text:
\section{Introduction}

We consider a point particle moving on a world line $\gamma$ in a
curved spacetime with metric $g_{\alpha\beta}$. The particle is either
endowed with a scalar charge $q$ or an electric charge $e$, and we
wish to calculate the effect of these charges on the motion of the
particle. This motion is not geodesic, because the (scalar or
electromagnetic) field created by the particle interacts with the
particle and causes it to accelerate. In flat spacetime this effect is
produced by a local distortion of the field lines associated with the
particle's acceleration. In curved spacetime there is no such local
distortion when the particle moves freely; what happens instead is
that the field interacts with the spacetime curvature and
back-scatters toward the particle. As far as the particle is
concerned, then, it interacts with an incoming wave, and the motion is
not geodesic.

There is a gravitational analogue to these (scalar and
electromagnetic) situations: Even in the absence of charges $q$ and
$e$, we may wish to go beyond the test-mass description and consider
the effect of the particle's mass $m$ on its motion. There are two
ways of describing this effect. We might say that the particle moves
on a {\it geodesic} in a {\it perturbed  spacetime} with metric
$g_{\alpha\beta} + h_{\alpha\beta}$.  Or we might say that the
particle moves on an {\it accelerated world line} in the
{\it original spacetime} with metric $g_{\alpha\beta}$. It is useful
to keep both points of view active, and most researchers working in
this field go freely back and forth between these modes of
description. In the second view, the particle's acceleration is
associated with the perturbation $h_{\alpha\beta}$, which produces a
gravitational self-force acting on the particle.

The scalar, electromagnetic, and gravitational self-force problems
share many physical and mathematical features. In each case a moving
charge is accompanied by a field: $q$ produces a scalar field
$\Phi$, $e$ produces an electromagnetic field $A_\alpha$, and $m$
produces a gravitational perturbation $h_{\alpha\beta}$. In each case
the field satisfies a linear wave equation in the background
spacetime: $\Phi$ satisfies a scalar wave equation, $A_\alpha$ a
vectorial equation derived from Maxwell's equations, and
$h_{\alpha\beta}$  a tensorial equation derived from the linearized
Einstein equations. And in each case the self-force is equal to the
gradient of the field evaluated on the particle's world line.

This last observation reveals the problematic nature of this
investigation. It is straightforward enough to calculate the scalar
field $\Phi$, the vector potential $A_\alpha$, and the gravitational
perturbation $h_{\alpha\beta}$ at a distance from the particle. But
because the particle is pointlike, these quantities diverge on the
world line, and derivatives of these quantities are even more
singular. How is one supposed to deal with these singular
expressions and extract from them the finite pieces that produce a
well-defined effect, namely the self-force acting on the particle?

The purpose of this lecture is to offer some elements of answer to
this question. My focus will be on the technical aspects of the
problem, which I will try to describe without going overboard with
derivations and mathematical precision. The preceding lecture by Bob
Wald offers more on the conceptual aspects of the self-force, and
other contributions describe ways of computing the self-force and its
consequences. This lecture can be considered to be a light
introduction to my massive review article  published in
{\it Living Reviews in Relativity} \cite{poisson:04b}, to which I will
frequently refer (as LRR); there the reader will find all the gory
details of all the derivations omitted in the lecture.

For simplicity I will focus on the simplest exemplar of a self-force:
the {\it scalar self-force} produced by a scalar field $\Phi$ on a
scalar charge $q$. Understanding the details of this construction is
a first step toward understanding the nature of the electromagnetic
and gravitational self-forces; the computations involved are simpler,
but the conceptual basis is essentially the same.

The self-force has a long history in theoretical physics, which is
nicely summarized in a book by Herbert Spohn \cite{spohn:08}. The
standard reference for the electromagnetic self-force in flat
spacetime is Dirac's famous 1938 paper \cite{dirac:38}. Dirac's
construction was generalized to curved spacetime in 1960 by DeWitt and
Brehme \cite{dewitt-brehme:60}; a technical error in their work was
corrected by Hobbs \cite{hobbs:68}. The gravitational self-force was
first computed in 1997 by Mino, Sasaki, and Tanaka
\cite{mino-etal:97}; a more direct derivation (based on an axiomatic
approach) was later provided by Quinn and Wald
\cite{quinn-wald:97}. Finally, the scalar self-force --- the main
topic of this lecture --- was first constructed in 2000 by Ted Quinn
\cite{quinn:00}.

\section{Geometric elements}

The construction of the self-force would be impossible without the
introduction of geometric tools that were first fashioned by Synge
\cite{synge:60} and independently by DeWitt and Brehme
\cite{dewitt-brehme:60}. In this section I introduce the
world function $\sigma(x,x')$ and the parallel propagator
$g^\alpha_{\ \alpha'}(x,x')$.

\begin{figure}
\includegraphics[width=0.6\linewidth]{segment}
\caption{Geodesic segment $\beta$ between the spacetime points $x'$ and
$x$. The vector $t^\mu$ is tangent to this geodesic.}
\end{figure}

Let $x$ and $x'$ be two points in spacetime, and let us assume that
they are sufficiently close that there is a unique geodesic segment
$\beta$ linking them. The segment is described by the parametric
relations $z^\mu(\lambda)$, in which $\lambda$ is an affine parameter
that runs from $0$ to $1$; we have that $z(0) = x'$ and $z(1) =
x$. The vector  $t^\mu := dz^\mu/d\lambda$ is tangent to $\beta$.

The {\it world function} is defined by
\begin{equation}
\sigma(x,x') := \frac{1}{2} \int_0^1 g_{\mu\nu}(z) t^\mu t^\nu\,
d\lambda .
\end{equation}
It is numerically equal to half the squared geodesic distance between
$x$ and $x'$. When $\sigma < 0$ the separation between $x$ and $x'$ is
timelike, and when $\sigma > 0$ it is spacelike. The equation
$\sigma(x,x') = 0$ describes the light cones of each point; if $x'$ is
kept fixed then $\sigma(x) = 0$ describes the past and future light
cones of $x'$; if instead $x$ is kept fixed then $\sigma(x') = 0$
describes the past and future light cones of $x$.

The world function can be differentiated with respect to each
argument. It can be shown (LRR Sec.~2.1.2) that
\begin{equation}
-\sigma^{\alpha'} := -\nabla^{\alpha'} \sigma(x,x')
\end{equation}
is a vector at $x'$ that is proportional to $t^\mu$ evaluated at that
point. I use the convention that primed indices refer to the point
$x'$, while unprimed indices refer to $x$. It can also be shown that
its length is given by
\begin{equation}
g_{\alpha'\beta'} \sigma^{\alpha'} \sigma^{\beta'} = 2\sigma;
\end{equation}
the length of $\sigma^{\alpha'}$ therefore measures the geodesic
distance between the two points. Because the vector points from $x'$
to $x$, we have a covariant notion of a displacement vector between
the two points.

The {\it parallel propagator} takes a vector $A^{\alpha'}$ at $x'$ and
moves it to $x$ by parallel transport on the geodesic segment
$\beta$. We express this operation as
\begin{equation}
A^\alpha(x) = g^\alpha_{\ \alpha'}(x,x') A^{\alpha'}(x'),
\end{equation}
in which $A^\alpha$ is the resulting vector at $x$. The operation is
easily generalized to dual vectors and other types of
tensors (LRR Sec.~2.3).

The world function and the parallel propagator can be employed in the
construction of a Taylor expansion of a tensor about a reference point
$x'$. Suppose that we have a tensor field $A^{\alpha\beta}(x)$ and
that we wish to express it as an expansion in powers of the
displacement away from $x'$. The role of the deviation vector is
played by $-\sigma^{\alpha'}$, and the expansion coefficients will be
ordinary tensors at $x'$. We might write something like
\[
A^{\alpha'\beta'}
+ A^{\alpha'\beta'}_{\ \ \ \ \gamma'} (-\sigma^{\gamma'})
+ \frac{1}{2} A^{\alpha'\beta'}_{\ \ \ \ \gamma'\delta'}
  (-\sigma^{\gamma'})(-\sigma^{\delta'}) + \cdots,
\]
but this defines a tensor at $x'$, not $x$. To get a proper
expression for $A^{\alpha\beta}(x)$ we must also involve the parallel
propagator, and we write
\begin{equation}
A^{\alpha\beta} = g^{\alpha}_{\ \alpha'} g^{\beta}_{\ \beta'}
\biggl[ A^{\alpha'\beta'}
- A^{\alpha'\beta'}_{\ \ \ \ \gamma'} \sigma^{\gamma'}
+ \frac{1}{2} A^{\alpha'\beta'}_{\ \ \ \ \gamma'\delta'}
  \sigma^{\gamma'} \sigma^{\delta'} + \cdots \biggr].
\end{equation}
Having postulated this form for the expansion, the expansion
coefficients $A^{\alpha'\beta'}$,
$A^{\alpha'\beta'}_{\ \ \ \ \gamma'}$, and so on can be computed by
repeatedly differentiating the tensor field and evaluating the results
in the limit $x \to x'$ (see LRR Sec.~2.4). For example,
$A^{\alpha'\beta'} = \lim\, A^{\alpha\beta}$, as we might expect.

