arXiv subjects

Alpha A. Lee

Publications and source records attributed to Alpha A. Lee.

33 records · Page 2Linked to original sources

arXiv2018

Energy-entropy competition and the effectiveness of stochastic gradient descent in machine learning

Finding parameters that minimise a loss function is at the core of many machine learning methods. The Stochastic Gradient Descent algorithm is widely used and delivers state of the art results for many problems. Nonetheless, Stochastic Gradient Descent typically cannot find the global minimum, thus its empirical effectiveness is hitherto mysterious. We derive a correspondence between parameter inference and free energy minimisation in statistical physics. The degree of undersampling plays the role of temperature. Analogous to the energy-entropy competition in statistical physics, wide but shallow minima can be optimal if the system is undersampled, as is typical in many applications. Moreover, we show that the stochasticity in the algorithm has a non-trivial correlation structure which systematically biases it towards wide minima. We illustrate our argument with two prototypical models: image classification using deep learning, and a linear neural network where we can analytically reveal the relationship between entropy and out-of-sample error.

cs.LG↗

arXiv2018

Casimir force in dense confined electrolytes

Understanding the force between charged surfaces immersed in an electrolyte solution is a classic problem in soft matter and liquid-state theory. Recent experiments showed that the force decays exponentially but the characteristic decay length in a concentrated electrolyte is significantly larger than what liquid-state theories predict based on analysing correlation functions in the bulk electrolyte. Inspired by the classical Casimir effect, we consider an alternative mechanism for force generation, namely the confinement of density fluctuations in the electrolyte by the walls. We show analytically within the random phase approximation, which assumes the ions to be point charges, that this fluctuation-induced force is attractive and also decays exponentially, albeit with a decay length that is half of the bulk correlation length. These predictions change dramatically when excluded volume effects are accounted for within the mean spherical approximation. At high ion concentrations the Casimir force is found to be exponentially damped oscillatory as a function of the distance between the confining surfaces. Our analysis does not resolve the riddle of the anomalously long screening length observed in experiments, but suggests that the Casimir force due to mode restriction in density fluctuations could be an hitherto under-appreciated source of surface-surface interaction.

cond-mat.soft↗

arXiv2018

Controlling polyelectrolyte adsorption onto carbon nanotubes by tuning ion-image interactions

Understanding and controlling polyelectrolyte adsorption onto carbon nanotubes is a fundamen- tal challenge in nanotechology. Polyelectrolytes have been shown to stabilise nanotube suspensions through adsorbing onto the nanotube surface, and polyelectrolyte-coated nanotubes are emerging as building blocks for complex and addressable self-assembly. The conventional wisdom suggests that polyelectrolyte adsorption onto nanotubes is driven by specific chemical or van der Waals interac- tions. We develop a simple mean-field model and show that ion-image attraction is a significant effect for adsorption onto conducting nanotubes at low salt concentrations. Our theory suggests a simple strategy to selectively and reversibly functionalize carbon nanotubes based on their electronic structure which in turn modifies the ion-image attraction.

cond-mat.soft↗

arXiv2017

Optimal design of experiments by combining coarse and fine measurements

In many contexts it is extremely costly to perform enough high quality experimental measurements to accurately parameterize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that indicate whether each sample is above or below a given threshold. Can many such categorical or "coarse" measurements be combined with a much smaller number of high resolution or "fine" measurements to yield accurate models? Here, we demonstrate an intuitive strategy, inspired by statistical physics, wherein the coarse measurements are used to identify the salient features of the data, while the fine measurements determine the relative importance of these features. A linear model is inferred from the fine measurements, augmented by a quadratic term that captures the correlation structure of the coarse data. We illustrate our strategy by considering the problems of predicting the antimalarial potency and aqueous solubility of small organic molecules from their 2D molecular structure.

physics.data-an↗

arXiv2017

Fluctuation Spectra and Force Generation in Non-equilibrium Systems

Many biological systems are appropriately viewed as passive inclusions immersed in an active bath: from proteins on active membranes to microscopic swimmers confined by boundaries. The non-equilibrium forces exerted by the active bath on the inclusions or boundaries often regulate function, and such forces may also be exploited in artificial active materials. Nonetheless, the general phenomenology of these active forces remains elusive. We show that the fluctuation spectrum of the active medium, the partitioning of energy as a function of wavenumber, controls the phenomenology of force generation. We find that for a narrow, unimodal spectrum, the force exerted by a non-equilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. We examine two apparently disparate examples: the Maritime Casimir effect and recent simulations of active Brownian particles. A key implication of our work is that important non-equilibrium interactions are encoded within the fluctuation spectrum. In this sense the noise becomes the signal.

