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Nanofluidic diodes are capable of rectifying the electrical current by several orders of magnitude. In the current state of affairs, determining the rectification factor is not possible as it depends on many system parameters. In this work, we systematically scan the effects of geometry and excess counterion concentrations (i.e., surface charge effects). We show that the current-voltage response varies between the two extreme behaviors of unipolar and bipolar responses. The exact behavior depends on the geometry and surface charge properties of the system. Here, we have gone beyond the typical setup that only considers the dynamics within the nanochannel itself and we have included the effects of the adjoining microchannels. Systems that include both nanochannels and microchannels exhibit the classical signatures of concentration polarization, such as ionic depletion and enrichment. Here, where we have scanned a wide range of parameters, we show that bipolar and semi-bipolar systems exhibit a wider range of phenomena that are intrinsically more complicated. Our system characterization is for both, the much more investigated case of steady state and the less investigated, but equally interesting, time-transient case. For example, it is common to characterize the system by its steady-state result (current-voltage response, rectification factor, and transport number). Here, we demonstrate that the time-transient behavior of the fluxes can also be used to characterize the system, and that the time-dependent rectification factors and transport numbers are meaningful. The systematic approach taken in this work, and the results presented herein, can be used to further elucidate the complicated behavior of the current-voltage response of nanofluidic diodes and to rationalize experimental results. The insights of this work can be used to enhance and improve the design of all nanofluidic diodes.

A nanopore's response to an electrical potential drop is characterized by its electrical conductance, . For the last two decades, it has been thought that at low electrolyte concentrations, , the conductance is concentration-independent such that . It has been recently demonstrated that surface charge regulation changes the dependency to , whereby the slope typically takes the values α = 1/3 or 1/2. However, experiments have observed slopes of 2/3 and 1 suggesting that additional mechanisms, such as convection and slip-lengths, appear. Here, we elucidate the interplay between three mechanisms: surface charge regulation, convection, and slip lengths. We show that the inclusion of convection does not change the slope, and when the effects of hydrodynamic slip are included, the slope is doubled. We show that when all effects are accounted for, α can take any value between 0 and 1 where the exact value of the slope depends on the material properties. This result is of utmost importance in designing any electro-kinetically driven nanofluidic system characterized by its conductance.

Current paradigm suggests that the Ohmic electrical response of nanochannel-microchannel systems is determined solely by the nanochannel while the effects of the adjacent microchannels are negligible. However, recent works have challenged this paradigm and have shown that at low concentrations the microchannels contribute in a non-negligible manner. As such, the two favored models used to explain experiments are inadequate in describing realistic nanochannel-microchannel systems. To partially reconcile some of these issues, two newer nanochannel-microchannel models were derived and suggested as a suitable replacement for the nanochannel-dominant models. Unfortunately, these two models are limited to either very low or very high concentrations. In this work, we review these four leading models. We discuss their key assumptions, advantages, shortcomings, and present a knowledge gap between all models pertaining to the effects of the microchannel resistance for all concentrations. To overcome this gap, we derive an analytical solution that accounts for the effects of the microchannels and holds for all concentrations. This solution unifies three of the existing models where we show that they are limiting cases of our more general solution. We are also able to disqualify the fourth model. Our derived solution shows remarkable correspondence to simulations and experiments. The insights from this unifying model can be used to improve the design of any nanofluidic based systems.

The relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer are currently unknown. Ten years ago, a method known as monolayer stress microscopy (MSM) was suggested from which intercellular stresses could be computed for a given traction field. The core assumption of MSM is that intercellular stresses within the monolayer obey a linear and passive constitutive law. Examples of these include a Hookean solid (an elastic sheet) or a Newtonian fluid (thin fluid film), which imply a specific relation between the displacements or velocities and the tractions. Due to the lack of independently measured intercellular stresses, a direct validation of the 2D stresses predicted by a linear passive MSM model is presently not possible. An alternative approach, which we give here and denote as the Stokes method, is based on simultaneous measurements of the monolayer velocity field and the cell-substrate tractions. Using the same assumptions as those underlying MSM, namely, a linear and passive constitutive law, the velocity field suffices to compute tractions, from which we can then compare with those measured by traction force microscopy. We find that the calculated tractions and measured tractions are uncorrelated. Since the classical MSM and the Stokes approach both depend on the linear and passive constitutive law, it follows that some serious modification of the underling rheology is needed. One possible modification is the inclusion of an active force. In the special case where this is additive to the linear passive rheology, we have a new relationship between the active force density and the measured velocity (or displacement) field and tractions, which by Newton's laws, must be obeyed.

