2 citations · 5 across the 12 of their papers we have counts for
14 papers
Construction of an isometric immersion of a bounded, planar region from a framed curve
Brian Seguin, Eliot Fried
We develop a framework for characterizing isometric immersions of simply connected, bounded, planar regions with piecewise smooth boundaries into three-dimensional space. Each imme…
A definition of fractional k-dimensional measure: bridging the gap between fractional length and fractional area
Cornelia Mihaila, Brian Seguin
Here we introduce a fractional notion of -dimensional measure, , that depends on a parameter that lies between and . When this coincides with the f…
On a notion of nonlocal curvature tensor
Roberto Paroni, Paolo Podio-Guidugli, Brian Seguin
In the literature various notions of nonlocal curvature can be found. Here we propose a notion of nonlocal curvature tensor. This we do by generalizing an appropriate representatio…
A transport theorem for nonconvecting open sets on an embedded manifold
Brian Seguin
Most transport theorems---that is, a formula for the rate of change of an integral in which both the integrand and domain of integration depend on time---involve domains that evolv…
A fractional notion of length and an associated nonlocal curvature
Brian Seguin
Here a new notion of fractional length of a smooth curve, which depends on a parameter , is introduced that is analogous to the fractional perimeter functional of sets that has…
On the Nonlocal Curvatures of Surfaces with or without Boundary
Roberto Paroni, Paolo Podio-Guidugli, Brian Seguin
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to s…
On the homogenization of a new class of locally periodic microstructures in linear elasticity with residual stress
Brian Seguin
Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may…
Homogenization of a viscoelastic model for plant cell wall biomechanics
Mariya Ptashnyk, Brian Seguin
The microscopic structure of a plant cell wall is given by cellulose microfibrils embedded in a cell wall matrix. In this paper we consider a microscopic model for interactions bet…
The impact of microfibril orientations on the biomechanics of plant cell walls and tissues: modelling and simulations
Mariya Ptashnyk, Brian Seguin
It is known that the orientation of cellulose microfibrils within plant cell walls has an important impact on the morphogenesis of plant cells and tissues. Viewing the shape of a p…
Periodic homogenization and material symmetry in linear elasticity
Mariya Ptashnyk, Brian Seguin
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic materia…
Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics
Mariya Ptashnyk, Brian Seguin
In this paper we present a derivation and multiscale analysis of a mathematical model for plant cell wall biomechanics that takes into account both the microscopic structure of a c…
Calculating the bending moduli of the Canham--Helfrich free-energy density from a particular potential
Brian Seguin, Eliot Fried
The Canham--Helfrich free-energy density for a lipid bilayer involves the mean and Gaussian curvatures of the midsurface of the bilayer. The splay and saddle-splay moduli and $…
Stable and unstable helices: Soap films in cylindrical tubes
Brian Seguin, Eliot Fried
Cox & Jones recently devised and studied an interesting variant of the classical Plateau problem, a variant in which a helical soap film is confined to a cylindrical tube with circ…
Microphysical derivation of the Canham--Helfrich free-energy density
Brian Seguin, Eliot Fried
The Canham--Helfrich free-energy density for a lipid bilayer has drawn considerable attention. Aside from the mean and Gaussian curvatures, this free-energy density involves a spon…