\section{Coordinate systems}

Self-force computations are best carried out using covariant
methods. It is convenient, however, to display the results in a
coordinate system that is well suited to the description of a
neighbourhood of the world line $\gamma$. In this transcription it is
advantageous to keep the coordinates in a close correspondence with
the geometric objects (such as $\sigma^{\alpha'}$) that appear in the
covariant expressions. I find that two coordinate systems are
particularly useful in this context: the {\it Fermi normal
coordinates} $(t,x^a = s\omega^a)$, and the {\it retarded null-cone
coordinates} $(u,x^a = r\Omega^a)$.

A third coordinate system, known as the {\it Thorne-Hartle-Zhang
coordinates} \cite{thorne-hartle:85, zhang:86}, has also appeared in
the self-force literature --- they are the favoured choice of the
Florida group led by Steve Detweiler and Bernard Whiting (see, for
example, Ref.~\cite{detweiler:05}). The THZ coordinates are a variant
of the Fermi coordinates, and they have some nice properties. But I
find them less convenient to deal with than the Fermi or retarded
coordinates, because they do not seem to possess a simple covariant
definition. (The THZ coordinates may enjoy the mild Florida winters,
but they are not robust enough to endure the tougher Canadian
winters.) I shall not discuss the THZ coordinates here.

\begin{figure}
\includegraphics[width=0.5\linewidth]{basis}
\caption{A tetrad of basis vectors on the world line $\gamma$. The
  unit timelike vector $u^\mu$ is tangent to the world line. The
  unit spatial vectors $e^\mu_a$ are mutually orthogonal and also
  orthogonal to $u^\mu$.}
\end{figure}

The Fermi and retarded coordinates share a basic geometrical
construction on the world line. At each point on $\gamma$ we erect a
basis $(u^\mu, e^\mu_a)$ of orthonormal vectors. The timelike vector
$u^\mu$ is the particle's velocity vector, and it is tangent to the
world line.  The spatial unit vectors $e^\mu_a$ are labeled with the
index $a = 1, 2, 3$, and they are all orthogonal to $u^\mu$; they are
also mutually orthogonal. The vectors are transported on $\gamma$ so
as to preserve their orthonormality properties. If the world line is a
geodesic, then we might take the vectors $e^\mu_a$ to be parallel
transported on $\gamma$. If instead the world line is accelerated,
then we might take the spatial vectors to be Fermi-Walker transported
on the world line (LRR Sec.~3.2.1). The tetrad of basis vectors
satisfies the completeness relation
\begin{equation}
g^{\mu\nu} = -u^{\mu} u^{\nu} + \delta^{ab} e^\mu_a e^\nu_b,
\end{equation}
which holds at any point on the world line.

Any tensor that is evaluated on $\gamma$ can be decomposed in the
basis $(u^\mu, e^\mu_a)$. For example, we might introduce the
{\it frame components} of the Riemann tensor,
\begin{subequations}
\begin{align}
R_{0a0b}(\tau) &:=  R_{\mu\alpha\nu\beta} \Bigr|_\gamma
u^\mu e^\alpha_a u^\nu e^\beta_b, \\
R_{0abc}(\tau) &:=  R_{\mu\alpha\beta\gamma} \Bigr|_\gamma
u^\mu e^\alpha_a e^\beta_b e^\gamma_c, \\
R_{abcd}(\tau) &:=  R_{\alpha\beta\gamma\delta} \Bigr|_\gamma
e^\alpha_a e^\beta_b e^\gamma_c e^\delta_d.
\end{align}
\end{subequations}
They are functions of proper time $\tau$ on the world line.

\begin{figure}
\includegraphics[width=0.6\linewidth]{fermi}
\caption{Fermi coordinates.}
\end{figure}

The Fermi coordinates $(t, x^a = s\omega^a)$ are constructed as
follows (LRR Sec.~3.2). We select a point $x$ in a neighbourhood of
the world line, and we locate the unique geodesic segment $\beta$ that
originates at $x$ and intersects $\gamma$ orthogonally. The
intersection point is labeled $\bar{x}$, and $t$ is the value
of the proper-time parameter at this point: $\bar{x} = z(\tau =
t)$. This defines the time coordinate $t$ of the point $x$. The
spatial coordinates $x^a$ are defined by
\begin{equation}
x^a := - e^a_{\bar{\alpha}}(\bar{x}) \sigma^{\bar{\alpha}}(x,\bar{x});
\end{equation}
they are the projections in the basis $e^{\bar{\alpha}}_a$ of the
deviation vector $-\sigma^{\bar{\alpha}}(x,\bar{x})$ between the
points $x$ and $\bar{x}$. The Fermi coordinates come with the
condition  $\sigma_{\bar{\alpha}}(x,\bar{x}) u^{\bar{\alpha}}(\bar{x})
= 0$, which states that the deviation vector is orthogonal to the
world line's tangent vector; it is this condition that identifies the
intersection point $\bar{x} = z(t)$.

It is useful to introduce $s$ as the proper distance between $x$ and
the world line. This is formally defined by $s^2 :=
2\sigma(x,\bar{x})$, and it is easy to involve the completeness
relation and show that $s^2 = \delta_{ab} x^a x^b$ (LRR Sec.~3.2.3);
the Fermi distance $s$ is therefore the usual Euclidean distance
associated with the quasi-Cartesian coordinates $x^a$. It is also
useful to introduce the direction cosines $\omega^a
:= x^a/s$; these quantities satisfy $\delta_{ab} \omega^a \omega^b =
1$, and they can be thought of as a radial unit vector that points
away from the world line.

Each hypersurface $t = \mbox{constant}$ is orthogonal to the world
line (in the sense described above), and each spacetime point $x$
within the surface can be said to be simultaneous with $\bar{x} =
z(t)$. The Fermi coordinates therefore provide a convenient notion of
{\it rest frame} for the particle.

\begin{figure}
\includegraphics[width=0.6\linewidth]{retarded}
\caption{Retarded coordinates.}
\end{figure}

The retarded coordinates $(u, x^a = r\Omega^a)$ are constructed as
follows (LRR Sec.~3.3). Once more we select a point $x$ in a
neighbourhood of the world line, but this time we locate the unique
{\it null geodesic segment} $\beta$ that originates at $x$ and travels
backward in time toward $\gamma$. The new intersection point is
labeled $x'$, and $u$ is the value of the proper-time parameter at
this point: $x' = z(\tau = u)$. This defines the time coordinate $u$
of the point $x$. The spatial coordinates $x^a$ are defined exactly as
before, by
\begin{equation}
x^a := - e^a_{\alpha'}(x') \sigma^{\alpha'}(x,x').
\end{equation}
The retarded coordinates come with the condition  $\sigma(x,x') = 0$,
which states that the points $x$ and $x' = z(u)$ are linked by a null
geodesic (which travels forward in time from $x'$ to $x$).

It is useful to introduce $r$ as a measure of light-cone distance
between $x$ and the world line. This is formally defined by $r :=
\sigma_{\alpha'}(x,x') u^{\alpha'}(x')$, and can be shown to be an
affine parameter on the null geodesic that links $x$ to $x'$ (LRR
Sec.~3.3.3). In addition, we have that $r^2 = \delta_{ab} x^a x^b$,
and $r$ is the usual Euclidean distance associated with the spatial
coordinates $x^a$. It is also useful to introduce the direction
cosines $\Omega^a := x^a/r$, which again play the role of a unit
radial vector that points away from the world line.

Each hypersurface $u = \mbox{constant}$ is the future light cone of
the point $z(u)$ on the world line. Any point $x$ on this light cone is
in direct causal contact with $z(u)$. For this reason the retarded
coordinates give the simplest description of the scalar field $\Phi$
produced by a point charge $q$ moving on the world line. The field
satisfies a wave equation, and the radiation produced by the field
essentially realizes the light cones that are so prominently featured
in the construction of the coordinates.

\section{Field equation and particle motion}

Let me recapitulate the problem that we wish to solve. We have a point
particle of mass $m$ and scalar charge $q$ moving on a world line
$\gamma$ described by the parametric relations $z^\mu(\tau)$. The
particle creates a scalar field $\Phi(x)$ and this field acts back on
the particle and produces a force $F_{\rm self}^\alpha$. We wish to
determine this self-force.

