82 research outputs found
Analisa Karakteristik Karbon Aerosol (Oc dan Ec) dari Emisi Pm2.5 dan Rekomendasi Perlindungan Lingkungan dari Emisi Pm2.5 Kebakaran Lahan Gambut secara Pembaraan (Smouldering) (Studi Kasus : Kabupaten Siak dan Kabupaten Kampar Provinsi Riau)
Penelitian ini memiliki tujuan untuk mengetahui karakteristik karbon organik (OC) dan karbon elemental (EC) dalam PM2.5 yang diketahui sebagai salah satu polutan udara akibat kebakaran lahan gambut dan rekomendasi perlindungan lingkungan. Metode yang digunakan untuk mengetahui konsentrasi PM2.5 adalah gravimetri dengan bantuan alat Sartorius ME5-F dan metode analisa konsentrasi karbon aerosol adalah metode pemantulan cahaya dan thermal (IMPROVE A) dengan bantuan alat Carbon Analyzer Model DRI 2001. Konsentrasi rata-rata dan tertinggi PM2.5 emisi kebakaran lahan gambut terutama pada fase pembaraan adalah 996,71 ± 531,01 µm/g3 dan 2163.49 µg/m3. Nilai tersebut lebih tinggi dari konsentrasi PM2.5 ketika tidak terjadi kebakaran (background) sebesar 48 kali. Rata-rata komposisi OC (sebagai salah satu penyusun utama PM2.5) dan EC dalam karbon total (TC) adalah 98,58 ± 0,91% dan 1,42 ± 0,91%. Fraksi OC (Organic Carbon) yang dominan adalah OC1 dan OC2 dengan rata-rata komposisi dalam karbon total (TC) adalah 40,34 ± 5,43% dan 31,58 ± 5,58%. Rasio OC/EC pada penelitian ini lebih besar dari rasio OC/EC pada kebakaran reruntuhan kayu dan kebakaran pohon pinus pada fase yang sama. Rasio OC/EC menunjukkan pengaruh emisi kebakaran lahan gambut terhadap emisi sumber kebakaran lain. Perlindungan lingkungan dari dampak yang ditimbulkan dari kebakaran lahan gambut dapat dilakukan dengan pencegahan penyebaran kebakaran dan penurunan konsentrasi PM2.5. Pencegahan penyebaran kebakaran dilakukan dengan menciptakan sistem pelindung lahan terhadap kebakaran dengan bantuan parit buatan. Penurunan konsentrasi PM2.5 dilakukan dengan menyediakan zona penyangga/penyerapan (buffer zone) menggunakan vegetasi khusus pada luas dan jarak tertentu
Un-reduction
This paper provides a full geometric development of a new technique called
un-reduction, for dealing with dynamics and optimal control problems posed on
spaces that are unwieldy for numerical implementation. The technique, which was
originally concieved for an application to image dynamics, uses Lagrangian
reduction by symmetry in reverse. A deeper understanding of un-reduction leads
to new developments in image matching which serve to illustrate the
mathematical power of the technique.Comment: 25 pages, revised versio
Continuous and discrete Clebsch variational principles
The Clebsch method provides a unifying approach for deriving variational
principles for continuous and discrete dynamical systems where elements of a
vector space are used to control dynamics on the cotangent bundle of a Lie
group \emph{via} a velocity map. This paper proves a reduction theorem which
states that the canonical variables on the Lie group can be eliminated, if and
only if the velocity map is a Lie algebra action, thereby producing the
Euler-Poincar\'e (EP) equation for the vector space variables. In this case,
the map from the canonical variables on the Lie group to the vector space is
the standard momentum map defined using the diamond operator. We apply the
Clebsch method in examples of the rotating rigid body and the incompressible
Euler equations. Along the way, we explain how singular solutions of the EP
equation for the diffeomorphism group (EPDiff) arise as momentum maps in the
Clebsch approach. In the case of finite dimensional Lie groups, the Clebsch
variational principle is discretised to produce a variational integrator for
the dynamical system. We obtain a discrete map from which the variables on the
cotangent bundle of a Lie group may be eliminated to produce a discrete EP
equation for elements of the vector space. We give an integrator for the
rotating rigid body as an example. We also briefly discuss how to discretise
infinite-dimensional Clebsch systems, so as to produce conservative numerical
methods for fluid dynamics
A Generalization of Chetaev's Principle for a Class of Higher Order Non-holonomic Constraints
The constraint distribution in non-holonomic mechanics has a double role. On
one hand, it is a kinematic constraint, that is, it is a restriction on the
motion itself. On the other hand, it is also a restriction on the allowed
variations when using D'Alembert's Principle to derive the equations of motion.