cond-mat.soft↗

arXiv2017

Scaling analysis of the screening length in concentrated electrolytes

The interaction between charged objects in an electrolyte solution is a fundamental question in soft matter physics. It is well-known that the electrostatic contribution to the interaction energy decays exponentially with object separation. Recent measurements reveal that, contrary to the conventional wisdom given by classic Poisson-Boltzmann theory, the decay length increases with ion concentration for concentrated electrolytes and can be an order of magnitude larger than the ion diameter in ionic liquids. We derive a simple scaling theory that explains this anomalous dependence of the decay length on ion concentration. Our theory successfully collapses the decay lengths of a wide class of salts onto a single curve. A novel prediction of our theory is that the decay length increases linearly with the Bjerrum length, which we experimentally verify by surface force measurements. Moreover, we quantitatively relate the measured decay length to classic measurements of the activity coefficient in concentrated electrolytes, thus showing that the measured decay length is indeed a bulk property of the concentrated electrolyte as well as contributing a mechanistic insight into empirical activity coefficients.

cond-mat.soft↗

arXiv2017

Hot Particles Attract in a Cold Bath

Controlling interactions out of thermodynamic equilibrium is crucial for designing addressable and functional self-organizing structures. These active interactions also underpin collective behavior in biological systems. Here we study a general setting of active particles in a bath of passive particles, and demonstrate a novel mechanism for long range attraction between active particles. The mechanism operates when the translational persistence length of the active particle motion is smaller than the particle diameter. In this limit, the system reduces to particles of higher diffusivity ("hot" particles) in a bath of particles with lower diffusivity ("cold" particles). This attractive interaction arises as a hot particle pushes cold particles away to create a large hole around itself, and the holes interact via a depletion-like attraction. Strikingly, the interaction range is more than an order of magnitude larger than the particle radius, well beyond the range of conventional depletion force. Although the mechanism occurs outside the parameter regime of typical biological swimmers, the mechanism could be realized in the laboratory.

cond-mat.soft↗

arXiv2017

Underscreening in concentrated electrolytes

Screening of a surface charge by electrolyte and the resulting interaction energy between charged objects is of fundamental importance in scenarios from bio-molecular interactions to energy storage. The conventional wisdom is that the interaction energy decays exponentially with object separation and the decay length is a decreasing function of ion concentration; the interaction is thus negligible in a concentrated electrolyte. Contrary to this conventional wisdom, we have shown by surface force measurements that the decay length is an increasing function of ion concentration and Bjerrum length for concentrated electrolytes. In this paper we report surface force measurements to test directly the scaling of the screening length with Bjerrum length. Furthermore, we identify a relationship between the concentration dependence of this screening length and empirical measurements of activity coefficient and differential capacitance. The dependence of the screening length on the ion concentration and the Bjerrum length can be explained by a simple scaling conjecture based on the physical intuition that solvent molecules, rather than ions, are charge carriers in a concentrated electrolyte.

physics.chem-ph↗

arXiv2017

Controlling turbulent drag across electrolytes using electric fields

Reversible in operando control of friction is an unsolved challenge crucial to industrial tribology. Recent studies show that at low sliding velocities, this control can be achieved by applying an electric field across electrolyte lubricants. However, the phenomenology at high sliding velocities is yet unknown. In this paper, we investigate the hydrodynamic friction across electrolytes under shear beyond the transition to turbulence. We develop a novel, highly parallelised, numerical method for solving the coupled Navier-Stokes Poisson-Nernest-Planck equation. Our results show that turbulent drag cannot be controlled across dilute electrolyte using static electric fields alone. The limitations of the Poisson-Nernst-Planck formalism hints at ways in which turbulent drag could be controlled using electric fields.