The scalar field obeys the linear wave equation
\begin{equation}
\Box \Phi = -4\pi \mu,
\end{equation}
where $\Box := g^{\alpha\beta} \nabla_\alpha \nabla_\beta$ is the wave
operator, and
\begin{equation}
\mu(x) = q \int_\gamma \delta_4\bigl(x,z(\tau) \bigr)\, d\tau
\end{equation}
is the scalar-charge density, expressed as an integral over the world
line. The four-dimensional delta function $\delta_4(x,z)$ is defined
as a scalar quantity; it is normalized by
$\int \delta_4(x,x')\, \sqrt{-g} d^4x  = 1$.

The particle moves according to
\begin{equation}
m(\tau) a^\mu = q \bigl( g^{\mu\nu} + u^\mu u^\nu\bigr) \Phi_\nu,
\label{EoM}
\end{equation}
where $a^\mu = Du^\mu/d\tau$ is the covariant acceleration and
$\Phi_\nu := \nabla_\nu \Phi$ is the field gradient. The presence of
the projector $g^{\mu\nu} + u^\mu u^\nu$ on the right-hand side
ensures that the acceleration is orthogonal to the velocity. The field
gradient, however, also has a component in the direction of the world
line, and this produces a change in the particle's rest mass (LRR
Sec.~5.1.1): $dm/d\tau = -q u^\mu \Phi_\mu$. We shall not be concerned
with this effect here. Suffice it to say that the mass is not
conserved because the scalar field can radiate monopole waves, which
is impossible for electromagnetic and gravitational radiation.

The wave equation for $\Phi$ can be integrated, as we shall do in the
following section, and the solution can be examined near the world
line. Not surprisingly, the field is singular on the world line. This
property makes the equation of motion meaningless as it stands, and we
shall have to make sense of it in the course of our analysis.

\section{Retarded Green's function}

The wave equation for $\Phi$ is solved by means of a {\it Green's
function} $G(x,x')$ that satisfies
\begin{equation}
\Box G(x,x') = -4\pi \delta_4(x,x').
\end{equation}
The solution is simply
\begin{equation}
\Phi(x) = \int G(x,x') \mu(x')\, \sqrt{-g'} d^4x'
= q \int_\gamma G(x,z)\, d\tau,
\end{equation}
and the difficulty of solving the wave equation has been transferred
to the difficulty of computing the Green's function. We wish to
construct the {\it retarded solution} to the wave equation, and this
is accomplished by selecting the retarded Green's function
$G_{\rm ret}(x,x')$ among all the solutions to Green's
equation. (Other choices will be considered below.) The retarded
Green's function possesses the important property that it vanishes
when the source point $x'$ is in the future of the field point
$x$. This ensures that $\Phi(x)$ depends on the past behaviour of the
source $\mu$, but not on its future behaviour.

The retarded Green's function is known to exist globally as a
distribution if the spacetime is globally hyperbolic. But knowledge of
the Green's function is required only in the immediate vicinity of the
world line, so as to identify the behaviour of $\Phi$ there; we shall
not be concerned with the behaviour of the Green's function when $x$
and $z(\tau)$ are widely separated.

In this context the Green's function can be shown (LRR Sec.~4.3) to
admit a {\it Hadamard decomposition} of the form
\begin{equation}
G_{\rm ret}(x,x') = U(x,x') \delta_{\rm future}(\sigma)
+ V(x,x') \Theta_{\rm future}(-\sigma),
\end{equation}
where $\sigma(x,x')$ is the world function introduced previously, and
the two-point functions $U(x,x')$ and $V(x,x')$ are smooth when
$x \to x'$. The retarded Green's function is not smooth in this limit,
however, as we can see from the presence of the delta and theta
functions. The first term involves $\delta_{\rm future}(\sigma)$, the
restriction of $\delta(\sigma)$ on the future light cone of the source
point $x'$.  The delta function is active when $\sigma(x,x') = 0$, and
this describes (for fixed $x'$) the future and past light cones of
$x'$. We then eliminate the past branch of the light cone --- for
example, by multiplying $\delta(\sigma)$ by the step function
$\Theta(t-t')$ --- and this produces
$\delta_{\rm future}(\sigma)$. The second term involves
$\Theta_{\rm future}(-\sigma)$, a step function that is
active when $\sigma < 0$, that is, when $x$ and $x'$ are timelike
related; we also restrict the interior of the light cone to the future
branch, so that $x$ is necessarily in the future of $x'$.

The delta term in $G_{\rm ret}(x,x')$ is sometimes called the
{\it direct term}, and it corresponds to propagation from $x'$ to $x$
that takes place directly on the light cone. If the Green's function
contained a direct term only (as it does in flat spacetime), the field
at $x$ would depend only on the conditions of the source $\mu$ at the
corresponding retarded events $x'$, the intersection between the
support of the source and $x$'s past light cone. In the case of a
point particle this reduces to a single point $x' \equiv z(u)$. The
theta term in $G_{\rm ret}(x,x')$, which is sometimes called the
{\it tail term}, corresponds to propagation within the light cone;
this extra term (which is generically present in curved spacetime)
brings a dependence from events $x'$ that lie in the past of the
retarded events. In the case of a point particle, the field at $x$
depends on the particle's entire past history, from $\tau = -\infty$ to
$\tau = u$.

There exists an algorithm to calculate $U(x,x')$ and $V(x,x')$ in the
form of Taylor expansions in powers of $-\sigma^{\alpha'}$
(LRR Sec.~4.3.2). It returns
\begin{equation}
U(x,x') = 1 + \frac{1}{12} R_{\alpha'\beta'} \sigma^{\alpha'}
\sigma^{\beta'} + \cdots
\end{equation}
and
\begin{equation}
V(x,x') = \frac{1}{12} R(x') + \cdots,
\end{equation}
where $R_{\alpha'\beta'}$ is the Ricci tensor at $x'$, and $R(x')$
the Ricci scalar at $x'$. In Ricci-flat spacetimes the expansions of
$U - 1$ and $V$ both begin at the fourth order in $\sigma^{\alpha'}$.

\section{Alternate Green's function}

The {\it advanced} Green's function is given by (LRR Sec.~4.3)
\begin{equation}
G_{\rm adv}(x,x') = U(x,x') \delta_{\rm past}(\sigma)
+ V(x,x') \Theta_{\rm past}(-\sigma),
\end{equation}
in terms of the same two-point functions $U(x,x')$ and $V(x,x')$ that
appear within the retarded Green's function. The difference is that
the light cones are now restricted to the past branch, so that
$G_{\rm adv}(x,x')$ vanishes when $x'$ is in the past of $x$.  A
solution to the wave equation constructed with the advanced Green's
function would display anti-causal behaviour: it would depend on the
future history of the source.

Another useful choice of Green's function is the
{\it Detweiler-Whiting singular} Green's function defined by (LRR
Sec.~4.3.5)
\begin{equation}
G_{\rm S}(x,x') = \frac{1}{2} U(x,x') \delta(\sigma)
- \frac{1}{2} V(x,x') \Theta(\sigma).
\end{equation}
Here the delta and theta functions are no longer restricted: both
future and past branches contribute to the Green's function. In fact,
the argument of the step function is now $+\sigma$, and this indicates
that the second term is active when $x$ and $x'$ are spacelike
related. For fixed $x'$, the singular Green's function is nonzero when
$x$ is either on, or outside, the (past and future) light cone of
$x'$. Unlike the retarded and advanced Green's functions,
$G_{\rm S}(x,x')$ is not known to exist globally as a distribution
(even for globally hyperbolic spacetimes); its local existence is not
in doubt, however, and this suffices for our purposes.

\begin{figure}
\includegraphics[angle=-90, width=0.5\linewidth]{ret_adv}
\hfill
\includegraphics[angle=-90, width=0.5\linewidth]{sing_regul}
\caption{Solutions to the wave equation. The retarded field is
  sourced by the past history of the point particle, up to the
  retarded position $z(u)$. The advanced field is sourced by the
  future history, starting from the advanced position $z(v)$. The
  singular field is sourced by the world-line segment that lies on and
  outside the light cone of the field-point $x$, starting from the
  retarded position $z(u)$ and ending at the advanced position
  $z(v)$. Finally, the regular field is sourced by the history of the
  particle up to the advanced position $z(v)$.}
\end{figure}

All three Green's functions satisfy the same wave equation, $\Box
G = -4\pi \delta_4$, and all three give rise to fields $\Phi(x)$ that
diverge on the particle's world line. A useful combination of Green's
functions is the {\it Detweiler-Whiting regular} two-point function
\begin{equation}
G_{\rm R}(x,x') = G_{\rm ret}(x,x') - G_{\rm S}(x,x'),
\end{equation}
which satisfies the homogeneous wave equation $\Box G_{\rm R}(x,x')
= 0$. This two-point function gives rise to a field
\begin{equation}
\Phi_{\rm R} = \Phi_{\rm ret} - \Phi_{\rm S}
\end{equation}
that also satisfies the homogeneous wave equation,
$\Box \Phi_{\rm R} = 0$. This field is the difference between two
singular fields, and since $\Phi_{\rm ret}$ and $\Phi_{\rm S}$ are
equally singular near the world line, we find that the {\it regular
remainder field} $\Phi_{\rm R}$ stays bounded when $x \to
z(\tau)$. And what's more, the regular field is smooth, in the sense
that it and any number of its derivatives possess a well-defined limit
when $x \to z(\tau)$.

