Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field

The classical problem of the buckling of an elastic rod in a magnetic ¯eld is investigated using modern techniques from dynamical systems theory. The Kirchhoff equations, which describe the static equilibrium equations of a geometrically exact rod under end tension and moment are extended by incorporating the evolution of a fixed external vector (in the direction of the magnetic field) that interacts with the rod via a Lorentz force. The static equilibrium equations (in body cordinates) are found to be noncanonical Hamiltonian equations. The Poisson bracket is generalised and the equilibrium equations found to sit, as the third member, in a family of rod equations in generalised magnetic fields. When the rod is linearly elastic, isotropic, inextensible and unshearable the equations are completely integrable and can be generated by a Lax pair. The isotropic system is reduced using the Casimirs, via the Euler angles, to a four-dimensional canonical system with a first integral provided the magnetic field is not aligned with the force within the rod at any point as the system losses rank. An energy surface is specified, defning three-dimensional flows. Poincare sections then show closed curves. Through Mel'nikov analysis it is shown that for an extensible rod the presence of a magnetic field leads to the transverse intersection of the stable and unstable manifolds and the loss of complete integrability. Consequently, the system admits spatially chaotic solutions and a multiplicity of multimodal homoclinic solutions exist. Poincare sections associated with the loss of integrability are displayed. Homoclinic solutions are computed and post-buckling paths found using continutaion methods. The rods buckle in a Hamiltonian-Hopf bifurcation about a periodic solution. A codimension-two point, which describes a double Hamiltonian-Hopf bifurcation, determines whether straight rods buckle into localised configurations at either two critical values of the magnetic field, a single critical value or do not buckle at all. The codimension-two point is found to be an organising centre for primary and multimodal solutions

Spatial chaos of an extensible conducting rod in a uniform magnetic field

The equilibrium equations for the isotropic Kirchhoff rod are known to form an integrable system. It is also known that the effects of extensibility and shearability of the rod do not break the integrable structure. Nor, as we have shown in a previous paper does the effect of a magnetic field on a conducting rod. Here we show, by means of Mel'nikov analysis, that, remarkably, the combined effects do destroy integrability; that is, the governing equations for an extensible current-carrying rod in a uniform magnetic field are nonintegrable. This result has implications for possible configurations of electrodynamic space tethers and may be relevant for electromechanical devices

The effects of microRNAs on human neural stem cell differentiation in two- and three-dimensional cultures

INTRODUCTION: Stem cells have the ability to self-renew or to differentiate into numerous cell types; however, our understanding of how to control and exploit this potential is currently limited. An emerging hypothesis is that microRNAs (miRNAs) play a central role in controlling stem cell-fate determination. Herein, we have characterized the effects of miRNAs in differentiated human neural stem cells (hNSCs) by using a cell line currently being tested in clinical trials for stroke disability (NCT01151124, Clinicaltrials.gov). METHODS: HNSCs were differentiated on 2- (2D) and 3-dimensional (3D) cultures for 1 and 3 weeks. Quantification of hNSC differentiation was measured with real-time PCR and axon outgrowth. The miRNA PCR arrays were implemented to investigate differential expression profiles in differentiated hNSCs. Evaluation of miRNA effects on hNSCs was performed by using transfection of miRNA mimics, real-time PCR, Western blot, and immunocytochemistry. RESULTS: The 3D substrate promoted enhanced hNSC differentiation coupled with a loss of cell proliferation. Differentiated hNSCs exhibited a similar miRNA profiling. However, in 3D samples, the degree and timing of regulation were significantly different in miRNA members of cluster mi-R17 and miR-96-182, and hsa-miR-302a. Overall, hNSC 3D cultures demonstrated differential regulation of miRNAs involved in hNSC stemness, cell proliferation, and differentiation. The miRNA mimic analysis of hsa-miR-146b-5p and hsa-miR-99a confirmed induction of lineage-committed progenitors. Downregulated miRNAs were more abundant; those most significantly downregulated were selected, and their putative target mRNAs analyzed with the aim of unraveling their functionality. In differentiated hNSCs, downregulated hsa-miR-96 correlated with SOX5 upregulation of gene and protein expression; similar results were obtained for hsa-miR-302a, hsa-miR-182, hsa-miR-7, hsa-miR-20a/b, and hsa-miR-17 and their target NR4A3. Moreover, SOX5 was identified as a direct target gene of hsa-miR-96, and NR43A, a direct target of hsa-miR-7 and hsa-mir-17 by luciferase reporter assays. Therefore, the regulatory role of these miRNAs may occur through targeting NR4A3 and SOX5, both reported as modulators of cell-cycle progression and axon length. CONCLUSIONS: The results provide new insight into the identification of specific miRNAs implicated in hNSC differentiation. These strategies may be exploited to optimize in vitro hNSC differentiation potential for use in preclinical studies and future clinical applications

