Effective optimization of irrigation networks with pressure-driven outflows at randomly selected installation nodes.

This paper presents an innovative methodology for the design of pressurized irrigation networks. Compared to other methodologies proposed in the scientific literature, it features three novel aspects: (i) construction of peak demand scenarios based on the random selection of installation nodes for hydrant heads available in each sector of irrigated properties; (ii) realistic hydraulic modelling of outflows from hydrant heads by means of the pressure driven approach; and (iii) adoption of linear constraints to enforce the telescopic property in the distribution of diameters from the source towards the external areas of the network in the optimized design. The applications of the methodology to the real network serving an irrigated area of 750 ha in Northern Italy proved that the aspects (i) and (ii) contribute to the accurate modelling of the current network while highlighting its hydraulic deficiencies. The adoption of the linear constraints described in (iii) in the context of the bi-objective genetic optimization of network diameters resulted in the speeding up of the algorithm convergence. The results show how decision makers can choose the ultimate configuration based on budget considerations from the trade-off solutions obtained between installation costs and hydraulic performance, considering network layouts with different level of topological redundancy.

Nonlinear behavior of the impedance spectrum of a kerosene based ferrofluid.

We investigate the nonlinear behavior of the electric impedance of a kerosene-based ferrofluid (FF) sample subjected to an ac electric voltage of amplitude ranging from 10 mV to 3 V in the frequency range 6.3 mHz, 100 kHz. The FF sample was inserted between two parallel gold electrodes separated by 127 µm distance. The results show that even a sinusoidal voltage of amplitude low as 80 mV can give origin to nonlinear effects for frequency of the applied voltage smaller than 100 mHz. Our experimental data confirm the results obtained by solving numerically the equations of the Poisson-Nernst-Planck model. From this agreement it follows that the model based on the equation of continuity for the mobile ions, and the equation of Poisson for the actual potential across the sample, works well also in its non-linear version.

Ions, adsorption and electric response of a ferrofluid cell.

We show that the electric response of a cell in the shape of a slab containing a ferrofluid (magnetic particles in kerosene) can be interpreted by means of a model based on the adsorption of ions from limiting surfaces. We report on three samples, identical in all aspects, but limited by electrodes in gold, platinum and titanium. For frequency larger than 1 kHz, the spectra of the real and imaginary parts of the total electrical impedance of the cells are identical. From this result it follows that in this frequency range the response of the cell is independent of the electrodes, which can be considered as blocking. In the low frequency region, up to 0.3 mHz, the response of the cells depends on the electrodes, as discussed recently by Batalioto et al., Phys. Chem. Chem. Phys., 2021, 23, 2819. A simple generalization of the PNP model with ohmic boundary conditions works well only up to 10 mHz. For frequencies smaller than this value the reactance of the cells tends to increase again, indicating a capacity behaviour that could be related to the adsorption effect of the electrodes. A generalization of the ohmic PNP model containing surface capacitance in series is able to fit the data. From the value of the surface capacitance, the thickness of the surface layer is estimated to be on the molecular scale. From this result, we conclude that the adsorption phenomenon could be important for the description of the electrical properties of these systems. A simple generalization of the PNP model with boundary conditions derived by the Langmuir model is in reasonable agreement with our experimental data. The analysis is performed at the impedance level, taking into account a test based on the tangent of the loss angle of the system.

Free ions in kerosene-based ferrofluid detected by impedance spectroscopy.

The influence of the free ions on the electric response of cells filled with kerosene-based ferrofluids in the low-frequency region is explored. The experimental investigations have been performed on cells limited by different types of electrodes, with the same kind of ferrofluid, by means of the impedance spectroscopy technique. The electrodes considered in our study are made of titanium, platinum, gold, brass and surgical steel. The analysis of the spectra of the real and imaginary parts of the electric impedance of the cell data has been done by means of a simplified version of the Poisson-Nernst-Planck model, in which only the carriers of a given sign are mobile. The agreement between the theoretical predictions and the experimental data is rather good on the whole frequency range. From the analysis of the data in the low-frequency range, dominated by the properties of the electrodes, we discovered that only gold electrodes behave in a manner different from the other electrodes. From the best fit of the experimental data the free-ions density is determined as well as their diffusion coefficient in kerosene. The estimated dielectric constant of the kerosene is in good agreement with the values reported in the literature. In the framework of our model, the surface conductivity of the electrodes has been also determined.