physics.flu-dyn↗

arXiv2016

Microscopic mechanism of thermomolecular orientation and polarization

Recent molecular dynamics simulations show that thermal gradients can induce electric fields in water that are comparable in magnitude to electric fields seen in ionic thin films and biomembranes. This surprising non-equilibrium phenomenon of thermomolecular orientation is also observed more generally in simulations of polar and non-polar size-asymmetric dumbbell fluids. However, a microscopic theory linking thermomolecular orientation and polarization to molecular properties is yet unknown. Here, we formulate an analytically solvable microscopic model of size-asymmetric dumbbell molecules in a temperature gradient using a mean-field, local equilibrium approach. Our theory reveals the relationship between the extent of thermomolecular orientation and polarization, and molecular volume, size anisotropy and dipole moment. Predictions of the theory agree quantitatively with molecular dynamics simulations. Crucially, our framework shows how thermomolecular orientation can be controlled and maximized by tuning microscopic molecular properties.

cond-mat.stat-mech↗

arXiv2016

The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration

According to classical electrolyte theories interactions in dilute (low ion density) electrolytes decay exponentially with distance, with the Debye screening length the characteristic length-scale. This decay length decreases monotonically with increasing ion concentration, due to effective screening of charges over short distances. Thus within the Debye model no long-range forces are expected in concentrated electrolytes. Here we reveal, using experimental detection of the interaction between two planar charged surfaces across a wide range of electrolytes, that beyond the dilute (Debye-Huuckel) regime the screening length increases with increasing concentration. The screening lengths for all electrolytes studied - including aqueous NaCl solutions, ionic liquids diluted with propylene carbonate, and pure ionic liquids - collapse onto a single curve when scaled by the dielectric constant. This non-monotonic variation of the screening length with concentration, and its generality across ionic liquids and aqueous salt solutions, demonstrates an important characteristic of concentrated electrolytes of substantial relevance from biology to energy storage.

cond-mat.soft↗

arXiv2016

Quantum Capacitance Modifies Interionic Interactions in Semiconducting Nanopores

Nanopores made with low dimensional semiconducting materials, such as carbon nanotubes and graphene slit pores, are used in supercapacitors. In theories and simulations of their operation, it is often assumed that such pores screen ion-ion interactions like metallic pores, i.e. that screening leads to an exponential decay of the interaction potential with ion separation. By introducing a quantum capacitance that accounts for the density of states in the material, we show that ion-ion interactions in carbon nanotubes and graphene slit pores actually decay algebraically with ion separation. This result suggests a new avenue of capacitance optimization based on tuning the electronic structure of a pore: a marked enhancement in capacitance might be achieved by developing nanopores made with metallic materials or bulk semimetallic materials.

cond-mat.mtrl-sci↗

arXiv2015

The role of extensibility in the birth of a ruck in a rug

Everyday experience suggests that a `ruck' forms when the two ends of a heavy carpet or rug are brought closer together. Classical analysis, however, shows that the horizontal compressive force needed to create such a ruck should be infinite. We show that this apparent paradox is due to the assumption of inextensibility of the rug. By accounting for a finite extensibility, we show that rucks appear with a finite, non-zero end-shortening and confirm our theoretical results with simple experiments. Finally, we note that the appropriate measure of extensibility, the stretchability, is in this case not determined purely by geometry, but incorporates the mechanics of the sheet.

cond-mat.soft↗

arXiv2015

Dynamics of Ion Transport in Ionic Liquids

A gap in understanding the link between continuum theories of ion transport in ionic liquids and the underlying microscopic dynamics has hindered the development of frameworks for transport phenomena in these concentrated electrolytes. Here, we construct a continuum theory for ion transport in ionic liquids by coarse graining a simple exclusion process of interacting particles on a lattice. The resulting dynamical equations can be written as a gradient flow with a mobility matrix that vanishes at high densities. This form of the mobility matrix gives rise to a charging behaviour that is different to the one known for electrolytic solutions, but which agrees qualitatively with the phenomenology observed in experiments and simulations.

cond-mat.soft↗

arXiv2012

Electroactuation with Single Charge Carrier Ionomers

A simple theory of electromechanical transduction for single-charge-carrier double-layer electroactuators is developed, in which the ion distribution and curvature are mutually coupled. The obtained expressions for the dependence of curvature and charge accumulation on the applied voltage, as well as the electroactuation dynamics, are compared with literature data. The mechanical- or sensor- performance of such electroactuators appears to be determined by just three cumulative parameters, with all of their constituents measurable, permitting a scaling approach to their design.

cond-mat.soft↗