Limitations and potential of commercially available rhodamine WT as a groundwater tracer

We conducted chemical characterization, batch, column, and modeling studies to elucidate the sorption and transport of rhodamine WT (RWT) in the subsurface. The sand-pack material from the Lizzie field site near Greenville, North Carolina, served as our porous media. Our study confirms earlier results that RWT consists of two isomers with different sorption properties. It also shows that the two isomers have distinct emission spectra and are equally distributed in the RWT solution. The presence of the two isomers with different sorption properties and distinct emission spectra introduces an error in measuring the RWT concentration with fluorometers during porous media tracer studies. The two isomers become chromatographically separated during transport and thus arrive in a different concentration ratio than that of the RWT solutions used for fluorometer calibration and test injection. We found that this groundwater tracer chromatographic error could be as high as 7.8%. We fit six different reactive-solute transport models of varying complexity to our four column experiments. A two-solute, two-site sorption transport model that accounts for nonequilibrium sorption accurately describes the breakthrough curves of the shorter-timescale column experiments. However, possibly due to the groundwater tracer chromatographic error we discovered, this model, or a similar one that accounts for a Freundlich isotherm for one of the solutes, fails to describe the RWT transport in the longer-timescale column experiments. The presence of the two RWT isomers may complicate the interpretation of field tracer tests because a shoulder, or any two peaks in a breakthrough curve, could result from either aquifer heterogeneity or the different arrival times of the two isomers. In cases where isomer 2 sorbs to such an extent that its breakthrough is not recorded during a test, only isomer 1 is measured, and therefore only 50% of the injected mass is recorded. Isomer 1 of RWT can be accurately modeled with a one-solute, two-site, nonequilibrium sorption model. This conclusion and the results from our batch studies suggest that RWT isomer 1 is an effective groundwater tracer but that the presence of isomer 2 hampers its effectiveness

Stochastic differential equations in theory of solute transport through inhomogeneous porous media

Stochastic differential equations for solute transport arc constructed from corresponding deterministic transport equations by re-interpreting their physical parameters as random functions of space and time. A partial differential equation for the ensemble-average solute concentration then can be derived from the stochastic transport equation by a cumulant expansion method used in non-equilibrium statistical mechanics. Examples of this approach are given for both conservative and reactive solutes moving through inhomogeneous porous media. The resulting ensemble- average: transport equations are shown to be similar formally to their local-scale, deterministic analogues; but they exhibit additional, field-scale physical parameters arising from correlations among fluctuating, local-scale convective or reactive properties of the solute. Some unresolved conceptual issues attending the interpretation of the ensemble-average solute concentration and the field-scale parameters are discussed briefly

Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years

Rousseau and the Qualified Support of Matriarchal Rule

The article investigates the relations between men and women in Rousseau’s major works to uncover the possibility of a long-term rule of women over men. Rousseau does provide examples of alternating rule between the sexes. However, given that the rule of prominent women like Sophie and Julie is indirect and more Machiavellian than that of men, I make the case that Rousseau sees straightforward control by women as more consistent with modern conditions (specifically in an indirect-rule as opposed to an instrumental-rationality sense). First, I provide examples of Sophie’s rule in Emile. Sophie rules Emile especially through acts of charity that incline Emile to participate in the project that Sophie has undertaken, making him more capable of willing generally. Second, I show that Julie at Clarens rules a number of the men there and particularly in the administration of the estate. Interestingly, like Sophie’s, her power is communicated through concrete examples of charitable action. Rousseau writes that, as a result, those around her are imbued with the spirit to contribute to the projects of importance to her, which also renders them more apt to will generally. Interestingly, two women as different as Sophie and Julie rule men in the same way: through charity. They do so as the result of a religious education. And, whereas religious education in Rousseau is in general anti-metaphysical, this is especially true for women compared to men. The examples of Sophie and Julie do, therefore, take us into territory of the sexes alternating in rule. But the difference in education suggests that for Rousseau their rule goes deeper and represents a relation more fundamental than the rule of men over women. The possibility is further confirmed through an analysis of Rousseau’s states of nature. At the end of the day, the reevaluation of relations between the sexes in Rousseau’s work is long overdue. I engage a rich scholarly literature and embark on a rereading of several of Rousseau’s works to offer a fresh interpretation that suggests the citizen of Geneva was not only open to a significant increase in the power of women over time, but that he actually favored matriarchy. The argument hopefully underscores the way in which great works are both timely and timeless

