arXiv subjects

Yukitaka Ishimoto

Publications and source records attributed to Yukitaka Ishimoto.

14 recordsLinked to original sources

arXiv2017

A mechanical model for diversified insect wing margin shapes

The wings in different insect species are morphologically distinct with regards to their size, outer contour (margin) shape, venation, and pigmentation. The basis of the diversity of wing margin shapes remains unknown, despite the fact that gene networks governing the Drosophila wing development have been well characterised. Among the different types of wing margin shapes, smoothly curved contour is the most frequently found and implies the existence of a highly organised, multicellular mechanical structure. Here, we developed a mechanical model for diversified insect wing margin shapes, in which non-uniform bending stiffness of the wing margin is considered. We showed that a variety of spatial distribution of the bending stiffness could reproduce diverse wing margin shapes. Moreover, the inference of the distribution of the bending stiffness from experimental images indicates a common spatial profile among insects tested. We further studied the effect of the intrinsic tension of the wing blade on the margin shape and on the inferred bending stiffness. Finally, we implemented the bending stiffness of the wing margin in the cell vertex model of the wing blade, and confirmed that the hybrid model retains the essential feature of the margin model. We propose that in addition to morphogenetic processes in the wing blade, the spatial profile of the bending stiffness in the wing margin can play a pivotal role in shaping insect wings.

q-bio.TO↗

arXiv2014

Bubbly vertex dynamics: a dynamical and geometrical model for epithelial tissues with curved cell shapes

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them on the vertex model. Thus, a model with the curvatures is constructed and its algorithm is given for simulation. Its possible extensions and applications will also be discussed.

physics.bio-ph↗

arXiv2012

2D Lattice Liquid Models

A family of novel models of liquid on a 2D lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle systems on a two-dimensional surface with no explicit viscosity. Among the family of the models, we have shown and constructed two stochastic models, a vicious walk model and a flow model, on an isotropic regular lattice and on the rectangular honeycomb lattice of various sizes. In both cases, the dynamics is governed by the nature of the frustration of the particle movements. By simulations, we have found the approximate functional form of the frustration probability, and peculiar anomalous diffusions in their time-averaged mean square displacements in the flow model. The relations to other existing statistical models and possible extensions of the models are also discussed.

cond-mat.soft↗

arXiv2007

Solving Infinite Kolam in Knot Theory

In south India, there are traditional patterns of line-drawings encircling dots, called ``Kolam'', among which one-line drawings or the ``infinite Kolam'' provide very interesting questions in mathematics. For example, we address the following simple question: how many patterns of infinite Kolam can we draw for a given grid pattern of dots? The simplest way is to draw possible patterns of Kolam while judging if it is infinite Kolam. Such a search problem seems to be NP complete. However, it is certainly not. In this paper, we focus on diamond-shaped grid patterns of dots, (1-3-5-3-1) and (1-3-5-7-5-3-1) in particular. By using the knot-theory description of the infinite Kolam, we show how to find the solution, which inevitably gives a sketch of the proof for the statement ``infinite Kolam is not NP complete.'' Its further discussion will be given in the final section.

cs.DM↗

arXiv2007

Analytic theory of DNA condensation

We introduce a novel model for DNA condensation (whip-toroid transition) using the path integral method in the framework of the non-linear sigma model on a line segment. We show that some of its classical configurations exhibit toroidal forms, and the system has phase transitions from a whip to toroidal phases with a parameter $c=W/(2l) (L/(2π))^2$. We also discuss stability and finite size effect on these states.

cond-mat.soft↗

arXiv2007

DNA toroid condensation as analytic solutions

It now becomes apparent that condensed DNA toroid which emerges in a poor solvent condition can be realised in the framework of the non-linear sigma model on a line segment. In fact, the classical solutions of the model, i.e., of the bending potential exhibit toroidal forms, and fit well with the delta-function term of the attractive interaction. The proposed theory is in good agreement with experimental observations that the toroid is the ground state. In this paper, we give a rigorous proof that the solutions are indeed the exact solutions of the equations of motion with the first derivatives of the attractive interaction term. We also show a refined mapping to experimental data, considering the finite size effects of the cross section and of the chain length.

cond-mat.soft↗

arXiv2007

Effect of interaction shape on the condensed DNA toroid

We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. For different interactions, the theory predicts different scaling behaviours of the mean toroidal and cross sectional radii, $r_c$ and $r_{cross}$, as functions of the contour length L: $(r_c, r_{cross}) \sim L^{ν(N_c)}$ with $ν=(1/5, 2/5)$ for the van der Waals type, $ν=(-1/3, 2/3)$ for the Coulomb type, $ν=(-1, 1)$ for the delta function type attractions in the asymptotic limit. For the toroids with finite winding number $N_c=100 \sim 400$, we find $ν\simeq 0$ for the Yukawa interaction with screening parameter $κ=0.5 \sim 1.0$, and $ν=0.1 \sim 0.13$ for the van der Waals type interactions. These findings could provide possible explanation for the experimentally well known observation $ν\simeq 0$ of the condensed DNA toroids. Conformational transitions are also discussed.

