arXiv subjects

Martin Charron

Publications and source records attributed to Martin Charron.

8 recordsLinked to original sources

arXiv2026

Exact Resistance of an Orifice in a 2D Membrane Blocked by a Cylindrical Obstruction

An exact solution is presented for the resistance of an orifice in a 2D membrane separating two infinitely large conductive reservoirs and obstructed by an infinitely long cylinder. The solution is obtained by constructing a curvilinear coordinate system that captures the symmetry of the obstructed system with constant-coordinate surfaces mapping the system boundaries, and by integrating the resistive contributions of infinitesimally thin equipotential slices. As commonly done when assessing the resistance of fluidic channels of finite length, the exact expression of the obstructed 2D orifice can be used as the access region of obstructed cylindrical channels and will thus find use in single molecule sensing applications.

physics.bio-ph↗

arXiv2024

Predicting Resistive Pulse Signatures in Nanopores by Accurately Modeling Access Regions

Resistive pulse sensing is used to characterize and count single particles in solution moving through channels under an electric bias, with nanoscale pores providing enough spatial resolution for single-molecule identification and sequencing. This technique relies on measuring the ionic current drop produced by the passage of a molecule and, through conductance models, translating the blockage signal into molecular dimensions. However, no generalized model exists that considers the resistive contributions of the pore exterior, i.e. the access regions, when obstructed by a molecule. This is becoming increasingly important with the advent of 2D materials and ultrathin membranes featuring low aspect ratio pores. In this work, a general method by which to model the resistance of access regions in the presence of an insulating obstruction is presented. Thin oblate spheroidal slices are used to partition access regions and infer their conductance when blocked by differently shaped objects. We show that our model accurately estimates the blocked-state conductance of 2D and finite-length pores in the presence of simple or complex structures positioned at varying distances from the pore opening. The model is shown to capture off-axis effects by predicting deeper blockages for obstructions offset from the pore's central axis. A model-based web app was created to predict the electrical signatures of a wide range of molecule geometries translocating through differently shaped pores. The introduced model and accompanying tool will help guide future experimental designs and thus present a straightforward way to extend the quantification of the resistive pulse technique at the nanoscale.

physics.app-ph↗

arXiv2024

Velocity fluctuation and force scaling during driven polymer transport through a nanopore

Inspired by its central role in many biological processes, the transport of biopolymers across nanoscale pores is at the heart of a single-molecule sensing technology aimed at nucleic acid and protein sequencing, as well as biomarker detection. When electrophoretically driven through a pore by an electric potential gradient, a translocating polymer hinders the flow of ions, producing a transient current blockage signature that can be mapped to physicochemical properties of the polymer. Although investigated theoretically and by simulations, few experimental studies have attempted to validate the predicted transport properties, mainly due to the complex nature of the non-equilibrium translocation process. Here, we elucidate these fundamental concepts by constructing a patterned DNA nanostructure whose current signatures allow measurement of the instantaneous velocity throughout the translocation process. With simple physical insights from polymer and fluid dynamics, we show how the resulting molecular velocity profiles can be used to investigate the nanoscale forces at play and their dependence on experimental parameters such as polymer length, pore size and voltage. These results allow testing of theoretical models and outline their limitations. In addition to bridging experiment and theory, knowledge of the velocity fluctuation and force scaling during passage can assist researchers in designing nanopore experiments with optimized sensing performance.

physics.bio-ph↗

arXiv2021

High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid

A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion covariantly and to describe the geometry of the rotated cubed-sphere grid. The spatial discretization is done with the direct flux reconstruction method, which is an alternative formulation to the discontinuous Galerkin approach. The equations of motion are solved in differential form and the resulting discretization is free from quadrature rules. It is well known that the time step of traditional explicit methods is limited by the phase velocity of the fastest waves. Exponential integration is employed to enable integrations with significantly larger time step sizes and improve the efficiency of the overall time integration. New multistep-type exponential propagation iterative methods of orders 4, 5 and 6 are constructed and applied to integrate the shallow-water equations in time. These new schemes enable time integration with high-order accuracy but without significant increases in computational time compared to low-order methods. The exponential matrix functions-vector products used in the exponential schemes are approximated using the complex-step approximation of the Jacobian in the Krylov-based KIOPS (Krylov with incomplete orthogonalization procedure solver) algorithm. Performance of the new numerical methods is evaluated using a set of standard benchmark tests.

