114 research outputs found
Theory of activated-rate processes under shear with application to shear-induced aggregation of colloids
Using a novel approximation scheme within the convective diffusion (two body
Smoluchowski) equation framework, we unveil the shear-driven aggregation
mechanism at the origin of structure-formation in sheared colloidal systems.
The theory, verified against numerics and experiments, explains the induction
time followed by explosive (irreversible) rise of viscosity observed in
charge-stabilized colloidal and protein systems under steady shear. The
Arrhenius-type equation with shear derived here, extending Kramers theory in
the presence of shear, is the first analytical result clearly showing the
important role of shear-drive in activated-rate processes as they are
encountered in soft condensed matter
Extension results for slice regular functions of a quaternionic variable
In this paper we prove a new representation formula for slice regular
functions, which shows that the value of a slice regular function at a
point can be recovered by the values of at the points and
for any choice of imaginary units This result allows us to
extend the known properties of slice regular functions defined on balls
centered on the real axis to a much larger class of domains, called axially
symmetric domains. We show, in particular, that axially symmetric domains play,
for slice regular functions, the role played by domains of holomorphy for
holomorphic functions
Effects of non-linear rheology on the electrospinning process: a model study
We develop an analytical bead-spring model to investigate the role of
non-linear rheology on the dynamics of electrified jets in the early stage of
the electrospinning process. Qualitative arguments, parameter studies as well
as numerical simulations, show that the elongation of the charged jet filament
is significantly reduced in the presence of a non-zero yield stress. This may
have beneficial implications for the optimal design of future electrospinning
experiments
On a Generalization of the Corona Problem
Let g, fl,...., fm EH (A). We provide conditions on fl,...,fm in order that Ig(z) lIfi(z)l+...+Ifm (z)I, for all z in 4, imply that g, or g2, belong to the ideal generated by fl,....,fm in H
A New Theory of Regular Functions of a Quaternionic Variable
In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series
Regular Functions on the Space of Cayley Numbers
In this paper we present a new definition of regularity on the space Ç of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions, and we develop the basic elements of a function theory on Ç. Particular attention is given to the structure of the zero sets of such functions
The Merchant and the Mathematician: Commerce and Accounting
In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved
The Merchant and the Mathematician: Commerce and Accounting
In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved
Music: Numbers in Motion
Music develops and appears as we allow numbers to acquire a dynamical aspect and create, through their growth, the various keys that permit the richness of the musical texture. This idea was simply adumbrated in Plato’s work, but its importance to his philosophical worldview cannot be underestimated. In this paper we begin by discussing what is probably the first written record of an attempt to create a good temperament and then follow the Pythagoreans approach, whose problems forced musicians, over the next several centuries up to the Renaissance and early modern times, to come up with many different variations
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