903 research outputs found
ANALISI STATISTICA DEI LIVELLI IDRICI NEI CORPI ARGINALI
No full textLe arginature fluviali sono opere fondamentali per la protezione del territorio. La progettazione degli argini richiede il rispetto di requisiti geotecnici e idraulici. Ad esempio, la linea di filtrazione non dovrebbe emergere sul lato campagna del rilevato arginale al fine di evitare l'innesco di fenomeni erosivi che riducono l'efficienza di contenimento dell'acqua e compromettono la stabilità dell’argine. Per identificare la posizione della linea di filtrazione sono disponibili criteri geometrici ed empirici. Una direttiva italiana, pubblicata dal Ministero dei Lavori Pubblici -MLLPP- (1952) per i materiali arginali con conducibilità idraulica inferiore a 10-4 m/s, suggerisce una linea con una pendenza tra 1:5 e 1:7 con origine lato fiume alla quota del livello dell'acqua in alveo, generalmente corrispondente alla piena con tempo di ritorno 200 anni (e.g. Autorità di bacino del fiume Po, 2010).
La progettazione di un argine in condizioni stazionarie può portare a sovradimensionare l’argine e quindi ad un progetto non economico (Butera & Tanda, 2006), inoltre può non tenere conto delle possibili instabilità indotte dalle variazioni del livello dell'acqua nel fiume (ad es. Rinaldi et al., 2004; Kwang Seok Yoon, 2005; Stark et al., 2014; Jafari et al., 2019). L'effetto degli abbassamenti sul paramento di monte può infatti essere piuttosto pericoloso ed un'analisi in condizioni stazionarie non considera tali situazioni.
Il presente lavoro esamina il processo di filtrazione in un argine, in condizioni non stazionarie, con particolare attenzione ai massimi livelli piezometrici annui raggiunti nell'argine. A tale scopo è stato utilizzato un modello numerico 3D saturo-insaturo; l'analisi qui riportata riguarda la caratterizzazione statistica dei livelli freatici raggiunti nell'argine.
L'analisi è stata effettuata con riferimento ai dati idrometrici osservati nella stazione di monitoraggio sul fiume Po a Pontelagoscuro (Ferrara, Italia)
Field Fluctuations in a One-Dimensional Cavity with a Mobile Wall
No full textWe consider a scalar field in a one-dimensional cavity with a mobile wall. The wall is assumed bounded by a harmonic potential and its mechanical degrees of freedom are treated quantum mechanically. The possible motion of the wall makes the cavity length variable, and yields a wall-field interaction and an effective interaction among the modes of the cavity. We consider the ground state of the coupled system and calculate the average number of virtual excitations of the cavity modes induced by the wall-field interaction, as well as the average value of the field energy density. We compare our results with analogous quantities for a cavity with fixed walls, and show a correction to the Casimir potential energy between the cavity walls. We also find a change of the field energy density in the cavity, particularly relevant in the proximity of the mobile wall, yielding a correction to the Casimir-Polder interaction with a polarizable body placed inside the cavity. Similarities and differences of our results with the dynamical Casimir effect are also discussed
Casimir Energies in a One-Dimensional Cavity with a Fluctuating Boundary
No full textWe consider a massless scalar field in a one-dimensional cavity with one fixed and one mobile wall. We assume that the mobile wall is also subjected to a harmonic potential, and its mechanical degrees of freedom are treated quantum-mechanically. The wall's position has
thus quantum fluctuations around the equilibrium position.
The possible motion of the wall makes the cavity length variable, and this gives rise to a wall-field interaction and an effective interaction between the modes of the cavity. We use an effective Hamiltonian, originally introduced by C. K. Law, to describe our system in terms of field modes
relative to the equilibrium position of the mobile wall. We obtain by perturbation theory the dressed ground state of the wall-field coupled system, which contains pairs of virtual quanta of the field and excitations of the wall's mechanical degrees of freedom.
We evaluate the average number of virtual excitations in each mode of the cavity, induced by the effective wall-field interaction, as well as the renormalized field energy density inside the cavity. We show that the quantum fluctuations of the wall's position significantly affect the field
energy density in the cavity, in particular in the proximity of the mobile wall. We also consider a statistical average of the energy density on the position of the fluctuating boundary, in order to discuss the known problem of the divergence of field energy densities at the boundaries. All these quantities are then compared with analogous quantities for a cavity with fixed walls. We find a correction to the Casimir potential energy and to the field energy density in the cavity,
due to the position fluctuations of the cavity wall, and discuss how these corrections depend on relevant parameters of the mobile wall, in particular its plasma frequency, mass and frequency of the harmonic potential. Observability of these new effects is also discussed, as well as the relation to the dynamical Casimir effect
Fractional differential equations solved by using Mellin transform
No full textIn this paper, the solution of the multi-order differential equations, by using Mellin transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin integral operates on the fractional derivatives, may be overcame. Then, the solution may be found for any fractional differential equation involving multi-order fractional derivatives (or integrals). The solution is found in the Mellin domain, by solving a linear set of algebraic equations, whose inverse transform gives the solution of the fractional differential equation at hands
Mellin transform approach for the solution of coupled systems of fractional differential equations
No full textIn this paper, the solution of a multi-order, multi-degree-of-freedom fractional differential equation is addressed by using the Mellin integral transform. By taking advantage of a technique that relates the transformed function, in points of the complex plane differing in the value of their real part, the solution is found in the Mellin domain by solving a linear set of algebraic equations. The approximate solution of the differential (or integral) equation is restored, in the time domain, by using the inverse Mellin transform in its discretized for
A physically based connection between fractional calculus and fractal geometry
No full textWe show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalous dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry. (C) 2014 Elsevier Inc. All rights reserved.</p
STRUTTURE A DIFESA DI RILEVATI E LORO INFLUENZA SUL COMPORTAMENTO DI FALDE FREATICHE SUPERFICIALI
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