The effect of feed frequency on growth, survival and behaviour of juvenile spiny lobster (Panulirus ornatus)

Spiny lobsters have a range of complex chemical communication pathways that contribute to feeding behaviour. Feed intake is modulated by feed availability and feed characteristics, such as attractiveness and palatability, with behavioural factors, such as social competition and circadian rhythm, providing an extra layer of complexity. In this study, we investigated the effect of feed frequency on survival and growth of early-stage (instar 26) juvenile Palunirus ornatus. In addition, we investigated the interactive effect of feed frequency and circadian rhythm on lobster feed response. Lobsters were fed a set ration at a frequency of either one, two, four, eight, sixteen or thirty-two times per day over 49 days. The effect of feed frequency on growth and survival was determined. Circadian feeding activity under these feeding treatments was assessed by time-lapse photography. Increased feed frequency from one to sixteen feeds daily improved growth by increasing apparent feed intake (AFI) and feed attraction, as confirmed by the increased presence of lobsters in the feeding area. The rapid leaching of feed attractant, particularly free amino acid, suggests a beneficial effect of multiple feeding frequencies on feed intake and growth. However, more than sixteen feeds per day resulted in decreased feed intake and a subsequent reduction in growth. The decrease in feed intake is thought to be associated with saturation of the culture environment with attractants, resulting in a reduced behavioural response to feed supplies. This may indicate the need for depletion of attractants to retrigger a feeding response. As lobsters were grown communally, faster growth at sixteen rations per day was also coupled with increased cannibalism, likely driven by increased vulnerability with the occurrence of more frequent ecdysis events. Whereas circadian rhythm indicated more activity at night, an interaction between daytime activity and feed frequency was not observed

Implicit difference methods for parabolic functional differential problems of the Neumann type

Nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type are considered. A general class of difference methods for the problem is constructed. Theorems on the convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability of the difference functional problem is based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given functions are used. Numerical examples are given.Розглянуто нелiнiйнi параболiчнi функцiонально-диференцiальнi рiвняння з початковими граничними умовами нейманiвського типу. Побудовано загальний клас рiзницевих методiв для розв’язку задачi. Доведено теореми про збiжнiсть рiзницевих схем та встановлено оцiнки похибок наближених розв’язкiв. Доведення стiйкостi рiзницевої функцiональної задачi базується на технiцi порiвняння. Використано нелiнiйнi оцiнки перронiвського типу вiдносно функцiональної змiнної для фiксованої функцiї. Наведено числовi приклади

Compact schemes for laser–matter interaction in Schrödinger equation based on effective splittings of Magnus expansion

Numerical solutions for laser–matter interaction in Schrödinger equation has many applications in theoretical chemistry, quantum physics and condensed matter physics. In this paper we introduce a methodology which allows, with a small cost, to extend any fourth-order scheme for Schrödinger equation with time-independent potential to a fourth-order method for Schrödinger equation with laser potential. This is made possible due to the highly specific form of the time dependent potential which is linear in space in the case of laser–matter interaction. This leads to a highly amenable structure of the commutators in the Magnus expansion, where, in particular, the first commutator reduces to a scalar multiple of the gradient. In turn, this special structure allows us to split the Magnus expansion effectively via a variety of fourth-order splittings. Additionally, the error constant remains tiny because we keep the integrals of the potential intact to the very last stage of computations. This is particularly important in the case of highly oscillatory potentials. As demonstrated via numerical examples, these fourth-order methods improve upon many leading schemes of order six due to their low costs and small error constants

Magnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential

The computation of the Schrödinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications often involve highly oscillatory potentials and require inexpensive but accurate solutions over large spatio-temporal windows. In this work we develop Magnus expansions where commutators have been simplified. Consequently, the exponentiation of these Magnus expansions via Lanczos iterations is significantly cheaper than that for traditional Magnus expansions. At the same time, and unlike most competing methods, we simplify integrals instead of discretizing them via quadrature at the outset—this gives us the flexibility to handle a variety of potentials, being particularly effective in the case of highly oscillatory potentials, where this strategy allows us to consider significantly larger time steps

Compact schemes for laser–matter interaction in Schrödinger equation based on effective splittings of Magnus expansion

Numerical solutions for laser–matter interaction in Schrödinger equation has many applications in theoretical chemistry, quantum physics and condensed matter physics. In this paper we introduce a methodology which allows, with a small cost, to extend any fourth-order scheme for Schrödinger equation with time-independent potential to a fourth-order method for Schrödinger equation with laser potential. This is made possible due to the highly specific form of the time dependent potential which is linear in space in the case of laser–matter interaction. This leads to a highly amenable structure of the commutators in the Magnus expansion, where, in particular, the first commutator reduces to a scalar multiple of the gradient. In turn, this special structure allows us to split the Magnus expansion effectively via a variety of fourth-order splittings. Additionally, the error constant remains tiny because we keep the integrals of the potential intact to the very last stage of computations. This is particularly important in the case of highly oscillatory potentials. As demonstrated via numerical examples, these fourth-order methods improve upon many leading schemes of order six due to their low costs and small error constants

Solving Schrödinger equation in semiclassical regime with highly oscillatory time-dependent potentials

Schrödinger equations with time-dependent potentials are of central importance in quantum physics and theoretical chemistry, where they aid in the simulation and design of systems and processes at atomic and molecular scales. Numerical approximation of these equations is particularly difficult in the semiclassical regime because of the highly oscillatory nature of solution. Highly oscillatory potentials such as lasers compound these difficulties even further. Altogether, these effects render a large number of standard numerical methods less effective in this setting. In this paper we will develop a class of exponential splitting schemes that allow us to use large time steps in our schemes even in the presence of highly oscillatory potentials and solutions. These are derived by combining the advantages of integral-preserving simplified-commutator Magnus expansions with those of symmetric Zassenhaus splittings. The efficacy of these methods is demonstrated through 1D, 2D and 3D numerical examples

Solving Schrödinger equation in semiclassical regime with highly oscillatory time-dependent potentials

Schrödinger equations with time-dependent potentials are of central importance in quantum physics and theoretical chemistry, where they aid in the simulation and design of systems and processes at atomic and molecular scales. Numerical approximation of these equations is particularly difficult in the semiclassical regime because of the highly oscillatory nature of solution. Highly oscillatory potentials such as lasers compound these difficulties even further. Altogether, these effects render a large number of standard numerical methods less effective in this setting. In this paper we will develop a class of exponential splitting schemes that allow us to use large time steps in our schemes even in the presence of highly oscillatory potentials and solutions. These are derived by combining the advantages of integral-preserving simplified-commutator Magnus expansions with those of symmetric Zassenhaus splittings. The efficacy of these methods is demonstrated through 1D, 2D and 3D numerical examples