The time-dependent behavior of one-dimensional ion transport into a permselective medium is theoretically modeled in this work for currents exceeding the diffusion limit. Leveraging the findings of Yariv [E. Yariv, Phys. Rev. E 80, 051201 (2009)10.1103/PhysRevE.80.051201], we derive three separate expressions for the potential drop for short, intermediate, and long times. We show that the potential drop correlates to the time evolution of the space-charge layer adjacent to the permselective interface. Our approximate models show remarkable correspondence to numerical simulations.

For the past decade, the interaction force between droplets flowing in a Hele-Shaw cell has been modelled as a dipole. In this work, we use the recently derived analytical solution of Sariget al.(J. Fluid Mech., vol. 800, 2016, pp. 264–277) of a two-droplet system, which satisfies the no-flux condition at both droplet interfaces, and compare it to results of the dipole model, which does not satisfy the no-flux condition. Unfortunately, the recently derived solution is given in terms of infinite Fourier series, making any additional straightforward analysis difficult. We derive simple approximations for these Fourier series. We show that at large spacing the approximations for the interactions reduce to the expected dipole-like solution. We also provide a new lower limit for the velocity for the case of almost touching droplets. For the case of large spacing, the derivation is extended to arbitrary droplet numbers – including an infinite lattice. We present a new correction for the dispersion relation for the perturbations. We investigate the effect of the number of droplets in a lattice,$N$, on the resulting dynamics.

It has recently been suggested that a breakdown of electroneutrality occurs in highly confined nanopores that are encompassed by a dielectric material. This work elucidates the conditions for this breakdown. We show that the breakdown within the pore results from the response of the electric field within the dielectric. Namely, we show that this response is highly sensitive to the boundary condition at the dielectric edge. The standard Neumann boundary condition of no-flux predicts that the breakdown does not occur. However, a Dirichlet boundary condition for a zero-potential predicts a breakdown. Within this latter scenario, the breakdown exhibits a dependence on the thickness of the dielectric material. Specifically, infinite thickness dielectrics do not exhibit a breakdown, while dielectrics of finite thickness do exhibit a breakdown. Numerical simulations confirm theoretical predictions. The breakdown outcomes are discussed with regard to single pore systems and multiple pore systems.

