A scaling procedure for straightforward computation of sorptivity

Sorptivity is a parameter of primary importance in the study of unsaturated flow in soils. This hydraulic parameter is required to model water infiltration into vertical soil profiles. Sorptivity can be directly estimated from the soil hydraulic functions (water retention and hydraulic conductivity curves), using the integral formulation of Parlange (1975). However, calculating sorptivity in this manner requires the prior determination of the soil hydraulic diffusivity and its numerical integration between initial and final saturation degrees, which may be difficult in some situations (e.g., coarse soil with diffusivity functions that are quasi-infinite close to saturation). In this paper, we present a procedure to compute sorptivity using a scaling parameter, cp, that corresponds to the sorptivity of a unit soil (i.e., unit values for all parameters and zero residual water content) that is utterly dry at the initial state and saturated at the final state. The cp parameter was computed numerically and analytically for five hydraulic models: delta (i.e., Green and Ampt), Brooks and Corey, van Genuchten–Mualem, van Genuchten–Burdine, and Kosugi. Based on the results, we proposed brand new analytical expressions for some of the models and validated previous formulations for the other models. We also tabulated the output values so that they can easily be used to determine the actual sorptivity value for any case. At the same time, our numerical results showed that the relation between cp and the hydraulic shape parameters strongly depends on the chosen model. These results highlight the need for careful selection of the proper model for the description of the water retention and hydraulic conductivity functions when estimating sorptivity.

The problem of diagnosing jet waveguidability in the presence of large-amplitude eddies

The waveguidability of an upper tropospheric zonal jet quantifies its propensity to duct Rossby waves in the zonal direction. This property has played a central role in previous attempts to explain large wave amplitudes and the subsequent occurrence of extreme weather. In these studies, waveguidability was diagnosed with the help of ray tracing arguments using the zonal average of the observed flow as the relevant background state. Here, it is argued that this method is problematic both conceptually and mathematically. The issue is investigated in the framework of the non-divergent barotropic model. This model allows the straightforward computation of an alternative “zonalized” background state, which is obtained through conservative symmetrization of potential vorticity contours and which is argued to be superior to the zonal average. Using an idealized prototypical flow configuration with large-amplitude eddies, it is shown that the two different choices for the background state yield very different results; in particular, the zonal-mean background state diagnoses a zonal waveguide, while the zonalized background state does not. This result suggests that the existence of a waveguide in the zonal mean background state is a consequence of, rather than a precondition for large wave amplitudes, and it would mean that the direction of causality is opposite to the usual argument. The analysis is applied to two heatwave episodes from summer 2003 and 2010, yielding essentially the same result. It is concluded that previous arguments about the role of waveguidability for extreme weather need to be carefully re-evaluated to prevent misinterpretation in the future.

Diagnosing jet waveguidability in the presence of large-amplitude eddies

<p>The waveguidability of an upper tropospheric zonal jet quantifies its propensity to duct Rossby waves in the zonal direction. This property has played a central role in previous attempts to explain large wave amplitudes and the subsequent occurrence of extreme weather. In these studies, waveguidability was diagnosed with the help of the refractive index using the zonal average of the observed flow as the relevant background state. Here, it is argued that this method is problematic both conceptually and mathematically.</p><p>The issue is investigated in the framework of the non-divergent barotropic model. This model allows the straightforward computation of an alternative "zonalized" background state, which is obtained through conservative symmetrisation of potential vorticity contours and which is argued to be superior to the zonal average. Using an idealized prototypical flow configuration with large-amplitude eddies, it is shown that the two different choices for the background state yield very different results; in particular, the zonal-mean background state diagnoses a zonal waveguide, while the zonalized background state does not. This result suggests that the existence of a waveguide in the zonal mean background state is a consequence of, rather than a precondition for large wave amplitudes, and it would mean that the direction of causality is opposite to the usual argument.</p><p>The analysis is applied to two heatwave episodes from summer 2003 and 2010, yielding essentially the same result. It is concluded that previous arguments about the role of waveguidability for extreme weather need to be carefully re-evaluated to prevent misinterpretation in the future.</p>

Quasipolynomial Computation of Nested Fixpoints

It is well-known that the winning region of a parity game with n nodes and k priorities can be computed as a k-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires $$\mathcal {O}(n^{\frac{k}{2}})$$ O ( n k 2 ) iterations of the function. Calude et al.’s recent quasipolynomial-time parity game solving algorithm essentially shows how to compute the same fixpoint in only quasipolynomially many iterations by reducing parity games to quasipolynomially sized safety games. Universal graphs have been used to modularize this transformation of parity games to equivalent safety games that are obtained by combining the original game with a universal graph. We show that this approach naturally generalizes to the computation of solutions of systems of any fixpoint equations over finite lattices; hence, the solution of fixpoint equation systems can be computed by quasipolynomially many iterations of the equations. We present applications to modal fixpoint logics and games beyond relational semantics. For instance, the model checking problems for the energy $$\mu $$ μ -calculus, finite latticed $$\mu $$ μ -calculi, and the graded and the (two-valued) probabilistic $$\mu $$ μ -calculus – with numbers coded in binary – can be solved via nested fixpoints of functions that differ substantially from the function for parity games but still can be computed in quasipolynomial time; our result hence implies that model checking for these $$\mu $$ μ -calculi is in $$\textsc {QP}$$ QP . Moreover, we improve the exponent in known exponential bounds on satisfiability checking.