Theoretical interpretation of Warburg's impedance in unsupported electrolytic cells.

We discuss the origin of Warburg's impedance in unsupported electrolytic cells containing only one group of positive and one group of negative ions. Our analysis is based on the Poisson-Nernst-Planck model, where the generation-recombination phenomenon is neglected. We show that to observe Warburg-like impedance the diffusion coefficient of the positive ions has to differ from that of the negative ones, and furthermore the electrodes have to be not blocking. We assume that the non-blocking properties of the electrodes can be described by means of an Ohmic model, where the charge exchange between the cell and the external circuit is described by means of an electrode conductivity. For simplicity we consider a symmetric cell. However, our analysis can be easily generalized to more complicated situations, where the cell is not symmetric and the charge exchange is described by the Chang-Jaffe model, or by a linearized version of the Butler-Volmer equation. Our analysis allows justification of the expression for Warburg's impedance proposed previously by several groups, based on wrong assumptions.

Analysis of Warburg's impedance and its equivalent electric circuits.

The derivation of Warburg's impedance is revisited and critically analyzed. We show that the original derivation where the electric current is assumed to be due only to the diffusion of ions, as proposed by Warburg, raises some fundamental questions. The roles of the drift current, in the absence of which the equilibrium is never reached in the dc case, and of the displacement current, which is important even in the low frequency region where the Warburg's impedance appears, are discussed. Finally, the utility of models based on equivalent electric circuits, ladder networks, or transmission lines in the analysis of impedance spectroscopy data is investigated.

Role of the displacement current on Warburg-type behavior.

We investigate the role of the displacement current in the analysis of the electric response of an electrolytic cell to an external stimulus. We show that several models proposed to interpret the spectra deduced by means of the impedance spectroscopy technique are questionable. In particular, we demonstrate that even in the frequency range below the Debye frequency the role of the displacement current is fundamental, and its omission leads to incorrect results for the impedance of the cell. In our analysis, the boundary conditions on the bulk current density are of Nernstian and of Ohmic type. The analysis is limited to a fully dissociated electrolyte, and for only one type of mobile ions, as discussed in several papers devoted to the subject. Particular attention is given to the spatial dependence of the current density. We show that Warburg-like behavior is never predicted in the framework of the Poisson-Nernst-Planck model, if the electric impedance of the cell is correctly evaluated. From this conclusion, valid for media with only one type of mobile ions, it follows that if Warburg-like behavior is experimentally observed the theoretical interpretation is still an open problem, and its origin is probably related to the boundary conditions.

Reanalysis of the electrode polarization in electrolytic cells limited by blocking electrodes.

We evaluate the effect of ions on the electric response of an insulting liquid by means of the total electric polarization induced in a cell by an external field. The limiting surfaces are assumed blocking and identical and the ions pointike nonpolarizable charged particles. The analysis is limited to the case where the selective ionic adsorption is absent, in such a manner that in the absence of external electric field the sample is locally and globally neutral. We obtain formulas for the effective dielectric constant renormalized by the presence of the ions in the absence and presence of adsorption from the surfaces. Our results coincide with those obtained by means of the electric impedance of the cell. From the coincidence of the results relevant to the effective dielectric constant we infer that the ions in an insulating liquid do not have a conductive or dielectric nature. They are just electric charges dissolved in an insulating liquid.

Warburg's impedance revisited.

The derivation of Warburg's impedance presented in several books and scientific papers is reconsidered. In the past it was obtained by assuming that the total electric current across the sample is just due to the diffusion, and that the external potential applied to the electrode is responsible for an increase of the bulk density of charge described by Nernst's model. We show that these assumptions are not correct, and hence the proposed derivations are questionable. When the electrochemical impedance of a cell of an insulating material where external charges are injected of a given sign is correctly determined, in the high frequency region the real and imaginary parts do not follow the trends predicted by Warburg's impedance. The analysis presented in this paper is relevant to a symmetric cell, in the Nernstian approximation. It can be easily generalized to the case of an asymmetric cell, assuming boundary conditions where the conduction current across the electrodes is proportional to the surface electric field.

Elastic continuum theory: towards understanding of the twist-bend nematic phases.

The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which K_{22}>K_{33}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

Comment on "Modeling of electrode polarization for electrolytic cells with a limited ionic adsorption".