Dynamic phase transition in the conversion of B-DNA to Z-DNA

The long time dynamics of the conformational transition from B-DNA to Z-DNA is shown to undergo a dynamic phase transition. We obtained the dynamic phase diagram for the stability of the front separating B and Z. The instability in this front results in two split fronts moving with different velocities. Hence, depending on the system parameters a denatured state may develop dynamically eventhough it is thermodynamically forbidden. This resolves the current controversies on the transition mechanism of the B-DNA to Z-DNA.Comment: 5 pages, 4 figures. New version with correction of typos, new references, minor modifications in Fig 2, 3. To appear in EP

A length-dynamic Tonks gas theory of histone isotherms

We find exact solutions to a new one-dimensional (1D) interacting particle theory and apply the results to the adsorption and wrapping of polymers (such as DNA) around protein particles (such as histones). Each adsorbed protein is represented by a Tonks gas particle. The length of each particle is a degree of freedom that represents the degree of DNA wrapping around each histone. Thermodynamic quantities are computed as functions of wrapping energy, adsorbed histone density, and bulk histone concentration (or chemical potential); their experimental signatures are also discussed. Histone density is found to undergo a two-stage adsorption process as a function of chemical potential, while the mean coverage by high affinity proteins exhibits a maximum as a function of the chemical potential. However, {\it fluctuations} in the coverage are concurrently maximal. Histone-histone correlation functions are also computed and exhibit rich two length scale behavior.Comment: 5 pp, 3 fig

Structural, mechanical and thermodynamic properties of a coarse-grained DNA model

We explore in detail the structural, mechanical and thermodynamic properties of a coarse-grained model of DNA similar to that introduced in Thomas E. Ouldridge, Ard A. Louis, Jonathan P.K. Doye, Phys. Rev. Lett. 104 178101 (2010). Effective interactions are used to represent chain connectivity, excluded volume, base stacking and hydrogen bonding, naturally reproducing a range of DNA behaviour. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization and hairpin formation, as well as structural properties such as the persistence length of single strands and duplexes, and the torsional and stretching stiffness of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bases and internal loops, and the effect of stacking and fraying on the thermodynamics of the duplex formation transition.Comment: 25 pages, 16 figure

Pyroelectric ultrasound sensor model: directional response

Ultrasound is typically measured using phase-sensitive piezoelectric sensors. Interest in phase-insensitive sensors has grown recently, with proposed applications including ultrasound attenuation tomography of the breast and acoustic power measurement. One advantage of phase-insensitive detectors, in contrast to conventional phase-sensitive detectors, is that they do not suffer from a narrow directional response at high frequencies due to phase cancellation. A numerical model of a phase-insensitive pyroelectric ultrasound sensor is presented. The model consists of three coupled components run in sequence: acoustic, thermal, and electrical. The acoustic simulation models the propagation and absorption of the incident ultrasound wave. The absorbed acoustic power density is used as a heat source in the thermal simulation of the time-evolution of the temperature in the sensor. Both the acoustic and thermal simulations are performed using the k-Wave MATLAB toolbox with an assumption that shear waves are not supported in the medium. The final component of the model is a pyroelectric circuit model which outputs the sensor response based on the temperature change in the sensor. The modelled pyroelectric sensor response and directional dependence are compared to empirical data