Hobbes and Spinoza on Sovereign Education

Most comparisons of Thomas Hobbes and Baruch Spinoza focus on the difference in understanding of natural right. We argue that Hobbes also places more weight on a rudimentary and exclusive education of the public by the state. We show that the difference is related to deeper disagreements over the prospect of Enlightenment. Hobbes is more sanguine than Spinoza about using the state to make people rational. Spinoza considers misguided an overemphasis on publicly educating everyone out of superstition—public education is important, but modes of superstition may remain and must be offset by institutions and a civil religion. The differences are confirmed by Spinoza’s interest in the philosopher who stands apart and whose flourishing may be protected, but not simply brought about, by rudimentary public education. Spinoza’s openness to a wisdom-loving elite in a democracy also sets up an interesting parallel with Thomas Jefferson’s own commitment to the natural aristocracy needed to sustain republicanism. In demonstrating the 17th century philosopher’s skepticism toward using the state exclusively to promote rationality, even as he recognizes the importance of a sovereign pedagogical role and the protection of philosophy, we move to suggest that Spinoza is relevant to contemporary debates about public education and may reinvigorate moral and political discourse in a liberal democracy

Hobbes and Spinoza on Sovereign Education

Most comparisons of Thomas Hobbes and Baruch Spinoza focus on the difference in understanding of natural right. We argue that Hobbes also places more weight on a rudimentary and exclusive education of the public by the state. We show that the difference is related to deeper disagreements over the prospect of Enlightenment. Hobbes is more sanguine than Spinoza about using the state to make people rational. Spinoza considers misguided an overemphasis on publicly educating everyone out of superstition—public education is important, but modes of superstition may remain and must be offset by institutions and a civil religion. The differences are confirmed by Spinoza’s interest in the philosopher who stands apart and whose flourishing may be protected, but not simply brought about, by rudimentary public education. Spinoza’s openness to a wisdom-loving elite in a democracy also sets up an interesting parallel with Thomas Jefferson’s own commitment to the natural aristocracy needed to sustain republicanism. In demonstrating the 17th century philosopher’s skepticism toward using the state exclusively to promote rationality, even as he recognizes the importance of a sovereign pedagogical role and the protection of philosophy, we move to suggest that Spinoza is relevant to contemporary debates about public education and may reinvigorate moral and political discourse in a liberal democracy

An American Notwithstanding Clause? Between Potestas and Potentia

Debates about judicial review and departmentalism have continued to rage, and in the wake of the last three Supreme Court appointments and current Presidential Commission on the Court, only look to intensify. Should the US adopt a notwithstanding or override provision, of the kind that exits in Canada and Israel? These countries take a departmentalist approach to allow the legislature to override the Court, “notwithstanding” its ruling. Although America is a presidential framework, a paradox emerges: evidence exists that its system already makes possible the equivalent of a notwithstanding clause. This consists of Congress and the President together “overruling” the Supreme Court. In another sense, however, this is not an accepted practice—large parts of the legal community hold that the US Constitution establishes judicial supremacy. To better understand this dynamic, we consider two kinds of power: formal and authorized (potestas) as well as direct and concrete (potentia). The contrast between the positions on both power and sovereignty of Thomas Hobbes (associated with potestas) and Baruch Spinoza (linked to potentia) helps clarify these issues in a contemporary context. It turns out that a robust departmentalist equivalent of the notwithstanding clause already exists in the US, as a matter of Hobbesian potestas but not of Spinozist potentia. Another term for the latter is pouvoir constituant. Spinoza’s perspective on political activity further clarifies the in-between nature of the American override capacity: the active or passive character of a multitude is not binary, but is a matter of degree. Without making an institutional recommendation, we note that Spinoza’s understanding of power also allows for dynamic interaction between potentia and potestas: formal authorization can contribute to the expression of direct power. It is, therefore, conceivable that additional codification of the existing American override capacity, either through a joint declaration of Congress and the Presidency or a Constitutional Amendment, can strengthen the effective sovereignty of the American people in relation to the courts

Flowing partially penetrating well: a solution of a mixed-type boundary value problem.

A new semi-analytic solution to the mixed-type boundary value problem for a flowing partially penetrating well with infinitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-infinite vertical extent or to packer tests with aquifer horizontal boundaries far enough from the tested area. The problem reduces to a system of dual integral equations (DE) and further to a deconvolution problem. Unlike the analogous Dagan's steady-state solution [Water Resour. Res. 1978; 14:929–34], our DE solution does not suffer from numerical oscillations. The new solution is validated by matching the corresponding finite-difference solution and is computationally much more efficient. An automated (Newton–Raphson) parameter identification algorithm is proposed for field test inversion, utilizing the DE solution for the forward model. The procedure is computationally efficient and converges to correct parameter values. A solution for the partially penetrating flowing well with no skin and a drawdown–drawdown discontinuous boundary condition, analogous to that by Novakowski [Can. Geotech. J. 1993; 30:600–6], is compared to the DE solution. The D–D solution leads to physically inconsistent infinite total flow rate to the well, when no skin effect is considered. The DE solution, on the other hand, produces accurate results