\section{Fields near the world line}

Using the ingredients presented in the preceding sections it is
possible to show (LRR Secs.~5.1.3, 5.1.4, and 5.1.5) that close to the
world line, the retarded, singular, and regular fields are given by
\begin{subequations}
\begin{align}
\Phi_{\rm ret} &= \frac{q}{r} + q \int_{-\infty}^u V(x,z)\, d\tau
+ O(r^2), \\
\Phi_{\rm S} &= \frac{q}{r} - \frac{1}{3} q \dot{a}_a x^a
+ O(r^2), \\
\Phi_{\rm R} &= \frac{1}{3} q \dot{a}_a x^a
+ q \int_{-\infty}^u V(x,z)\, d\tau + O(r^2),
\end{align}
\end{subequations}
in the retarded coordinates $(u,x^a = r\Omega^a)$. These expressions
involve the retarded distance $r$ from $x$ to $z(u)$ and the frame
component $\dot{a}_a(u) := \dot{a}_\mu e^\mu_a$ of
$\dot{a}^\mu := D a^\mu/d\tau$, the proper-time derivative of the
acceleration vector. They involve also an integration over the past
history of the particle. These expressions are valid for Ricci-flat
spacetimes.  We observe that the retarded and singular fields both
diverge as $q/r$ as we approach the world line, but that the regular
remainder $\Phi_{\rm R}$ is free of singularities.

In the Fermi coordinates $(t, x^a = s\omega^a)$ we have the more
complicated expressions
\begin{subequations}
\begin{align}
\Phi_{\rm ret} &= \frac{q}{s} - \frac{1}{2} q a_a \omega^a
+ qs \biggl( \frac{1}{8} \dot{a}_0 + \frac{1}{3} \dot{a}_a \omega^a
- \frac{1}{6} R_{0a0b} \omega^a \omega^b \biggr)
\nonumber \\  & \qquad \mbox{}
+ q \int_{-\infty}^{t} V(x,z)\, d\tau + O(s^2), \\
\Phi_{\rm S} &= \frac{q}{s} - \frac{1}{2} q a_a \omega^a
+ qs \biggl( \frac{1}{8} \dot{a}_0
- \frac{1}{6} R_{0a0b} \omega^a \omega^b \biggr) + O(s^2), \\
\Phi_{\rm R} &= \frac{1}{3} q \dot{a}_a x^a
+ q \int_{-\infty}^{t} V(x,z)\, d\tau + O(s^2).
\end{align}
\end{subequations}
They involve the spatial distance $s$ between $x$ and $z(t)$, the
frame components of the acceleration vector and its proper-time
derivative, the frame components of the Riemann tensor, and the
integration over the past history of the particle. Once more we see
that the retarded and singular fields diverge in the limit $s \to 0$,
but that the regular field is free of singularities. (The singular
nature of $\Phi_{\rm S}$ is also observed in a term such as
$\frac{1}{2} q a_a \omega^a$ that stays bounded when $s \to 0$, but is
directionally ambiguous on the world line.)

From these equations we may calculate the spatial derivatives of the
singular and regular fields. We obtain
\begin{subequations}
\label{gradients}
\begin{align}
\nabla_a \Phi_{\rm S} &= -\frac{q}{s^2} \omega_a
- \frac{q}{2s} \bigl( \delta^b_a - \omega^b \omega_a \bigr) a_b
+ \frac{q}{8} \dot{a}_0\, \omega_a
\nonumber \\ & \qquad \mbox{}
+ \frac{q}{6} R_{0b0c}\, \omega_a \omega^b \omega^c
- \frac{q}{3} R_{0a0b}\, \omega^b + O(s), \\
\nabla_a \Phi_{\rm R} &=\frac{1}{3} q \dot{a}_a
+ q \int_{-\infty}^t \nabla_a V(x,z)\, d\tau + O(s).
\end{align}
\end{subequations}
As expected, the gradient of the singular field diverges as $q/s^{2}$,
but the gradient of  the regular field is free of singularities. The
gradient of the retarded field is $\nabla_a \Phi_{\rm ret} =
\nabla_a \Phi_{\rm S} + \nabla_a \Phi_{\rm R}$.

We notice that many terms in $\nabla_a \Phi_{\rm S}$ are proportional
to an odd number of radial vectors $\omega^a$; all such terms vanish
when we average the field gradient over a spherical surface of
constant $s$. This averaging leaves behind
\begin{equation}
\bigl\langle \nabla_a \Phi_{\rm S} \bigr\rangle
= -\biggl( \frac{q}{3s} \biggr) a_a+ O(s),
\end{equation}
which is still singular. To obtain this result we made use of the
identity $\langle \omega^b \omega_a \rangle = \frac{1}{3}
\delta^b_a$. Notice that because $\nabla_a \Phi_{\rm R}$ is
smooth at $s=0$, an averaging simply returns the same expression:
$\langle \nabla_a \Phi_{\rm R} \rangle = \nabla_a \Phi_{\rm R}$.

\section{Self-force}

Let us now reflect on the results of the preceding section and try to
make sense of Eq.~(\ref{EoM}) as an equation of motion for the
particle. Our first attempt will be entirely heuristic; we shall add
refinement to our treatment in the following section.

Given that Eq.~(\ref{EoM}) does not make sense as it stands when we
insert $\Phi = \Phi_{\rm ret}$ on its right-hand side, let us take
the view that the equation is meant to apply to an extended body
instead of a point particle, and let us average $\Phi_\mu :=
\nabla_\mu \Phi$ over the body's volume. This operation should be
carried out in the body's rest frame, and for this purpose it is
natural to adopt the Fermi coordinates. We aim, therefore, to average
the spatial components $\Phi^{\rm ret}_a$ of the field gradient. The
simplest form of averaging was carried out already in the preceding
section, and we obtained
\begin{equation}
\langle \Phi^{\rm ret}_a \rangle =
\langle \Phi^{\rm S}_a \rangle + \langle \Phi^{\rm R}_a \rangle
= -\biggl( \frac{q}{3s} \biggr) a_a + \Phi^{\rm R}_a+ O(s),
\end{equation}
in which $\Phi^{\rm R}_a$ is evaluated (without obstacle) at
$s=0$. This expression corresponds to pretending that the body is a
thin spherical shell of radius $s$.

Substitution into Eq.~(\ref{EoM}) and evaluation in the Fermi
coordinates produces
\begin{equation}
( m + \delta m ) a^a = q  \Phi_{\rm R}^a,
\end{equation}
with $\delta m := q^2/(3s)$ denoting the contribution to the
total body mass that comes from the field's energy. Absorbing this
into a redefinition of the inertial mass $m$, the final tensorial
expression for the equation of motion is
\begin{equation}
m a^\alpha = q \bigl( g^{\alpha\beta} + u^\alpha u^\beta \bigr)
\nabla_\beta \Phi_{\rm R},
\label{Quinn}
\end{equation}
with
\begin{equation}
\nabla_\beta \Phi_{\rm R} = \frac{1}{3} q \dot{a}_\beta
+ q \int_{-\infty}^\tau \nabla_\beta V(x,z)\, d\tau'.
\end{equation}
This is Quinn's equation of motion \cite{quinn:00} for a scalar charge
$q$ moving in a curved spacetime with metric $g_{\alpha\beta}$. The
self-force involves an instantaneous term proportional to
$\dot{a}^\alpha = D a^\alpha/d\tau$, as well as an integral over the
particle's past history.

Equation (\ref{Quinn}) informs us that of the complete retarded field
$\Phi_{\rm ret} = \Phi_{\rm S} + \Phi_{\rm R}$, only the
Detweiler-Whiting regular field $\Phi_{\rm R}$ contributes to the
self-force. The role of the singular field is merely to contribute to
the particle's inertia, through a shift $\delta m$ in its inertial
mass. This contribution diverges in the limit $s \to 0$, but it would
be finite for any extended body.

I must confess that this computation returns the wrong expression for
the particle's self-energy. We obtained $\delta m = q^2/(3s)$, while
the correct expression is $\delta m = q^2/(2s)$; we are wrong by a
factor of $2/3$.  I believe that this discrepancy originates in an
inconsistency between our assumed shape for the extended body --- a
spherical shell of radius $s$ ---  and the field it produces, which we
took to be equal to the field produced by a point
particle. I would conjecture that calculating the field actually
produced by a spherical shell would give rise to the correct
expression for $\delta m$, but leave unchanged the final result of
Eq.~(\ref{Quinn}) for the equation of motion.