Simplified Modelling of Inclined Turbulent Dense Jets

An analytical approximation to the entire centerline trajectory of inclined round dense jets in dimensionless form is proposed, in terms of a fourth degree polynomial. The coefficients of the polynomial for a certain inclination angle can be easily obtained if the position of the maximum height and the return point are known. Experimental data of the authors are used to determine these coefficients for six inclination angles between 35° and 75°. The resulting trajectories are then compared to data of other investigators and found to be in good agreement. The variation of the polynomial coefficients with inclination angle is also studied. The proposed analytical expression allows for a straightforward computation of the trajectory length for any inclination angle in the range studied. It is found that the longest trajectory occurs for the 60° angle. The relation between the computed length and the measured minimum (centerline) dilutions at the location of maximum height and at the return point is examined. Finally, the laws governing the variation of the minimum dilution with the axial distance from the source are explored and similarities with the laws of simple jets and plumes are discussed.

A new multistage Parker-Sochacki method for solving the Troesch’s problem

In this article, we introduce a new method to obtain an approximate analytical solution of the highly unstable Troesch’s problem. In the proposed method, without recourse to any hyperbolic tangent transformation or finite term approximation of the hyperbolic sine function, the problem is recast as a system of projectively polynomials which allows straightforward computation of the series solution of the problem. The radius of convergence of the series solution to the problem is derived a-priorly in terms of the parameters of the polynomial system. Using a step length ; the problem domain is divided into subintervals, where corresponding subproblems are defined and solved with Parker-Sochacki method with very high accuracy. Highly accurate piecewise continuous approximate solution is thus obtained on the entire integration interval. The obtained solution, which is valid for every choice of the Troesch parameter , showed comparable accuracy to known numerical solutions in the literature. In particular, new results are presented for large values of in the range [20;500].

A Similarity-Ranking Method on Semantic Computing for Providing Information-Services in Station-Concierge System

The prevalence of smartphones and wireless broadband networks have been progressing as a new Railway infomration environment.　According to the spread of such devices and information technology, various types of information can be obtained from databases connected to the Internet. One scenario of obtaining such a wide variety of information resources is in the phase of user’s transportation. This paper proposes an information provision system, named the Station Concierge System that matches the situation and intention of passengers. The purpose of this system is to estimate the needs of passengers like station staff or hotel concierge and to provide information resources that satisfy user’s expectations dynamically. The most important module of the system is constructed based on a new information ranking method for passenger intention prediction and service recommendation. This method has three main features, which are (1) projecting a user to semantic vector space by using her current context, (2) predicting the intention of a user based on selecting a semantic vector subspace, and (3) ranking the services by a descending order of relevant scores to the user’ intention. By comparing the predicted results of our method with those of two straightforward computation methods, the experimental studies show the effectiveness and efficiency of the proposed method. Using this system, users can obtain transit information and service map that dynamically matches their context.

Assessment of Welded Joints by Strain Energy Density Approach Accounting for Misalignments and Geometrical Imperfections

Among recently introduced fatigue assessment approaches, the ones based on the notch stress intensity factor (N-SIF) concept appear to be very promising, both because of their theoretically soundness and because of the possibility of straightforward computation of parameters believed to govern the fatigue process. Actually, while such approaches can be considered in between stress-based approaches and crack propagation ones, quantities like N-SIF and strain energy density in a control volume can be evaluated by finite element analysis according to nowadays well-established procedures, mostly already implemented in commercial FEM software. The present study moves from a former one, dealing with butt joints between typical shipbuilding shell plates, and aims at assessing how the misalignment influences the fatigue strength estimation when applying the strain energy density approach. Eventually, the capabilities of such approach in accounting for misalignments is demonstrated and results are found in agreement with magnification factors currently recommended by guidelines and rules when applying other, stress based, fatigue assessment approaches.

Location of Farmers Warehouse at Adaklu Traditional Area, Volta Region, Ghana

Postharvest loss is one major problem farmers in Adaklu Traditional Area that most Ghanaian farmers face. As a result, many farmers wallow in abject poverty. Warehouses are important facilities that help to reduce postharvest loss. In this research, Beresnev pseudo-Boolean Simple Plant Location Problem (SPLP) model is used to locate a warehouse at Adaklu Traditional Area, Volta Region, Ghana. This model was used because it gives a straightforward computation and produces no iteration as compared with other models. The SPLP is a problem of selecting a site from candidate sites to locate a plant so that customers can be supplied from the plant at a minimum cost. The model is made up of fixed cost and transportation cost. Location index ordering matrix was developed from the transportation cost matrix and we used it with the fixed cost and differences between variable costs to formulate the Beresnev function. Linear term developed from the function which was partial is pegged to obtain a complete solution. Of the 14 notable communities considered,Adaklu Wayais found most suitable for the setting of the warehouse. The total cost involved is Gh₵78,180.00.

Chern classes of blow-ups

We extend the classical formula of Porteous for blowing-up Chern classes to the case of blow-ups of possibly singular varieties along regularly embedded centers. The proof of this generalization is perhaps conceptually simpler than the standard argument for the nonsingular case, involving Riemann–Roch without denominators. The new approach relies on the explicit computation of an ideal, and a mild generalization of a well-known formula for the normal bundle of a proper transform ([8, B·6·10]).We also discuss alternative, very short proofs of the standard formula in some cases: an approach relying on the theory of Chern–Schwartz–MacPherson classes (working in characteristic 0), and an argument reducing the formula to a straightforward computation of Chern classes for sheaves of differential 1-forms with logarithmic poles (when the center of the blow-up is a complete intersection).