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J. C. Neu

Publications and source records attributed to J. C. Neu.

8 recordsLinked to original sources
arXiv2023

Charging capacitors from thermal fluctuations using diodes

We theoretically consider a graphene ripple as a Brownian particle coupled to an energy storage circuit. When circuit and particle are at the same temperature, the second law forbids harvesting energy from the thermal motion of the Brownian particle, even if the circuit contains a rectifying diode. However, when the circuit contains a junction followed by two diodes wired in opposition, the approach to equilibrium may become ultraslow. Detailed balance is temporarily broken as current flows between the two diodes and charges storage capacitors. The energy harvested by each capacitor comes from the thermal bath of the diodes while the system obeys the first and second laws of thermodynamics.

cond-mat.mes-hall↗
arXiv2009

Theory of surface deposition from boundary layers containing condensable vapour and particles

Heterogeneous condensation of vapours mixed with a carrier gas in the stagnation point boundary layer flow near a cold wall is considered in the presence of solid particles much larger than the mean free path of vapour particles. The supersaturated vapour condenses on the particles by diffusion and particles and droplets are thermophoretically attracted to the wall. Assuming that the heat of vaporization is much larger than the Boltzmann constant times the temperature far from the wall, vapour condensation occurs in a {\em condensation layer} (CL). The CL width and characteristics depend on the parameters of the problem, and a parameter $R$ yielding the rate of vapour scavenging by solid particles is particularly important. Assuming that the CL is so narrow that temperature, particle density and velocity do not change appreciably inside it, an asymptotic theory is found, the $δ$-CL theory, that approximates very well the vapour and droplet profiles, the dew point shift and the deposition rates at the wall for wide ranges of the wall temperature $\tilde{T}_{w}$ and the scavenging parameter $R$. This theory breaks down for $\tilde{T}_{w}$ very close to the maximum temperature yielding non-zero droplet deposition rate, $\tilde{T}_{w,M}$. For large $R$, we can either assume that the width of the CL is zero (0-CL theory, then the vapour density reaches local equilibrium with the condensate immediately after it enters the dew surface), or use a nonlinear multiple scales theory. The 0-CL theory corrects the $δ$-CL theory for $\tilde{T}_w$ very close to $\tilde{T}_{w,M}$ and any $R$, whereas the multiple scales theory is appropriate for large and moderate $R$.

cond-mat.other↗
arXiv2008

Exhaustion of Nucleation in a Closed System

We determine the distribution of cluster sizes that emerges from an initial phase of homogeneous aggregation with conserved total particle density. The physical ingredients behind the predictions are essentially classical: Super-critical nuclei are created at the Zeldovich rate, and before the depletion of monomers is significant, the characteristic cluster size is so large that the clusters undergo diffusion limited growth. Mathematically, the distribution of cluster sizes satisfies an advection PDE in "size-space". During this creation phase, clusters are nucleated and then grow to a size much larger than the critical size, so nucleation of super-critical clusters at the Zeldovich rate is represented by an effective boundary condition at zero size. The advection PDE subject to the effective boundary condition constitutes a "creation signaling problem" for the evolving distribution of cluster sizes during the creation era. Dominant balance arguments applied to the advection signaling problem show that the characteristic time and cluster size of the creation era are exponentially large in the initial free-energy barrier against nucleation, G_*. Specifically, the characteristic time is proportional to exp(2 G_*/ 5 k_B T) and the characteristic number of monomers in a cluster is proportional to exp(3G_*/5 k_B T). The exponentially large characteristic time and cluster size give a-posteriori validation of the mathematical signaling problem. In a short note, Marchenko obtained these exponentials and the numerical pre-factors, 2/5 and 3/5. Our work adds the actual solution of the kinetic model implied by these scalings, and the basis for connection to subsequent stages of the aggregation process after the creation era.

cond-mat.mtrl-sci↗
arXiv2006

Asymptotic and numerical studies of the Becker-Doering model for transient homogeneous nucleation

Transient homogeneous nucleation is studied in the limit of large critical sizes. Starting from pure monomers, three eras of transient nucleation are characterized in the classic Becker-Döring kinetic equations with the Turnbull-Fisher discrete diffusivity. After an initial stage in which the number of monomers decreases, many clusters of small size are produced and a continuous size distribution is created. During the second era, nucleii are increasing steadily in size in such a way that their distribution appears as a wave front advancing towards the critical size for steady nucleation. The nucleation rate at critical size is negligible during this era. After the wave front reaches critical size, it ignites the creation of supercritical clusters at a rate that increases monotonically until its steady value is reached. Analytical formulas for the transient nucleation rate and the time lag are obtained that improve classical ones and compare very well with direct numerical solutions. In addition, we propose and solve numerically a modified Becker-Döring model having a discrete diffusivity proportional to the area of a spherical cluster with $k$ monomers for small $k$ (as in the Turnbull-Fisher case) and to the cluster radius for large $k$ (as in the case of diffusive growth of clusters).

cond-mat.stat-mech↗
arXiv2006

Kinetics of helium bubble formation in nuclear materials

The formation and growth of helium bubbles due to self-irradiation in plutonium has been modelled by a discrete kinetic equations for the number densities of bubbles having $k$ atoms. Analysis of these equations shows that the bubble size distribution function can be approximated by a composite of: (i) the solution of partial differential equations describing the continuum limit of the theory but corrected to take into account the effects of discreteness, and (ii) a local expansion about the advancing leading edge of the distribution function in size space. Both approximations contribute to the memory term in a close integrodifferential equation for the monomer concentration of single helium atoms. The present boundary layer theory for discrete equations is compared to the numerical solution of the full kinetic model and to previous approximation of Schaldach and Wolfer involving a truncated system of moment equations.

cond-mat.mtrl-sci↗
arXiv2004

Igniting homogeneous nucleation

Transient homogeneous nucleation is studied in the limit of large critical sizes. Starting from pure monomers, three eras of transient nucleation are characterized in the classic Becker-Döring kinetic equations with two different models of discrete diffusivity: the classic Turnbull-Fisher formula and an expression describing thermally driven growth of the nucleus. The latter diffusivity yields time lags for nucleation which are much closer to values measured in experiments with disilicate glasses. After an initial stage in which the number of monomers decreases, many clusters of small size are produced and a continuous size distribution is created. During the second era, nucleii are increasing steadily in size in such a way that their distribution appears as a wave front advancing towards the critical size for steady nucleation. The nucleation rate at critical size is negligible during this era. After the wave front reaches critical size, it ignites the creation of supercritical clusters at a rate that increases monotonically until its steady value is reached. Analytical formulas for the transient nucleation rate and the time lag are obtained that improve classical ones and compare very well with direct numerical solutions.

cond-mat.mtrl-sci↗
arXiv2002

Three eras of micellization

Micellization is the precipitation of lipids from aqueous solution into aggregates with a broad distribution of aggregation number. Three eras of micellization are characterized in a simple kinetic model of Becker-Döring type. The model asigns the same constant energy to the $(k-1)$ monomer-monomer bonds in a linear chain of $k$ particles. The number of monomers decreases sharply and many clusters of small size are produced during the first era. During the second era, nucleii are increasing steadily in size until their distribution becomes a self-similar solution of the diffusion equation. Lastly, when the average size of the nucleii becomes comparable to its equilibrium value, a simple mean-field Fokker-Planck equation describes the final era until the equilibrium distribution is reached.

cond-mat.mtrl-sci↗