Author(s): Schulze, S; Yaron, O; Sollerman, J; Leloudas, G; Gal, A; Wright, AH; Lunnan, R; Gal-Yam, A; Ofek, EO; Perley, DA; Filippenko, AV; Kasliwal, MM; Kulkarni, SR; Neill, JD; Nugent, PE; Quimby, RM; Sullivan, M; Strotjohann, NL; Arcavi, I; Ben-Ami, S; Bianco, F; Bloom, JS; De, K; Fraser, M; Fremling, CU; Horesh, A; Johansson, J; Kelly, PL; Kneževic, N; Kneževic, S; Maguire, K; Nyholm, A; Papadogiannakis, S; Petrushevska, T; Rubin, A; Yan, L; Yang, Y; Adams, SM; Bufano, F; Clubb, KI; Foley, RJ; Green, Y; Harmanen, J; Ho, AYQ; Hook, IM; Hosseinzadeh, G; Howell, DA; Kong, AKH; Kotak, R; Matheson, T; McCully, C; Milisavljevic, D; Pan, YC; Poznanski, D; Shivvers, I; Van Velzen, S; Verbeek, KK | Abstract: Several thousand core-collapse supernovae (CCSNe) of different flavors have been discovered so far. However, identifying their progenitors has remained an outstanding open question in astrophysics. Studies of SN host galaxies have proven to be powerful in providing constraints on the progenitor populations. In this paper, we present all CCSNe detected between 2009 and 2017 by the Palomar Transient Factory. This sample includes 888 SNe of 12 distinct classes out to redshift z ≈ 1. We present the photometric properties of their host galaxies from the far-ultraviolet to the mid-infrared and model the host-galaxy spectral energy distributions to derive physical properties. The galaxy mass function of Type Ic, Ib, IIb, II, and IIn SNe ranges from 105 to 1011.5 M o˙, probing the entire mass range of star-forming galaxies down to the least-massive star-forming galaxies known. Moreover, the galaxy mass distributions are consistent with models of star-formation-weighted mass functions. Regular CCSNe are hence direct tracers of star formation. Small but notable differences exist between some of the SN classes. Type Ib/c SNe prefer galaxies with slightly higher masses (i.e., higher metallicities) and star formation rates than Type IIb and II SNe. These differences are less pronounced than previously thought. H-poor superluminous supernovae (SLSNe) and SNe Ic-BL are scarce in galaxies above 1010 M o˙. Their progenitors require environments with metallicities of l 0.4 and l 1 solar, respectively. In addition, the hosts of H-poor SLSNe are dominated by a younger stellar population than all other classes of CCSNe. Our findings corroborate the notion that low metallicity and young age play an important role in the formation of SLSN progenitors.

Investigation of ion transport through nanopores with highly overlapping electric double layers is extremely challenging. This can be attributed to the non-linear Poisson-Boltzmann equation that governs the behavior of the electrical potential distribution as well as other characteristics of ion transport. In this work, we leverage the approach of Schnitzer and Yariv [Phys. Rev. E 87, 054301 (2013)] to reduce the complexity of the governing equation. An asymptotic solution is derived, which shows remarkable correspondence to simulations of the non-approximated equations. This new solution is leveraged to address a number of highly debated issues. We derive the equivalent of the Gouy-Chapman equation for systems with highly overlapping electric double layers. This new relationship between the surface charge density and the surface potential is then utilized to determine the power-law scaling of nanopore conductances as a function of the bulk concentrations. We derive the coefficients of transport for the case of overlapping electric double layers and compare it to the renowned uniform potential model. We show that the uniform potential model is only an approximation for the exact solution for small surface charges. The findings of this work can be leveraged to uncover additional hidden attributes of ion transport through nanopores.

Collective cell polarization and alignment play important roles in tissue morphogenesis, wound healing and cancer metastasis. How cells sense the direction and position in these processes, however, has not been fully understood. Here we construct a theoretical model based on describing cell layers as a nemato-elastic medium, by which the cell polarization, cell alignment and cell active contraction are explicitly expressed as functions of components of the nematic order parameter. To determine the order parameter we derive two sets of governing equations, one for the force equilibrium of the system, and the other for the minimization of the system's free energy including the energy of cell polarization and alignment. By solving these coupled governing equations, we can predict the effects of substrate stiffness, geometries of cell layers, external forces and myosin activity on the direction- and position-dependent cell aspect ratio and cell orientation. Moreover, the axisymmetric problem with cells on a ring-like pattern is solved analytically, and the analytical solution for cell aspect ratio are governed by parameter groups which include the stiffness of the cell and the substrate, the strength of myosin activity and the external forces. Our predictions of the cell aspect ratio and orientation are generally comparable to experimental observations. These results show that the pattern of cell polarization is determined by the anisotropic degree of active contractile stress, and suggest a stress-driven polarization mechanism that enables cells to sense their spatial positions to develop direction- and position-dependent behavior. This, in turn, sheds light on the ways to control pattern formation in tissue engineering for potential biomedical applications.

