with orientation of 30°, 45°, 60°, 90°, 120°, 135°, 150° and 180°, respectively. Finally, the uniaxial tensile tests were applied on three groups of samples at the loading rates of 1, 5 and 10 mm/min, respectively, to obtain the elastic modulus and ultimate stress of the aorta in different directions and at different loading rates. Results: The stress-strain curves exhibited different viscoelastic behaviors. With the increase of sample orientations, the elastic modulus gradually increased from 30°, reached the maximum value at 90°, and then gradually decreased till 180°. The variation trend of ultimate stress was similar to that of elastic modulus. Moreover, different loading rates showed a significant influence on the results of elastic modulus and ultimate stress, but a weak influence on the anisotropic degree. Conclusions: The porcine thoracic aorta is highly anisotropic. This research finding provides parameter references for assignment of material properties in finite element modeling, and is significant for understanding biomechanical properties of the arteries.

A Doubly curved Quadrilateral finite-element for the analysis of laminated anisotropic thin shells of revoution

The details of development of the stiffness matrix for a doubly curved quadrilateral element suited for static and dynamic analysis of laminated anisotropic thin shells of revolution are reported. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first order Hermite polynomials, it is possible to ensure that the displacement state for the assembled set of such elements, is geometrically admissible. Monotonic convergence of total potential energy is therefore possible as the modelling is successively refined. Systematic evaluation of performance of the element is conducted, considering various examples for which analytical or other solutions are available.

Anisotropic gaussian beams

Anisotropic gaussian beams are obtained as exact solutions to the parabolic wave equation. These beams have a quadratic phase front whose principal radii of curvature are non-degenerate everywhere. It is shown that, for the lowest order beams, there exists a plane normal to the beam axis where the intensity distribution is rotationally symmetric about the beam axis. A possible application of these beams as normal modes of laser cavities with astigmatic mirrors is noted.

Numerical studies on columnar-to-equiaxed transition in directional solidification of binary alloys

A numerical study on columnar-to-equiaxed transition (CET) during directional solidification of binary alloys is presented using a macroscopic solidification model. The position of CET is predicted numerically using a critical cooling rate criterion reported in literature. The macroscopic solidification model takes into account movement of solid phase due to buoyancy, and drag effect on the moving solid phase because of fluid motion. The model is applied to simulate the solidification process for binary alloys (Sn-Pb) and to estimate solidification parameters such as position of the liquidus, velocity of the liquidus isotherm, temperature gradient ahead of the liquidus, and cooling rate at the liquidus. Solidification phenomena under two cooling configurations are studied: one without melt convection and the other involvin thermosolutal convection. The numerically predicted positions of CET compare well with those of experiments reported in literature. Melt convection results in higher cooling rate, higher liquidus isotherm velocities, and stimulation of occurrence of CET in comparison to the nonconvecting case. The movement of solid phase aids further the process of CET. With a fixed solid phase, the occurrence of CET based on the same critical cooling rate is delayed and it occurs at a greater distance from the chill.

Estimation of light interception in research environments: A joint approach using directional light sensors and 3D virtual plants applied to sunflower (Helianthus annuus) and Arabidopsis thaliana in natural and artificial conditions

Light interception is a major factor influencing plant development and biomass production. Several methods have been proposed to determine this variable, but its calculation remains difficult in artificial environments with heterogeneous light. We propose a method that uses 3D virtual plant modelling and directional light characterisation to estimate light interception in highly heterogeneous light environments such as growth chambers and glasshouses. Intercepted light was estimated by coupling an architectural model and a light model for different genotypes of the rosette species Arabidopsis thaliana (L.) Heynh and a sunflower crop. The model was applied to plants of contrasting architectures, cultivated in isolation or in canopy, in natural or artificial environments, and under contrasting light conditions. The model gave satisfactory results when compared with observed data and enabled calculation of light interception in situations where direct measurements or classical methods were inefficient, such as young crops, isolated plants or artificial conditions. Furthermore, the model revealed that A. thaliana increased its light interception efficiency when shaded. To conclude, the method can be used to calculate intercepted light at organ, plant and plot levels, in natural and artificial environments, and should be useful in the investigation of genotype-environment interactions for plant architecture and light interception efficiency. This paper originates from a presentation at the 5th International Workshop on Functional–Structural Plant Models, Napier, New Zealand, November 2007.

Differential expression profiling of components associated with exoskeletal hardening in crustaceans

Background: Exoskeletal hardening in crustaceans can be attributed to mineralization and sclerotization of the organic matrix. Glycoproteins have been implicated in the calcification process of many matrices. Sclerotization, on the other hand, is catalysed by phenoloxidases, which also play a role in melanization and the immunological response in arthropods. Custom cDNA microarrays from Portunus pelagicus were used to identify genes possibly associated with the activation pathways involved in these processes. Results: Two genes potentially involved in the recognition of glycosylation, the C-type lectin receptor and the mannose-binding protein, were found to display molt cycle-related differential expression profiles. C-type lectin receptor up-regulation was found to coincide with periods associated with new uncalcified cuticle formation, while the up-regulation of mannose-binding protein occurred only in the post-molt stage, during which calcification takes place, implicating both in the regulation of calcification. Genes presumed to be involved in the phenoloxidase activation pathway that facilitates sclerotization also displayed molt cycle-related differential expression profiles. Members of the serine protease superfamily, trypsin-like and chymotrypsin-like, were up-regulated in the intermolt stage when compared to post-molt, while trypsin-like was also up-regulated in pre-molt compared to ecdysis. Additionally, up-regulation in pre- and intermolt stages was observed by transcripts encoding other phenoloxidase activators including the putative antibacterial protein carcinin-like, and clotting protein precursor-like. Furthermore, hemocyanin, itself with phenoloxidase activity, displayed an identical expression pattern to that of the phenoloxidase activators, i.e. up-regulation in pre- and intermolt. Conclusion: Cuticle hardening in crustaceans is a complex process that is precisely timed to occur in the post-molt stage of the molt cycle. We have identified differential expression patterns of several genes that are believed to be involved in biomineralization and sclerotization and propose possible regulatory mechanisms for these processes based on their expression profiles, such as the potential involvement of C-type lectin receptors and mannose binding protein in the regulation of calcification.

Dispersion in Unilateral Finlines on Anisotropic Substrates

The dispersion characteristics of the dominant and higher order modes in unilateral firdines on uniaxially anisotropic substrates have been obtained. The solution has been obtained by applying the equivalent transmission-line concept in the spectral domain and by using Galerkhr’s method. Numericaf results for the propagation constant as a function of the slot-width ratio and freqnency are presented.

Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.