School of Mechanical Engineering Seminar

Monday, November 21, 2022 at 14:00
Wolfson Building of Mechanical Engineering, Room 206

"Verifying k-contraction without computing k-compounds"

Omri Dalin

MSc of Lea Belkin

A dynamical system is called contractive if any two solutions approach one another at
an exponential rate. More precisely, the dynamics contracts lines at an exponential rate.
This property implies highly ordered asymptotic behavior including entrainment to time-
varying periodic vector fields and, in particular, global asymptotic stability of the equilib-
rium for time-invariant vector fields.

A dynamical system is called k-contractive if the dynamics contracts k-parallelotopes
at an exponential rate. A sufficient condition for k-contraction is that a matrix measure
(also called logarithmic norm) of the k-additive compound of the Jacobian of the vector
field is uniformly negative. However, this may be difficult to check in practice because
the k-additive compound of an n × n matrix has dimensions nk×nk.

For an n×n matrix A, we prove a duality relation between the k and (n−k) compounds
of A. We use this duality relation to derive a sufficient condition for k-contraction that does
not require the computation of any k-compounds. We demonstrate our results by deriving
a sufficient condition for k-contraction of an n-dimensional Hopfield network that does
not require to compute any compounds. In particular, for k = 2 this sufficient condition
implies that the network is 2-contracting and this implies a strong asymptotic property:
every bounded solution of the network converges to an equilibrium point, that may not be
unique. This is relevant, for example, when using the Hopfield network as an associative
memory that stores patterns as equilibrium points of the dynamics.

Join Zoom Meetin https://us02web.zoom.us/j/82108132163?pwd=Z2h4UzNzUS9mbXplT0lMU1pZenFEQT09

God made the bulk; the surface was invented by the devil.” Wolfgang Pauli’s quote epitomizes the field of nanofluidics. In such small systems, the relatively large surface-area to volume ratio leads to surface phenomena dominating the overall response of such systems. The multiple scales (length and time) inherent to these systems, as well as the expected breakdown of the continuum mechanics framework, continue to frustrate the advancement of our fundamental understanding of this field.

This talk focuses on the particularly challenging and interdisciplinary sub-field of ion transport through highly charged nanopores. The electrical response of these systems is determined by an interplay of bulk phenomena (diffusion, electromigration, and advection), with surface mechanisms (surface charges and their regulation and hydrodynamic slip lengths) and the effects of various interfaces manifested by a wide range of boundary conditions.

I will delineate the contribution of each phenomenon separately as well as the response of their collective interplay. I will demonstrate that only after accounting for the full array of surface phenomena can theoretical analysis rationalize experimental measurements of the electrical conductance of nanopores. Finally, I will briefly review the future directions my lab is taking.

Yoav Green joined the Department of Mechanical Engineering at Ben-Gurion University in 2019 as a Senior Lecturer. Yoav heads the Fluid Mechanics Laboratory, where his current research focus is nanofluidics and electrokinetics. In particular, Yoav’s r

MECHANICAL ENGINEERING SEMINAR

Monday, Dec. 5 2022 at 14:30, D. Dan and Betty Kahn Building, Auditorium 1

Nanofluidics: surfaces, interfaces, and boundary conditions – a devil’s masterpiece

Dr. Yoav Green

Senior Lecturer of Mechanical Engineering

Ben-Gurion University

Email: yoavgreen@bgu.ac.il; Website: https://fluidmechlab.com/

Hosted by: Prof. Moran Bercovici

“

MECHANICAL ENGINEERING SEMINAR

Monday, Dec. 5 2022 at 14:30, D. Dan and Betty Kahn Building, Auditorium 1

Nanofluidics: surfaces, interfaces, and boundary conditions – a devil’s masterpiece

Dr. Yoav Green

Senior Lecturer of Mechanical Engineering

Ben-Gurion University

Email: yoavgreen@bgu.ac.il; Website: https://fluidmechlab.com/

Hosted by: Prof. Moran Bercovici

“God made the bulk; the surface was invented by the devil.” Wolfgang Pauli’s quote epitomizes the field of nanofluidics. In such small systems, the relatively large surface-area to volume ratio leads to surface phenomena dominating the overall response of such systems. The multiple scales (length and time) inherent to these systems, as well as the expected breakdown of the continuum mechanics framework, continue to frustrate the advancement of our fundamental understanding of this field.

This talk focuses on the particularly challenging and interdisciplinary sub-field of ion transport through highly charged nanopores. The electrical response of these systems is determined by an interplay of bulk phenomena (diffusion, electromigration, and advection), with surface mechanisms (surface charges and their regulation and hydrodynamic slip lengths) and the effects of various interfaces manifested by a wide range of boundary conditions.

I will delineate the contribution of each phenomenon separately as well as the response of their collective interplay. I will demonstrate that only after accounting for the full array of surface phenomena can theoretical analysis rationalize experimental measurements of the electrical conductance of nanopores. Finally, I will briefly review the future directions my lab is taking.

Yoav Green joined the Department of Mechanical Engineering at Ben-Gurion University in 2019 as a Senior Lecturer. Yoav heads the Fluid Mechanics Laboratory, where his current research focus is nanofluidics and electrokinetics. In particular, Yoav’s research group utilizes a combination of theoretical modeling, numerical simulations, and experiments to investigate the electrical response of nanochannel systems.