cond-mat.soft↗

arXiv2006

Low energy states of a semiflexible polymer chain with attraction and the whip-toroid transitions

Based on our previous paper [cond-mat/0507477], we establish a general model for the whip-toroid transitions of a semiflexible homopolymer chain using the path integral method and the O(3) nonlinear sigma model on a line segment with the local inextensibility constraint. We exactly solve the energy levels of classical solutions, and show that some of its classical configurations exhibit toroidal forms, and the system has phase transitions from a whip to toroidal states with a conformation parameter $c=\frac{W}{2 l} (\frac{L}{2π})^2$. We also discuss the stability of the toroid states and propose the low-energy effective Green function. Finally, with the finite size effect on the toroid states, predicted toroidal properties are successfully compared to experimental results of DNA condensation.

cond-mat.soft↗

arXiv2005

Polyakov's String: Twenty Five Years After

An International Workshop dedicated to the anniversary of the Polyakov's String (of course today there is no need to remind the meaning and the role of this theory) was held in Chernogolovka in June 2005. Apart from the 25-th anniversary of the first appearance of the Polyakov's String theory, this conference, to our mind, might be also thought of as a 35 years from the discovery of the Conformal Invariance, 30 years of the Monopole and the Instantons and, finally, as the 20-th anniversary of the CFT. A case of mysterious coincidence, this year is also a jubilee of Sasha himself, whose contribution to the Theoretical Physics of 20-th century is far from being exhausted by the achievements listed above.

hep-th↗

arXiv2004

Minimal String Theory is Logarithmic

We study the simplest examples of minimal string theory whose worldsheet description is the unitary (p,q) minimal model coupled to two-dimensional gravity (Liouville field theory). In the Liouville sector, we show that four-point correlation functions of `tachyons' exhibit logarithmic singularities, and that the theory turns out to be logarithmic. The relation with Zamolodchikov's logarithmic degenerate fields is also discussed. Our result holds for generic values of (p,q).

hep-th↗

arXiv2003

Two-Point Functions and Boundary States in Boundary Logarithmic Conformal Field Theories

Our main aim in this thesis is to address the results and prospects of boundary logarithmic conformal field theories: theories with boundaries that contain the above Jordan cell structure. We have investigated c_{p,q} boundary theory in search of logarithmic theories and have found logarithmic solutions of two-point functions in the context of the Coulomb gas picture. Other two-point functions have also been studied in the free boson construction of BCFT with SU(2)_k symmetry. In addition, we have analyzed and obtained the boundary Ishibashi state for a rank-2 Jordan cell structure [hep-th/0103064]. We have also examined the (generalised) Ishibashi state construction and the symplectic fermion construction at c=-2 for boundary states in the context of the c=-2 triplet model. The differences between two constructions are interpreted, resolved and extended beyond each case.

hep-th↗

arXiv2001

Boundary states in boundary logarithmic CFT

There exist logarithmic CFTs(LCFTs) such as the $c_{p,1}$ models. It is also well known that it generally contains Jordan cell structure. In this paper, we obtain the boundary Ishibashi state for a rank-2 Jordan cell structure and, with these states in $c=-2$ rational LCFT, we derive boundary states in the closed string picture, which correspond to boundary conditions in the open string picture. We also discuss the Verlinde formula for LCFT and possible applications to string theory.

hep-th↗

arXiv1999

Classical Hamiltonian Reduction On $D(2|1;α)$ Chern-Simons Gauge Theory and Large N=4 Superconformal Symmetry

3d Chern-Simons gauge theory has a strong connection with 2d CFT and link invariants in knot theory. We impose some constraints on the $D(2|1;α)$ CS theory in the similar context of the hamiltonian reduction of 2d superconformal algebras. There Hilbert states in $D(2|1;α)$ CS theory are partly identified with characters of the large N=4 SCFT by their transformation properties.

hep-th↗

arXiv1996

Feigin-Fuchs Representations for Nonequivalent Algebras of N=4 Superconformal Symmetery

The $N=4$ SU(2)$_k$ superconformal algebra has the global automorphism of SO(4) $\approx$ SU(2)$\times$SU(2) with the {\it left} factor as the Kac-Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by $ρ$ corresponding to the conjugate classes of the {\it outer} automorphism group SO(4)/SU(2)=SU(2) are obtained à la Schwimmer and Seiberg. We construct Feigin-Fuchs representations with the $ρ$ parameter embedded for the infinite set of the $N=4$ nonequivalent algebras. In our construction the extended global SU(2) algebras labeled by $ρ$ are self-consistently represented by fermion fields with appropriate boundary conditions.

hep-th↗