Recently, Sawada [Phys. Rev. E 88, 032406 (2013)] proposed a model to take into account the dielectric dispersion of ionic origin in a weak electrolyte cell. We first show that the model is based on questionable assumptions. Next, we point out an error in the author's calculation of the current in the external circuit. Finally, we demonstrate why some criticism on recent papers is irrelevant.

Independence of the effective dielectric constant of an electrolytic solution on the ionic distribution in the linear Poisson-Nernst-Planck model.

We consider the influence of the spatial dependence of the ions distribution on the effective dielectric constant of an electrolytic solution. We show that in the linear version of the Poisson-Nernst-Planck model, the effective dielectric constant of the solution has to be considered independent of any ionic distribution induced by the external field. This result follows from the fact that, in the linear approximation of the Poisson-Nernst-Planck model, the redistribution of the ions in the solvent due to the external field gives rise to a variation of the dielectric constant that is of the first order in the effective potential, and therefore it has to be neglected in the Poisson's equation that relates the actual electric potential across the electrolytic cell to the bulk density of ions. The analysis is performed in the case where the electrodes are perfectly blocking and the adsorption at the electrodes is negligible, and in the absence of any ion dissociation-recombination effect.

Cholesteric-nematic transition in an asymmetric strong-weak anchoring cell.

We discuss the cholesteric-nematic transition induced by an external field in a cell in the shape of a slab of finite thickness whose anchoring energy is infinitely strong on one surface and negligible on the other. The case where the surface orientations of the cholesteric director are parallel in the ground state is considered. In a sample of thickness ℓ, multiple of the natural periodicity of the system Λ, the number of complete twists in the cholesteric liquid crystal is reduced by increasing the strength of the external distorting field. The sequence of the field values for expelling complete twists accumulate as the strength of the field approaches a critical value. Beyond this critical value the system assumes an unwinding configuration going toward a uniform structure, corresponding to nematic phase. Generalization of the results to the weak-weak anchoring cell case is also discussed. In our analysis the anisotropic part of the surface energy is assumed or very large or very small with respect to the total energy per unit surface due to the bulk distortion induced by the magnetic field.

Cholesteric pitch transitions induced by mechanical strain.

We investigate thickness and surface anchoring strength influence on pitch transitions in a planar cholesteric liquid crystal layer. The cholesteric-nematic transition is also investigated. We assume planar boundary conditions, with strong anchoring strength at one interface and weak anchoring strength at the other. The surface anchoring energy we consider to describe the deviation of the surface twist angle from the easy axis induced by a bulk deformation is a parabolic potential or Rapini and Papoular periodic potential, respectively. We show that under strain, all pitch transitions take place at a critical thickness that is equal to the quarter of the natural cholesteric pitch. The latter result does not depend on the anchoring strength, the particular surface potential, or material properties. The twist angle on the limiting surface characterized by weak anchoring varies with strain either by slipping and or in a discontinuous manner according to the thickness of the sample. The position of the bifurcation point depends only on the ratio of the extrapolation length over the layer thickness, but its value is model dependent. Multistability and multiplicity of the transition are discussed.

Comparison of two generation-recombination terms in the Poisson-Nernst-Planck model.

Two phenomenological forms proposed to take into account the generation-recombination phenomenon of ions are investigated. The first form models the phenomenon as a chemical reaction, containing two coefficients describing the dissociation of neutral particles in ions, and the recombination of ions to give neutral particles. The second form is based on the assumption that in thermodynamical equilibrium, a well-defined density of ions is stable. Any deviation from the equilibrium density gives rise to a source term proportional to the deviation, whose phenomenological coefficient plays the role of a life time. The analysis is performed by evaluating the electrical response of an electrolytic cell to an external stimulus for both forms. For simplicity we assume that the electrodes are blocking, that there is only a group of negative and positive ions, and that the negative ions are immobile. For the second form, two cases are considered: (i) the generation-recombination phenomenon is due to an intrinsic mechanism, and (ii) the production of ions is triggered by an external source of energy, as in a solar cell. We show that the predictions of the two models are different at the impedance as well as at the admittance level. In particular, the first model predicts the existence of two plateaux for the real part of the impedance, whereas the second one predicts just one. It follows that impedance spectroscopy measurements could give information on the model valid for the generation-recombination of ions.