\section{Axiomatic approach}

The procedure outlined above is admittedly heuristic. It can, however,
be formalized and put on an axiomatic basis that supplies
Eq.~(\ref{Quinn}) with a much improved pedigree. This is the approach
that was first pursued by Ted Quinn and Bob Wald \cite{quinn-wald:97,
  quinn:00}. They formulate two axioms that the scalar self-force
$F^\alpha$ should satisfy:

\begin{description}
\item[{\bf Quinn-Wald Axiom 1.}] Two scalar particles move on world
lines $\gamma$ and  $\tilde{\gamma}$ in two different spacetimes. At
points $z$ and $\tilde{z}$ their acceleration vectors have equal
lengths. The neighbourhoods of $z$ and $\tilde{z}$, as well as the
acceleration vectors, are identified in Fermi coordinates. Then the
difference in the self-forces is given by
\begin{equation}
F^\alpha - \tilde{F}^\alpha =
q \bigl( g^{\alpha\beta} + u^\alpha u^\beta \bigr)
\lim_{s \to 0} \Bigl\langle \Phi_\beta  - \tilde{\Phi}_\beta
\Bigr\rangle.
\end{equation}
Here $\Phi$ and $\tilde{\Phi}$ are the retarded fields in each
spacetime, and $\Phi_\beta := \nabla_\beta \Phi$ while
$\tilde{\Phi}_\beta := \tilde{\nabla}_\beta \tilde{\Phi}$. The limit
is well defined after the difference of field gradients is averaged
over a sphere of radius $s$.
\item[{\bf Quinn-Wald Axiom 2.}] $\tilde{F}^\alpha = 0$ in flat spacetime, for
a particle with uniform acceleration.
\end{description}
The first axiom is essentially a statement that when two particles
momentarily share the same acceleration, their fields are equally
singular, and the difference (after averaging) possesses a
well-defined limit when $s \to 0$. The second axion is a scalar-charge
analogue to a well-known result from flat-spacetime electrodynamics: a
charged particle moving with a uniform acceleration does not undergo
radiation reaction.

According to Eqs.~(\ref{gradients}), the curved-spacetime expression
for the gradient of the retarded field is
\begin{eqnarray}
\Phi_a &=& -\frac{q}{s^2} \omega_a
- \frac{q}{2s} \bigl( \delta^b_a - \omega^b \omega_a \bigr) a_b
+ \frac{q}{8} \dot{a}_0\, \omega_a
\nonumber \\ & & \mbox{}
+ \frac{q}{6} R_{0b0c}\, \omega_a \omega^b \omega^c
- \frac{q}{3} R_{0a0b}\, \omega^b + \nabla_a \Phi_{\rm R} + O(s);
\end{eqnarray}
this holds at time $t$ in Fermi coordinates. The flat-spacetime
expression is
\begin{equation}
\tilde{\Phi}_a = -\frac{q}{s^2} \omega_a
- \frac{q}{2s} \bigl( \delta^b_a - \omega^b \omega_a \bigr) a_b
+ O(s),
\end{equation}
and this also holds at time $t$ in the same system of Fermi
coordinates. Under the conditions of the Quinn-Wald axioms, the
acceleration $a_a$ that appears in $\Phi_a$ and $\tilde{\Phi}_a$ is
one and the same. In the flat-spacetime expression we set $\dot{a}_0$
and $\dot{a}_a$ to zero because the acceleration is chosen to be
uniform. In addition we eliminate the Riemann-tensor terms,  as well
as the integral over the particle's past history --- $V$ necessarily
vanishes in flat spacetime.

Subtraction yields
\begin{equation}
\Phi_a - \tilde{\Phi}_a =  \frac{q}{8} \dot{a}_0\, \omega_a
+ \frac{q}{6} R_{0b0c}\, \omega_a \omega^b \omega^c
- \frac{q}{3} R_{0a0b}\, \omega^b + \nabla_a \Phi_{\rm R} + O(s),
\end{equation}
and we get
\begin{equation}
\bigl\langle \Phi_a - \tilde{\Phi}_a \bigr\rangle
=  \nabla_a \Phi_{\rm R} + O(s)
\end{equation}
after averaging over a sphere of constant $s$. The difference in the
self-forces is therefore $F_a - \tilde{F}_a =  q\nabla_a
\Phi_{\rm R}$. The second axiom finally returns $F_a = q \nabla_a
\Phi_{\rm R}$, which is equivalent to Eq.~(\ref{Quinn});
we have reproduced Quinn's expression for the scalar self-force.
Notice that the second axiom eliminates the need to carry out an
explicit renormalization of the mass.

Another axiomatic approach provides an even more immediate derivation
of Quinn's equation. This is the approach suggested by Steve Detweiler
and Bernard Whiting  \cite{detweiler-whiting:03}, which is based on an
observation and an alternate axiom:
\begin{description}
\item[{\bf Detweiler-Whiting Observation.}] The retarded field
$\Phi_{\rm ret}$ can be decomposed uniquely into a singular piece
$\Phi_{\rm S}$ and a regular remainder $\Phi_{\rm R}$.
\item[{\bf Detweiler-Whiting Axiom.}] The singular field produces no
force on the particle.
\end{description}
The immediate consequence of the axiom is that only the regular field
participates in the self-force, and we once more arrive at Quinn's
equation.

The Detweiler-Whiting approach is very clean and provides a quick
route to the final answer. The observation is not at all
controversial, because the singular field is indeed uniquely defined
by the prescription outlined in Sec.~6. The axiom, on the other hand,
seems too good to be true. How can it just be asserted that the
singular field produces no force?

A fairly compelling line of argument rests on the fact that according
to its definition, the singular field is strongly time-symmetric, in
the sense that the field at $x$ does not depend on the future nor the
past of the spacetime point; it instead depends on source points $x'$
that are in a spacelike or lightlike relation with $x$. Since we would
expect the self-force to be sensitive to the direction of time --- an
advanced field should produce a different force  from a retarded field
--- it seems plausible that the singular field would not know whether
to push or pull, and would therefore choose to do neither.

The argument is not water-tight. For example, an alternate
singular field, defined by Dirac's prescription $\frac{1}{2}
\Phi_{\rm ret} + \frac{1}{2} \Phi_{\rm adv}$, would also be
time-symmetric (though not strongly time-symmetric), and could also be
asserted to produce no force. The resulting self-force, however, would
be produced by $\frac{1}{2} \Phi_{\rm ret}
- \frac{1}{2} \Phi_{\rm adv}$, and would depend on the entire history
of the particle, both past and future. We would of course reject this
candidate self-force on grounds of causality violation, but the
argument nevertheless shows that there is more to the
Detweiler-Whiting singular field than a time-symmetry
property. Another hole in the argument lies in the link between the
time-symmetry of the singular field and the statement that it must
exert no force: While the time-symmetry property clearly implies
that the singular field cannot produce dissipative effects on the
particle, there is no reason to rule out an eventual conservative
contribution to the self-force.

The conclusion is that additional axioms are necessarily required to
make sense of the equations of motion formulated for a point
particle. The axioms may seem plausible and perhaps even self-evident,
but they cannot be derived from first principles in the context of a
classical field theory coupled to a point particle. Such a theory is
inherently singular and ambiguous, and it necessarily requires
external input in the form of additional axioms.

\section{Conclusion}

Can one do better than this? The answer is `no' if we insist in
treating the point particle as a fundamental classical object. The
answer, however, is `yes' if we properly understand that a point
particle is merely a convenient substitute for what is fundamentally
an extended body. In this view, the length scale of the moving body is
$\ell$, not zero. The body possesses a finite density of scalar
charge, the scalar field is finite everywhere, and its motion traces a
world tube in spacetime instead of a single world line. To determine
this motion is a well-posed problem, but the  description now involves
a lot of additional details. Under usual circumstances, however,
$\ell$ is much smaller than all other length scales present in the
problem, such as the radius of curvature ${\cal R}$ of the body's
trajectory. Under these circumstances the description of the motion
can be simplified so as to involve a much smaller number of variables;
in the limit $\ell/{\cal R} \to 0$ only the position of the
center-of-mass matters, and all couplings between the body's multipole
moments and the external field become irrelevant. In this limit we
recover a point-particle description, with the essential understanding
that it is merely an approximate description that should not be
considered to be fundamental.

To go through the details of this program is difficult, and it appears
that very few authors have attempted it since the old days of Lorentz
and Abraham. For a recent discussion, and a review of this literature,
see the work by Harte \cite{harte:06}. Another important exception
concerns the gravitational self-force acting on a small black hole
(LRR Sec.~5.4), which is decidedly not treated as a point mass.