Permselective nanochannels can rectify the electric current transported through them similar to solid-state diodes. The rectification is due to symmetry breaking related to distribution of the nanochannels' surface charge as well as the geometry. Thus far, most of the works related to the asymmetric current response have been primarily experimental. Here, we theoretically model a funnel-shaped nanochannel with a nonhomogeneous surface charge from which we derive a current-voltage relation (I-V). If the effects of the adjacent microchannels are ignored, the I-V is shown to behave like a unipolar diodes. When the effects of the adjacent microchannels are accounted for, the channel behaves like a diode only in a small voltage domain, while at larger voltages, the response is determined by the microchannels. The theoretical results are confirmed by numerical simulations.

The Palomar Transient Factory (PTF) is systematically charting the optical transient and variable sky. A primary science driver of PTF is building a complete inventory of transients in the local Universe (distance less than 200 Mpc). Here, we report the discovery of PTF10fqs, a transient in the luminosity "gap" between novae and supernovae. Located on a spiral arm of Messier 99, PTF 10fqs has a peak luminosity of Mr = -12.3, red color (g-r = 1.0) and is slowly evolving (decayed by 1 mag in 68 days). It has a spectrum dominated by intermediate-width H (930 km/s) and narrow calcium emission lines. The explosion signature (the light curve and spectra) is overall similar to thatof M85OT2006-1, SN2008S, and NGC300OT. The origin of these events is shrouded in mystery and controversy (and in some cases, in dust). PTF10fqs shows some evidence of a broad feature (around 8600A) that may suggest very large velocities (10,000 km/s) in this explosion. Ongoing surveys can be expected to find a few such events per year. Sensitive spectroscopy, infrared monitoring and statistics (e.g. disk versus bulge) will eventually make it possible for astronomers to unravel the nature of these mysterious explosions., 12 pages, 12 figures, Replaced with published version

The Palomar Transient Factory (PTF) is an optical wide-field variability survey carried out using a camera with a 7.8 square degree field of view mounted on the 48-in Oschin Schmidt telescope at Palomar Observatory. One of the key goals of this survey is to conduct high-cadence monitoring of the sky in order to detect optical transient sources shortly after they occur. Here, we describe the real-time capabilities of the PTF and our related rapid multiwavelength follow-up programs, extending from the radio to the gamma-ray bands. We present as a case study observations of the optical transient PTF10vdl (SN 2010id), revealed to be a very young core-collapse (Type II-P) supernova having a remarkably low luminosity. Our results demonstrate that the PTF now provides for optical transients the real-time discovery and rapid-response follow-up capabilities previously reserved only for high-energy transients like gamma-ray bursts., Comment: ApJ, in press; all spectroscopic data available from the Weizmann Institute of Science Experimental Astrophysics Spectroscopy System (WISEASS; http://www.weizmann.ac.il/astrophysics/wiseass/)

We present the discovery and characterisation of PTF10iya, a short-lived (dt ~ 10 d, with an optical decay rate of ~ 0.3 mag per d), luminous (M_g ~ -21 mag) transient source found by the Palomar Transient Factory. The ultraviolet/optical spectral energy distribution is reasonably well fit by a blackbody with T ~ 1-2 x 10^4 K and peak bolometric luminosity L_BB ~ 1-5 x 10^44 erg per s (depending on the details of the extinction correction). A comparable amount of energy is radiated in the X-ray band that appears to result from a distinct physical process. The location of PTF10iya is consistent with the nucleus of a star-forming galaxy (z = 0.22405 +/- 0.00006) to within 350 mas (99.7 per cent confidence radius), or a projected distance of less than 1.2 kpc. At first glance, these properties appear reminiscent of the characteristic "big blue bump" seen in the near-ultraviolet spectra of many active galactic nuclei (AGNs). However, emission-line diagnostics of the host galaxy, along with a historical light curve extending back to 2007, show no evidence for AGN-like activity. We therefore consider whether the tidal disruption of a star by an otherwise quiescent supermassive black hole may account for our observations. Though with limited temporal information, PTF10iya appears broadly consistent with the predictions for the early "super-Eddington" phase of a solar-type star disrupted by a ~ 10^7 M_sun black hole. Regardless of the precise physical origin of the accreting material, the large luminosity and short duration suggest that otherwise quiescent galaxies can transition extremely rapidly to radiate near the Eddington limit; many such outbursts may have been missed by previous surveys lacking sufficient cadence.