We will show that many systems of physical interest where D'Alembert's
Principle does not apply can be conveniently modeled within the general idea of
the Principle of Virtual Work by the introduction of both kinematic constraints
and variational constraints as being independent entities. This includes, for
example, elastic rolling bodies and pneumatic tires. Also, D'Alembert's
Principle and Chetaev's Principle fall into this scheme. We emphasize the
geometric point of view, avoiding the use of local coordinates, which is the
appropriate setting for dealing with questions of global nature, like
reduction.Comment: 27 pages. Journal of Mathematical Physics (to zappear
The Dynamics of a Rigid Body in Potential Flow with Circulation
We consider the motion of a two-dimensional body of arbitrary shape in a
planar irrotational, incompressible fluid with a given amount of circulation
around the body. We derive the equations of motion for this system by
performing symplectic reduction with respect to the group of volume-preserving
diffeomorphisms and obtain the relevant Poisson structures after a further
Poisson reduction with respect to the group of translations and rotations. In
this way, we recover the equations of motion given for this system by Chaplygin
and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force
as a curvature-related effect. In addition, we show that the motion of a rigid
body with circulation can be understood as a geodesic flow on a central
extension of the special Euclidian group SE(2), and we relate the cocycle in
the description of this central extension to a certain curvature tensor.Comment: 28 pages, 2 figures; v2: typos correcte
Discrete Routh Reduction
This paper develops the theory of abelian Routh reduction for discrete
mechanical systems and applies it to the variational integration of mechanical
systems with abelian symmetry. The reduction of variational Runge-Kutta
discretizations is considered, as well as the extent to which symmetry
reduction and discretization commute. These reduced methods allow the direct
simulation of dynamical features such as relative equilibria and relative
periodic orbits that can be obscured or difficult to identify in the unreduced
dynamics. The methods are demonstrated for the dynamics of an Earth orbiting
satellite with a non-spherical correction, as well as the double
spherical pendulum. The problem is interesting because in the unreduced
picture, geometric phases inherent in the model and those due to numerical
discretization can be hard to distinguish, but this issue does not appear in
the reduced algorithm, where one can directly observe interesting dynamical
structures in the reduced phase space (the cotangent bundle of shape space), in
which the geometric phases have been removed. The main feature of the double
spherical pendulum example is that it has a nontrivial magnetic term in its
reduced symplectic form. Our method is still efficient as it can directly
handle the essential non-canonical nature of the symplectic structure. In
contrast, a traditional symplectic method for canonical systems could require
repeated coordinate changes if one is evoking Darboux' theorem to transform the
symplectic structure into canonical form, thereby incurring additional
computational cost. Our method allows one to design reduced symplectic
integrators in a natural way, despite the noncanonical nature of the symplectic
structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added,
fixed typo
Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge
We define the {\it rest-frame instant form} of tetrad gravity restricted to
Christodoulou-Klainermann spacetimes. After a study of the Hamiltonian group of
gauge transformations generated by the 14 first class constraints of the
theory, we define and solve the multitemporal equations associated with the
rotation and space diffeomorphism constraints, finding how the cotriads and
their momenta depend on the corresponding gauge variables. This allows to find
quasi-Shanmugadhasan canonical transformation to the class of 3-orthogonal
gauges and to find the Dirac observables for superspace in these gauges.
The construction of the explicit form of the transformation and of the
solution of the rotation and supermomentum constraints is reduced to solve a
system of elliptic linear and quasi-linear partial differential equations. We
then show that the superhamiltonian constraint becomes the Lichnerowicz
equation for the conformal factor of the 3-metric and that the last gauge
variable is the momentum conjugated to the conformal factor. The gauge
transformations generated by the superhamiltonian constraint perform the
transitions among the allowed foliations of spacetime, so that the theory is
independent from its 3+1 splittings. In the special 3-orthogonal gauge defined
by the vanishing of the conformal factor momentum we determine the final Dirac
observables for the gravitational field even if we are not able to solve the
Lichnerowicz equation. The final Hamiltonian is the weak ADM energy restricted
to this completely fixed gauge.Comment: RevTeX file, 141 page
Zermelo Navigation in the Quantum Brachistochrone
We analyse the optimal times for implementing unitary quantum gates in a constrained finite dimensional controlled quantum system. The family of constraints studied is that the permitted set of (time dependent) Hamiltonians is the unit ball of a norm induced by an inner product on su(n). We also consider a generalisation of this to arbitrary norms. We construct a Randers metric, by applying a theorem of Shen on Zermelo navigation, the geodesics of which are the time optimal trajectories compatible with the prescribed constraint. We determine all geodesics and the corresponding time optimal Hamiltonian for a specific constraint on the control i.e. k (Tr(Hc(t)^2) = 1 for any given value of k > 0. Some of the results of Carlini et. al. are re-derived using alternative methods. A first order system of differential equations for the optimal Hamiltonian is obtained and shown to be of the form of the Euler Poincare equations. We illustrate that this method can form a methodology for determining which physical substrates are effective at supporting the implementation of fast quantum computation
Collisionless kinetic theory of rolling molecules
We derive a collisionless kinetic theory for an ensemble of molecules
undergoing nonholonomic rolling dynamics. We demonstrate that the existence of
nonholonomic constraints leads to problems in generalizing the standard methods
of statistical physics. In particular, we show that even though the energy of
the system is conserved, and the system is closed in the thermodynamic sense,
some fundamental features of statistical physics such as invariant measure do
not hold for such nonholonomic systems. Nevertheless, we are able to construct
a consistent kinetic theory using Hamilton's variational principle in
Lagrangian variables, by regarding the kinetic solution as being concentrated
on the constraint distribution. A cold fluid closure for the kinetic system is
also presented, along with a particular class of exact solutions of the kinetic
equations.Comment: Revised version; 31 pages, 1 figur
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