math.NA↗

arXiv2021

Addendum: Hidden symmetries, trivial conservation laws and Casimir invariants in geophysical fluid dynamics (2018 J. Phys. Commun. 2 115018)

An extension is proposed to the internal symmetry transformations associated with mass, entropy and other Clebsch-related conservation in geophysical fluid dynamics. Those symmetry transformations were previously parameterized with an arbitrary function $\cal F$ of materially conserved Clebsch potentials. The extension consists in adding potential vorticity $q$ to the list of fields on which a new arbitrary function $\cal G$ depends. If ${\cal G}=q{\cal A}(s)$, where ${\cal A}(s)$ is an arbitrary function of specific entropy $s$, then the symmetry is trivial and gives rise to a trivial conservation law. Otherwise, the symmetry is non-trivial and an associated non-trivial conservation law exists. Moreover, the notions of trivial and non-trivial Casimir invariants are defined. All non-trivial symmetries that become hidden following a reduction of phase space are associated with non-trivial Casimir invariants of a non-canonical Hamiltonian formulation for fluids, while all trivial conservation laws are associated with trivial Casimir invariants.

physics.flu-dyn↗

arXiv2018

On the dissociation between potential vorticity conservation and symmetries

Using a four-dimensional manifestly covariant formalism suitable for classical fluid dynamics, it is shown that the conservation of potential vorticity is not associated with any symmetry of the equations of motion but is instead a trivial conservation law of the second kind. The demonstration is provided in arbitrary coordinates and therefore applies to comoving (or label) coordinates. Since this is at odds with previous studies, which claimed that potential vorticity conservation is associated with a symmetry under particle-relabeling, a detailed discussion on relabeling transformations is also presented.

physics.flu-dyn↗

arXiv2017

Non-trivial and trivial conservation laws in covariant formulations of geophysical fluid dynamics

Using a manifestly invariant Lagrangian density based on Clebsch fields and suitable for geophysical fluid dynamics, the conservation of mass, entropy, momentum and energy, and the associated symmetries are investigated. In contrast, it is shown that the conservation of Ertel's potential vorticity is not associated with any symmetry of the equations of motion, but is instead a trivial conservation law of the second kind. This is at odds with previous studies which claimed that potential vorticity conservation relates to a symmetry under particle-relabeling transformations. From the invariant Lagrangian density, a canonical Hamiltonian formulation is obtained in which Dirac constraints explicitly include the (possibly time-dependent) metric tensor. In this case, it is shown that all Dirac constraints are primary and of the second class, which implies that no local gauge symmetry transformations of Clebsch fields exist. Finally, the corresponding non-canonical Hamiltonian structure with time-dependent strong constraints is derived using tensor components. The existence of Casimir invariants is then investigated in arbitrary coordinates for two choices of dynamical variables in phase space.

physics.flu-dyn↗

arXiv2016

Topographical coloured plasmonic coins

The use of metal nanostructures for colourization has attracted a great deal of interest with the recent developments in plasmonics. However, the current top-down colourization methods based on plasmonic concepts are tedious and time consuming, and thus unviable for large-scale industrial applications. Here we show a bottom-up approach where, upon picosecond laser exposure, a full colour palette independent of viewing angle can be created on noble metals. We show that colours are related to a single laser processing parameter, the total accumulated fluence, which makes this process suitable for high throughput industrial applications. Statistical image analyses of the laser irradiated surfaces reveal various distributions of nanoparticle sizes which control colour. Quantitative comparisons between experiments and large-scale finite-difference time-domain computations, demonstrate that colours are produced by selective absorption phenomena in heterogeneous nanoclusters. Plasmonic cluster resonances are thus found to play the key role in colour formation.

physics.optics↗