For a symmetric ion permselective system, in terms of geometry and bulk concentrations, the system response is also symmetric under opposite electric field polarity. In this work we derive an analytical solution for the concentration distribution, electric potential, and current-voltage response for a four-layered system comprised of two microchambers connected by two permselective regions of varying properties. It is shown that any additional asymmetry in the system, in terms of the geometry, bulk concentration, or surface charge property of the permselective regions, results in current rectification. Our work is divided into two parts: when both permselective regions have the same surface charge sign and the case of opposite signs. For the same sign case we are able to show that the system behaves as a dialytic battery while accounting for field-focusing effects. For the case of opposite signs (i.e., bipolar membrane), our system exhibits the behavior of a bipolar diode where the magnitude of the rectification can be of order 10^{2}-10^{3}.

To bridge the gap between single and isolated pore systems to multipore systems, such as membranes and electrodes, we studied an array of nanochannels with varying interchannel spacing that controlled the degree of channel communication. Instead of treating them as individual channels connected in parallel or an assembly like a homogeneous membrane, this study resolves the pore-pore interaction. We found that increased channel isolation leads to current intensification, whereas at high voltages electroconvective effects control the degree of communication via suppression of the diffusion layer growth.

The current study extends previous two-dimensional (2D) analysis of concentration polarization to account for three-dimensional effects in realistic heterogeneous ion-permselective systems, e.g., microchamber-nanoslot devices. An analytical solution of the electrodiffusive problem, decoupled from electroconvection along with the local electroneutrality approximation, was obtained using the separation of variables technique. It is able to account for the previously neglected effects of microchamber and nanoslot heights on concentration polarization in terms of concentration profiles, limiting current, and current-voltage curves. The resultant heterogeneity in the third dimension adds to that already existing in the 2D in plane problem to further increase geometric field-focusing effects. As a result the currents no longer scale linearly with the nanoslot area, but rather depend on its shape and relative size compared to that of the nonconducting region (i.e., level of heterogeneity). This is turn leads to pronounced current density intensification with increased system heterogeneity found to be in qualitative agreement with previously reported experiments in which both microchamber and nanoslot geometries were varied.

This study extends previous analytical solutions of concentration-polarization occurring solely in the depleted region, to the more realistic geometry consisting of a three dimensional (3D) heterogeneous ion-permselective medium connecting two opposite microchambers (i.e. 3 layers system). Under the local electro-neutrality approximation, the separation of variable methods is used to derive an analytical solution of the electro-diffusive problem for the two opposing asymmetric microchambers. Assuming an ideal permselective medium allows for the analytic calculation of the 3D concentration and electric potential distributions as well as a current-voltage relation. It is shown that any asymmetry in the microchamber geometries will result in current rectification. Moreover, it is demonstrated that for non-negligible microchamber resistances the conductance does not exhibit the expected saturation at low concentrations but instead shows a continuous decrease. The results are intended to facilitate a more direct comparison between theory and experiments as now the voltage drop is across a realistic 3D and 3-layer system., Comment: 7 figures

By applying a stepwise overlimiting voltage to a nanoslot system in equilibrium, it is possible to follow the time evolution of the electroconvective instability vortex array via the depletion dynamics or, alternatively, by following dielectrophoretically trapped particles at the stagnation points of each of the hydrodynamic vortex pairs. Particles are advected to the stagnation point by the hydrodynamics, where they are trapped by a short-range dielectrophoretic force. It is experimentally confirmed that the wavelength selection process occurs at the diffusive time scale and that the wavelength selection mechanism, started by the Rubinstein and Zaltzman electroconvective instability is eventually determined by the system lateral geometry and dictated by Dukhin's electro-osmosis of the second kind. The steady-state case was numerically studied by solving the fully coupled electroconvective problem, confirming that the vortex stagnation point is indeed of a converging type. The particle's planar (two-dimensional) equations of motion are solved after adding a dielectrophoretic force that accounts for quasi-three-dimensional effects. It is shown that this force can account for trapping at the nanoslot interface.