Similarities and differences among the models proposed for real electrodes in the Poisson-Nernst-Planck theory.

The ionic distribution induced by an external field is investigated by means of the Poisson-Nernst-Planck model, by taking into account the non-blocking properties of the limiting electrodes. Three types of models proposed for the description of real electrodes are considered. The first two assume an ionic current on the electrodes proportional to the variation of the bulk density of ions and to the surface electric field, respectively. The third model assumes that the sample is limited by perfectly blocking electrodes with a true resistance in parallel to the cell. Here we show that the first two models are equivalent, in the sense that it is possible to find a phenomenological parameter by means of which the predictions of the two models, for what concerns the spectra of the real and imaginary parts of the impedance of the cell, are the same. On the contrary, the third model is equivalent to the others only if the conduction current across the electrodes is small with respect to the displacement current.

One sign ion mobile approximation.

The electrical response of an electrolytic cell to an external excitation is discussed in the simple case where only one group of positive and negative ions is present. The particular case where the diffusion coefficients of the negative ions, D(m), is very small with respect to that of the positive ions, D(p), is considered. In this framework, it is discussed under what conditions the one mobile approximation, in which the negative ions are assumed fixed, works well. The analysis is performed by assuming that the external excitation is sinusoidal with circular frequency ω, as that used in the impedance spectroscopy technique. In this framework, we show that there exists a circular frequency, ω*, such that for ω > ω*, the one mobile ion approximation works well. We also show that for D(m) ≪ D(p), ω* is independent of D(m).

Anomalous diffusion and memory effects on the impedance spectroscopy for finite-length situations.

The contribution of ions to the electrical impedance of an electrolytic cell limited by perfect blocking electrodes is determined by considering the role of the anomalous diffusion process and memory effects. Analytical solutions for fractional diffusion equations together with Poisson's equation relating the effective electric field to the net charge density are found. This procedure allows the construction of general expressions for the electrochemical impedance satisfying the Kramers-Kronig relations when the diffusion of ions in the cell is characterized by the usual, as well as by anomalous, behavior.

Electrical response of a medium containing dissociable impurities.

The effect of the generation-recombination phenomenon on the electrical impedance of an electrolytic cell is investigated. We show that this phenomenon could be responsible for the appearance of a plateau in the real part of the impedance of the cell. The possibility to observe the plateau, arising from the generation-recombination phenomenon, is discussed in relation to the values of the association-dissociation coefficients. The analysis is done by assuming that the generation-recombination phenomenon can be described as a chemical reaction of first order, that the sample is in the shape of a slab, and that the electrodes of the cell are perfectly blocking. To simplify the analysis, the case where only one type of ions can move is considered. The extension of the results to the more general case, in which both types of ions are mobile, is also discussed.

Non-fatal suicidal behaviour in Padua, Italy, in two different periods: 1992-1996 and 2002-2006.

PURPOSE: The WHO/EURO multicentre study on suicidal behaviour showed the lowest rates of suicide attempts in the Italian centre of Padua. Present study aims to discover changes in non-fatal suicidal behaviour rates and characteristics by comparing hospital-admitted subjects in two study periods (1992-1996 and 2002-2006). METHODS: Data were obtained from the University Hospital of Padua. The crude prevalence rates of events and persons by year per 100,000 (subjects aged 15+ years) were calculated. Rate ratios, Chi-square tests and t tests were calculated. RESULTS: The mean prevalence rate per year showed a significant increase during the second study period from 59.2 to 93.6 per 100,000 (RR = 1.58, 95%CI = 1.24-2.02). Changes were significant for both genders, but the increase was stronger in males. The proportion of subjects with non-fatal suicidal behaviour was highest in the youngest age group (15-29 years) in the first period and in adults (30-44 years) in the second period. The absolute number of subjects with non-fatal suicidal behaviour increased more than two times for adults aged 30-44 years. Changes in other age groups were minor. The absolute numbers of non-Italian-born subjects with non-fatal suicidal behaviour increased from 11 to 135 persons. The proportion of poisoning was significantly lower in the second period. CONCLUSIONS: When comparing the time periods 1992-1996 and 2002-2006, there was a significant increase in suicidal events in Padua. There have been remarkable changes in the characteristics of suicide attempt(er)s. The most remarkable change was in the number of non-Italian-born subjects, who should be specifically targeted by suicide prevention activities.