It is well known that in general relativity, the motion of gravitating
bodies is determined, along with the spacetime metric, by the Einstein
field equations; the equations of motion are not separately
imposed. This observation provides a means of deriving the
gravitational self-force without having to rely on the fiction
of a point mass. In the powerful method of {\it matched asymptotic
expansions}, the metric of the small black hole, perturbed by the tidal
gravitational field of the external spacetime, is matched to the metric
of the external spacetime, perturbed by the black hole. The equations
of motion are then recovered by demanding that the metric be a valid
solution to the vacuum field equations. In my opinion, this method
(which was first applied to the gravitational self-force problem by
Mino, Sasaki, and Tanaka \cite{mino-etal:97}) gives what is by far the
most compelling derivation of the gravitational self-force. Indeed,
the method is entirely free of conceptual and technical pitfalls ---
there are no singularities (except deep inside the black hole) and
only retarded fields are employed.

In this assessment I respectfully disagree with my colleague Bob
Wald, who finds that the method incorporates a number of unjustified
assumptions. I would concede that expositions of the method ---
including my own in LRR --- might not have sufficiently clarified some
of its subtle aspects. But I see this as faulty exposition, not as an
intrinsic difficulty with the method of matched asymptotic
expansions. I refer the reader to the recent work by Sam Gralla and
Bob Wald \cite{gralla-wald:08} for their views on this issue, and
their own approach to the motion of an extended body in general
relativity.

The introduction of a point particle in a classical field theory
appears at first sight to be severely misguided. This is all the more
true in a nonlinear theory such as general relativity. The lesson
learned here is that surprisingly often, {\it one can get away with
it}. The derivation of the gravitational self-force based on the
method of matched asymptotic expansions does indeed show that the
result obtained on the basis of a point-particle description can be
reliable, in spite of all its questionable aspects. This is a
remarkable observation, and one that carries a lot of convenience: It
is indeed much easier to implement the point-mass description than to
perform the matching of two metrics in two coordinate systems. The
lesson, of course, carries over to the scalar and electromagnetic
cases.

\begin{acknowledgement}
I wish to thank the organizers of the school for their kind invitation
to lecture; Orl\'eans in the summer is a very nice place to be. I wish
to thank the participants for many interesting discussions. And
finally, I wish to thank Bernard Whiting for his patience. This work
was supported by the Natural Sciences and Engineering Research Council
of Canada.
\end{acknowledgement}

redpajama_set_name: RedPajamaArXiv


text:
Focus on people to maximize plant efficiency
Balancing people and technology to optimize plant operations.
By Andreas Eschbach and Dr. Andy Brazier December 27, 2021
Courtesy: eschbach
In its relentless march toward end-to-end automation, technology has continually up-ended the boundaries between man and machine in industrial enterprises. With recent advances in artificial intelligence supported by endless computing resources in the cloud, we must now ask ourselves, "how much longer will we need people directly involved in manufacturing?"
The fact is, we will always have people involved in process manufacturing plants. So perhaps the better approach is to look for ways to create an environment where we are able to balance the best attributes of people and technology to assure optimization of communication, safety and production. This article will explore new roles within an organization and how technology, created to support critical human factors, will help people and machines collaborate to provide the breakthrough advances in productivity that society needs in the decades to come.
The machine/human connection
As long ago as the 1950s, scientists were exploring the relationships between people and machines with the launch of the field of inquiry known as function allocation research. While technology has certainly evolved over the last 70 years, the basic findings of a scientist by the name of Paul Fitts, the creator of the Fitts list, remain largely valid. Function allocation has become a central component of systems engineering and its main aim is to provide a rational means of determining which system-level functions should be carried out by humans and which by machines. Although other methods have been developed, Fitts list still remains the most oft-cited research in the more complex manufacturing world of today.
In his research, Fitts outlined six areas where people prevail. These areas include detection, perception, judgement, induction, improvisation and long-term memory. Conversely, according to Fitts, machines excel at speed, power, computation, replication, simultaneous operations, and short-term memory.
So, in looking toward technology investments, the focus should not be simply on replacing people with machines but rather how, using the positive attributes of both people and machines, there can be productive and symbiotic relationships.
Highlighting the human factor
You may think that the massive reduction in the price of computer memory over time would mean that the original Fitts list from the 1950s no longer applies. However, many organizations have simply invested in data storage without considering how it will be accessed, understood and used in practice. Storing data only makes sense if it is relevant and actionable. This requires data that can be processed and appropriately visualized for people. It is very easy to overwhelm people with data and make things too complicated. Understanding human factors is essential to avoid these problems.
Human memory works differently than machine memory. While machines are very good at capturing and storing data, humans are able to remember perceptions, images and feelings. Thus, only people can draw on human attributes to create a better understanding from things that have been experienced or memorized from past experiences.
Reliability is another example. Machines are reliable only for certain defined situations for which they've been programmed, i.e. repeating the same set of actions on a production line. People, however, through their powers of perception, improvisation, detection, among other attributes, are reliable within and outside of the defined operational domain because they can continually adapt. Thus, the reliability of people and machines cannot be measured in the same way. Technology can only do what we've asked it to do while people are able to create new processes or situations when the unexpected arises.
Perhaps the most relevant example of human adaptability has been the response to the upheaval caused by the COVID-19 pandemic. Business as usual required creative workarounds to keep manufacturing processes in motion while workers at almost all levels were working from home or managing processes with skeleton crews. In many ways, these adaptations have been successful because of the creativity and adaptability of people, not the machines.
As technology has evolved, particularly with automation in process manufacturing plants, systems have become more complex. As the price of storing data has declined and cloud-based systems have emerged, more and more information is available for data mining, but in general, the process industry has not invested the millions of dollars necessary to ensure that the data can be utilized effectively.
Managing and mining the data is a 'people' activity. Thus, the concept of replacing people with machines should not be the focus. Instead, the emphasis should be on implementing technology that can be used effectively by people on the shop floor.
Complexities and advantages of IoT
IoT and the Industrial Internet of Things (IIoT) have delivered even more complexities as well as great advantages to process manufacturing. IIoT has brought together more components, delivered more data and connections, created situations where fewer people are needed to manage processes, and has hastened the speed to manage manufacturing processes. But with all these exponential – and ever- growing – changes, the question still remains. How do we handle how people will work and thrive in this fast-changing environment?
If we want technology to work, we need to design it for people. Referring back to the Fitts list and the understanding of human factors, it is important to recognize the true relevance of people in a process manufacturing environment.
Processes are run by many people at different levels and different sites within an organization. There is not one person who knows everything. There are – at the operations level – for example, several teams. Each of which has different goals and interests. The teams are active on different shifts and reporting up the line to various supervisors who, in turn, may be reporting into the corporate structure. All of these people and teams are using technology in some way to do their jobs. Technology deployed that is designed to help people and teams work together more collaboratively and thus, effectively will be far more successful that technology that is difficult to use and requires people to adapt their behaviors to use it.
Generally, people have a good memory when it comes to experiences, perceptions and emotions, but they are not so reliable when processing data when compared to a machine. Take, for example, a 12-hour shift. How much data is retained or forgotten during that shift? On a good day, a high proportion of data generated may be retained. On a stressful shift, it maybe only half. Transfer of data to the next team will be directly affected by this, especially when errors and omissions of communication are factored in.
People are always a bit imprecise. Relying on people to remember all information and to communicate it reliably either verbally or via written documents will always be problematic.. Inaccurate communication can result in many different issues including safety issues.
Recognizing the issues caused by imprecise transfer of information leads to a need to provide easy-to- use technology to support people to overcome their natural limitations. However, there will be much greater benefits if the technology does more than just handle data and enhances the natural human capabilities by allowing insights created during the shift to be transferred to the next shift so that they get a better understanding of what is happening and can act on it more quickly and effectively. Collaboration, via technology, among the shift teams creates a higher level of efficiency, quality and safety.
Quality digital shift handover process
Information shared during shift handovers represents a critical foundation for continuity. It serves as a running protocol of relevant events and conditions that together describe the state of manufacturing processes within a specific period. To align all these sources, technology in the form of a digital shift management solution, allows handovers and provides a formal digital record of plant operations that can be delivered digitally to all members of the manufacturing organization.
Experience from handling the COVID-19 pandemic highlighted the advantages of digital communication among manufacturing teams. Digital support for teams helped them to sustain production processes, manage safety issues and maintain quality in abnormal situations during the crisis, but can continue to provide valuable support as normality returns.
Embrace technology and the human factor
Technology won't replace people. Our aim should be to use technology to enable people to use their natural capabilities and increase their performance. Successful manufacturing enterprises will embrace an approach that elevates the attributes of both people and technology to help the human-machine network work together in a more collaborative way. This will ensure more transparency, reliability and visibility across all plant functions to help teams better communicate and optimize outcomes. People-centric technology, in other words, technology that has been designed with people in mind, enables organizational teams to improve productivity, cost efficiencies, quality and safety.
Original content can be found at Plant Engineering.
Andreas Eschbach and Dr. Andy Brazier
Author Bio: Andreas Eschbach is the CEO of eschbach and Dr. Andy Brazier is an industry consultant for risk and process safety
Training and certifications help system integrators succeed
Robert Huschka
Developing the existing and future workforce
Randy Otto
Three ways to build a future-proof factory with millennial manufacturing
Terri Ghio
Top 5 Control Engineering content: June 20-26, 2022
Five tips for women who want to succeed in engineering
Semiconductor degrees program launched
Brian Huchel
Top 5 Control Engineering content: May 16-22, 2022