We present detailed optical photometry for 25 Type Ibc supernovae within d\approx150 Mpc obtained with the robotic Palomar 60-inch telescope in 2004-2007. This study represents the first uniform, systematic, and statistical sample of multi-band SNe Ibc light curves available to date. We correct the light curves for host galaxy extinction using a new technique based on the photometric color evolution, namely, we show that the (V-R) color of extinction-corrected SNe Ibc at t\approx10 days after V-band maximum is tightly distributed, (V-R)=0.26+-0.06 mag. Using this technique, we find that SNe Ibc typically suffer from significant host galaxy extinction, E(B-V)\approx0.4 mag. A comparison of the extinction-corrected light curves for SNe Ib and Ic reveals that they are statistically indistinguishable, both in luminosity and decline rate. We report peak absolute magnitudes of M_R=-17.9+-0.9 mag and M_R=-18.3+-0.6 mag for SNe Ib and Ic, respectively. Focusing on the broad-lined SNe Ic, we find that they are more luminous than the normal SNe Ibc sample, M_R=-19.0+-1.1 mag, with a probability of only 1.6% that they are drawn from the same population of explosions. By comparing the peak absolute magnitudes of SNe Ic-BL with those inferred for local engine-driven explosions (GRB-SN 1998bw, XRF-SN 2006aj, and SN2009bb) we find a 25% probability that they are drawn from the SNe Ic-BL population. Finally, we fit analytic models to the light-curves to derive typical Ni-56 masses of M_Ni \approx0.2 and 0.5 M_sun for SNe Ibc and SNe Ic-BL, respectively. With reasonable assumptions for the photospheric velocities, we extract kinetic energy and ejecta mass values of M_ej \approx 2 M_sun and E_K\approx1e+51 erg for SNe Ibc, while for SNe Ic-BL we find higher values, M_ej\approx5 M_sun and E_K\approx1e+52 erg. We discuss the implications for the progenitors of SNe Ibc and their relation to engine-driven explosions [ABRIDGED]., Comment: 44 pages, 23 figures, 7 tables, as published in ApJ

We present the discovery and follow-up observations of a broad-line type-Ic supernova (SN), PTF 10bzf (SN 2010ah), detected by the Palomar Transient Factory (PTF) on 2010 February 23. The SN distance is \cong 218 Mpc, greater than GRB 980425 / SN 1998bw and GRB 060218 / SN 2006aj, but smaller than the other SNe firmly associated with gamma-ray bursts (GRBs). We conducted a multi-wavelength follow-up campaign with Palomar-48 inch, Palomar 60-inch, Gemini-N, Keck, Wise, Swift, the Allen Telescope Array, CARMA, WSRT, and EVLA. Here we compare the properties of PTF 10bzf with those of SN 1998bw and other broad-line SNe. The optical luminosity and spectral properties of PTF 10bzf suggest that this SN is intermediate, in kinetic energy and amount of 56Ni, between non GRB-associated SNe like 2002ap or 1997ef, and GRB-associated SNe like 1998bw. No X-ray or radio counterpart to PTF 10bzf was detected. X-ray upper-limits allow us to exclude the presence of an underlying X-ray afterglow as luminous as that of other SN-associated GRBs like GRB 030329 or GRB 031203. Early-time radio upper-limits do not show evidence for mildly-relativistic ejecta. Late-time radio upper-limits rule out the presence of an underlying off-axis GRB, with energy and wind density similar to the SN-associated GRB 030329 and GRB 031203. Finally, by performing a search for a GRB in the time window and at the position of PTF 10bzf, we find that no GRB in the IPN catalog could be associated with this SN., Comment: 34 pages, 7 figures, to appear in ApJ; revised version addresses referee's comments; P60 data added; results unchanged