redpajama_set_name: RedPajamaCommonCrawl


text:
United States France Magyarország
Anna Cave
Local nameAnna-barlang
LocationMiskolc, Hungary
The Anna Cave is a natural limestone cave in Miskolc-Lillafüred, Hungary, near the waterfall.
The cave was discovered in 1833, when opening a shaft in the limestone in order to provide the iron furnace at Hámor with water. It soon became a tourist attraction, even Sándor Petőfi visited it in 1847. However, in the second part of the century, when the iron furnaces were closed, the cave was forgotten.
It was opened again in 1912. In 1927, when the Palace Hotel was built, new caverns were found. The entrance that's used today was constructed then.
Tags Cave
Lillafured Palacehotel
Wikipedia https://en.wikipedia.org/wiki/Anna_Cave
Address 50 Lux Kálmán lépcsősor, Hámor 3517, Hungary
Coordinates 48°6'18.233" N 20°37'29.869" E
Google Trips Alternative What to See in Europe What to See in Hungary What to See in Borsod-Abaúj-Zemplén What to See in Northern Hungary What to See in Miskolci járás Best Guest Houses in Miskolc István Cave


We love outdoor sports and adrenaline. But not without professional development and building a nice career. We thought about dropping out of college to go snowboarding full-time.. We thought about quitting our job and travel fulltime… But then.. would this not be a little selfish?
Is there not a middle road?
Yes! We found it. Or at least, we are discovering it as we speak. We are a group of young professionals: employees, trainees and freelancers that have found a pretty good balance in combining career building with outdoor adventure.
Some call us digital nomads but we're not nomadic. We just enjoy what Europe has to offer. The best adventures can be found closer than you think.
This site is for those who grow tired of the nomadism hype that is selfish. For those who grew tired of the 'quit your job and go travel the world' blogposts.
This site is for those who want to get creative in enjoying the outdoors – without quitting your job. When you feel forced to choose between surfing and a career – you can have both.


text:
Mar 11, 2019 - Mar 15, 2019 - in Frankfurt am Main, Germany
ISH is the world's leading trade fair focusing on the responsible management of water and energy in buildings.
ISH meets the growing demand for comfort, convenience, individualisation, well-being and aesthetics. Integrated solutions are able to cover all these requirements and make a decisive contribution to energyefficient and resource-friendly building systems.
Over 2,400 exhibitors, including all market leaders from home and abroad, launch their latest products, technologies and solutions onto the world market at ISH. ISH has, therefore, a leading role worldwide as the occasion per se when the sector comes together – 64 percent of the exhibitors and 40 percent of the around 200,000 visitors come from outside Germany.
https://ish.messefrankfurt.com/frankfurt/en.html
ATMO/DTI Technical Conference
Jun 23, 2020 - Jun 23, 2020 - in Online, Belgium
The world's first conference on NatRefs in air conditioning.
Feb 03, 2020 - Feb 05, 2020 - in Orlando, United States of America
The International Air-Conditioning, Heating, Refrigerating Exposition (AHR Expo), which started 87 years ago as a heating...
Natural Refrigerants Virtual Trade Show 2.0
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StreamingVideo
How to create a two-way variable grid that adjusts to the weather dependent nature of solar and wind
The U.S. electric grid is outdated. It was designed for a world that runs on fossil fuels.
By Editorial Team February 1, 2021 0
The grid needs some major tech upgrades in order to transition to a more distributed, all-renewable system.
That means smart, internet-connected hardware working in tandem with advanced data analytics software to ensure that supply and demand are balanced, even when the sun isn't shining or the wind isn't blowing.
The United States has ample opportunity to transform its energy sector through decarbonization; however, this will require more than investments in just solar and wind technology.
The primary obstacle for renewable energy is actually the American electrical grid system, composed of the Eastern Interconnection, Western Interconnection, and Texas Interconnection. The modern grid hasn't changed much in terms of design since it was initially composed.
The grid is designed for fossil fuel power plants, where large amounts of electricity are produced in relatively few locations. To clarify, the grid is designed for the one-way transmission of power, which is a problem for renewable energy. Solar and wind installations are cheap to install but are highly decentralized in nature.
They rely on individual companies and consumers producing, storing, and selling excess power to balance out the intermittency of renewable energy.
There are several improvements that must be made to grid systems across the United States if decarbonization is to be successfully undergone. Standard electrical transformers are not designed to accommodate backward electricity flows, meaning electricity produced by a homeowner or business that is fed into the grid.
These transformers must be adapted to the changing nature of electricity generation, which, while expensive, is a much-needed investment to improve the efficiency of electrical grids. Transmission and distribution infrastructure is built for peak hours of utilization, meaning the design ensures an uninterrupted flow of electricity to consumers.
Unfortunately, this often means "peaker" plants (fossil fuel plants used only during peak electricity hours) have to be maintained as backups, which can be incredibly costly and inefficient. Due to the decentralized nature of solar and wind energy, massive investments in new distribution lines would be a necessity to make a "green grid" viable, in which fossil fuel powerplants would be done away with altogether.
However, battery and other utility-scale storage technologies would also need be included in these infrastructure investments. Among these are pumped-storage hydro and Li-ion, thermal, solid-state, and flow batteries. These technologies tend to be fairly expensive, but have witnessed rapid cost decreases in the past decade.
Alongside large infrastructure investments, policies promoting the adoption and further innovation of smart technologies, including meters and censors, will be critical.
Smart technologies provide detailed electricity usage analytics, which can be used to improve the balancing of electricity demand and supply — a feat that will get harder as energy production becomes decentralized. Whereas traditional grids are based on matching supply to demand, new grids could instead seek to match demand to supply.
Through the use of smart devices, household electricity consumption could be automatically reduced during times of low renewable energy production. Demand response policies could effectively create a dispatchable source of electricity if integrated into the market properly.
Policies such as net metering, which enables consumers to sell power back into the grid, will help accomplish this goal by fostering the beginning of a new relationship between utilities and consumers, one which is based on reciprocity.
There are many logistical challenges, such as the coordination of jurisdictional regulations for private, public, and cooperative utilities that need to be answered before the United States will be able to effectively move towards a green grid.
To do so successfully will require the integration of everyday consumers into the energy market as well as the transformation of entire electrical systems. By no means will this be an inexpensive undertaking, but the moral imperative of climate change and the economic opportunities that lie in clean technology should make decarbonization a top priority for the United States.
It must be kept in mind, however, that investments alongside solar and wind to modernize the grid and transform the consumer-utility relationship will be needed to allow for a safe, reliable, and economically prosperous decarbonization.
The Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with data and insights to deliver useful news updates. We are experts with the mission to inform, educate and inspire the industry. We are passionately curious, enthusiastic, and motivated to positively impact the world. Send us a tip via hello @ pvbuzz [dot] com.
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Heinz Triendl
Künstler und Tempelbauer
EXPRESSING THE SUBJECT
Break free from the Clutches of Tradition
Modern Art per se did not consider the regular subjects such as flowers, nature, sunset etc as the only subjects worthy of painting. Just anything was accepted as a subject. For example, a group of urchins playing next to an overflowing dustbin is still regarded as a subject for painting.
Client : University
Service : Modern Art
Project : Student Demography
ART FOR ART SAKE
Art was Initially serving a utilitarian purpose, followed by imperial, private, civic, and religious patronage. The distinct schools of Eastern and Western paintings later found audiences and patrons in the aristocracy and the middle class.
Cubism is one of the most influential art movements of the 20th century that was pioneered by great names such as Pablo Picasso, Georges Braque, Andre Lhote, Jean Metzinger, Albert Gleizes, Robert Delaunay amongst others. Cubism term is broadly used in connection with a wide variety of art produced in Paris and its precincts such as Montmartre, Montparnasse, and Puteaux during the early 20th century up to 1920s.
Art movement such as Cubism is a 20th-century art movement bringing the European painters and sculptors together and enabled them to move forward successfully towards 20th century Modern Art. Cubism as such had its impact in other fields of art such as architecture, literature, and music. Cubism brings the 3rd dimension into the picture clearly making a stunning painting of immeasurable beauty.
© by Heinz Triendl, Oberperfuss | Impressum + Datenschutz


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Mamá, mamá, mamá es una película de Argentina filmada en colores dirigida por Sol Berruezo Pichon-Rivière sobre su propio guion que se estrenó el 7 de enero de 2021 y que tuvo como actores principales a Agustina Milstein, Chloé Cherchyk, Camila Zolezzi, Matilde Creimer Chiabrando y Siumara Castillo.

Argumento
A partir de un desgraciado suceso -una niña se ahoga en la pileta de su casa- la película muestra a su hermana Cleo, de doce años, afrontar la pérdida con sus tres primas  en un mundo sin adultos.

Reparto
Participaron del filme los siguientes intérpretes:
  Agustina Milstein...Cleo
 Chloé Cherchyk...Nerina
 Camila Zolezzi...Manuela
 Matilde Creimer Chiabrando...Leoncia
 Siumara Castillo...Aylín
 Vera Fogwill...Tía
 Jennifer Moule...Madre
 Shirley Giménez...Karen
 Ana María Monti...Abuela
 Florencia González...Erín

Comentarios
Paraná Sendrós en Ámbito Financiero opinó:
Adolfo C. Martínez escribió en La Nación:

Referencias

Enlaces externos
 Información sobre  Mamá, mamá, mamá en el sitio del cine nacional
 Información sobre  Mamá, mamá, mamá Mamá, mamá, mamá en Filmaffinity

Primer largometraje de un director
Películas dramáticas de Argentina
Películas dramáticas de los años 2020

redpajama_set_name: RedPajamaWikipedia


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May 7, 2022 Omar Faith
Cat With Only One Eye Washes Up After Missing for 5 Years on Offshore Oil Rig Confusing Owners
A five year odyssey for a feline by the name of Dexter appears to have finally reached a conclusion, after a long-long covert stay at a prison was interfered with by his appearance onboard an offshore oil rig, which finally resulted in a call to animal services.
The cat was a normal "well loved and cherished" hangout at Her Majesty's Prison Grampian in Peterhead, Scotland, where staff used to "fuss over" him and even gave him the nickname One-eyed Joe.
At that point, a most unexplainable thing happened: One-eyed Joe somehow wound up in a shipping container a mile and a half away at the town's port, prior to being transported onto an offshore oil rig, where the workers "ran away frightened" after the jet black cat leaped out of the container.
After finishing up an episode card, (which was most likely entertaining) the staff on board the rig took to Joe most generously, who was now quite comfortable with living alongside the laborers. As indicated by The National, he was "spoiled rotten" during the time he lived there.
However, eventually someone called the Society for the Prevention of Cruelty to Animals (SPCA) in Aberdeen, who recovered Joe after the feline had been taken off the rig by a helicopter – a remarkable accomplishment when you consider how hard getting a cat into a carrier ordinarily is.
"We were alerted to an incident of a cat being found in a shipping container offshore," Aimee Findlay, a Scottish SPCA animal rescue officer, said in a statement. "We've no idea how the cat ended up there, but we attended the heliport to collect him."
One-eyed Joe was then microchipped, and after checking the staff discovered his name was actually Dexter, and that his owner had lost the feline five years ago.
A microchip is a small, electronic chip encased in a glass chamber that is about the same size as a grain of rice. The microchip itself does not have a battery – it is activated by a scanner that is passed over the area, and the radio waves put out by the scanner activates the chip. The chip transmits the identification number to the scanner which displays the number on the screen. The microchip itself is also called a transponder. Contradictory to belief, It is not a GPS device and cannot track your animal if it gets lost. However, your information is used by the company to contact you.
"We are so glad that he was well looked after for the time he was missing but we're even more delighted to be able to reunite him with his original owner, thanks to his microchip being up to date," Findlay said.
What a heartwarming story, full of luck! Had it not been for the benefit of the microchip in Dexter, he would have been lost forever. This goes to show that if you've got furry family members, that it is important to get them microchipped. Sure, not all animals will wash offshore like this, but nevertheless they can be returned to you at any moment if the unfortunate happens. Statistics show that 1 out of 3 pets will go missing in their lifetime, and 90% of them will never return home (that's a very high percentage). However, on the upside, a chipped cat is 20 times more likely to get back to its owner, and most pets brought to the shelters are never reunited with their family if they have not been microchipped. With technology always evolving, and processes getting better these statistics are bound to climb as well, which is great news for all furry companions and their families.
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Daikaiju. Green Lantern, Lexington, KY. 2014.
Hans Condor. Egan's, Tuscaloosa, AL. 2015.
Blood of the Wolf Fest. Al's Bar, Lexington, KY. 2013.
Nerves Baddington. Saturn. Birmingham, AL. 2016.
Hans Condor. Saturn. Birmingham, AL. 2016.
James Hand. Austin, TX. March 2016.
Lee Bains III & the Glory Fires. Egan's, Tuscaloosa, AL. 2014.
Black Willis. Seasick Records. Birmingham, AL. 2016. Film.
Lee Bains III & the Glory Fires. The Basement, Nashville, TN. 2014.
Black Willis. Egan's, Tuscaloosa, AL. 2015.
Thelma & the Sleaze. Birmingham, AL. March 2016.
Leon Russell. Buster's, Lexington, KY. 2014.
Lee Bains III & the Glory Fires. MOTR Pub, Cincinnati, OH. 2015.
Lee Bains III & the Glory Fires. MOTR Pub, Cincinnati, OH. 2014.
Tombstalker. Al's Sidecar, Lexington, KY. 2013.
NerdRage. Best Friend Bar, Lexington, KY. 2015.
Lee Bains III & the Glory Fires. The Nick. Birmingham, AL. 2016.
Thelma & the Sleaze. Green Lantern, Lexington, KY. 2014.
KISS Army. The Nick, Birmingham, AL. 2014.
Ralph Stanley & the Clinch Mountain Boys. Muddy Roots Spring Weekender, Nashville, IN. 2014.
Lee Bains III & the Glory Fires. The Earl, Atlanta, GA. 2014.
High on Fire. The Revelry Room, Chattanooga, TN. 2015.
Lee Bains III & the Glory Fires. The Nick, Birmingham, AL. 2015.
Black Willis. The Nick, Birmingham, AL. 2015.
GT. Siberia, New Orleans, LA. 2015.
The Ghost Wolves. Cosmic Charlie's, Lexington, KY. 2014.
Mothership. The End, Nashville, TN. 2014.
Ride. Saturn, Birmingham, AL. 2015.
Ronnie Fest. The Nick. Birmingham, AL. 2016.
Lee Bains III & the Glory Fires. The Knitting Factory, Brooklyn, NY. 2015.
Banda la Colonial. El Rancho Centenario, Mt. Olive, AL. 2015.
Lee Bains III & the Glory Fires. Happening Fest. Good People Brewing Company. Birmingham, AL. 2016.
Bombs. Best Friend Bar, Lexington, KY. 2015.
Lee Bains III & the Glory Fires. Siberia, New Orleans, LA. 2015.
Hans Condor. Saturn. Birmingham, AL. 2016..
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Capsula. The Nick, Birmingham, AL. 2015.
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Those Darlins. Mercy Lounge, Nashville, TN. 2015.
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Hans Condor. The Earl, Atlanta, GA. 2015.
Hans Condor. JJ's Bohemia, Chattanooga, TN. 2015.
James Leg. Green Lantern, Lexington, KY. 2015.
Bad Cologne. Saturn. Birmingham, AL. 2016.
Lee Bains & the Glory Fires. DC9, Washington, D.C. 2015.
Hexxus. The Nick. Birmingham, AL. 2016.
Fifth on the Floor. Midwest Mecca of Bar Hoppers, Middletown, OH. 2014.
Al's Sidecar, Lexington, KY. 2013.
Lee Bains III & the Glory Fires. Zanzabar, Louisville, KY. 2014.
Red Fang. The Drunken Unicorn, Atlanta, GA. 2013.
Turbo Fruits. Cosmic Charlie's Lexington, KY. 2014.
The Dictators NYC. Red 7, Austin, TX. 2014.
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Justin Wells & Shooter Jennings. Midwest Mecca of Bar Hoppers, Middletown, OH. 2014.
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The Jim Jones Revue. The Southgate House Revival, Newport, KY. 2014.
Ma Turner. Al's Bar, Lexington, KY. 2014.
Paradox. Al's Sidecar, Lexington, KY. 2013.
Shooter Jennings. Muddy Roots, Cookeville, TN. 2013.
Ma Turner. Institute 193, Lexington, KY. 2014.
Dopebody. Zanzabar, Louisville, KY. 2015.
Joe Buck. Muddy Roots, Cookeville, TN. 2013.


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Tim and Nicole's Ampersand Wedding!
Tim and Nicole love Austin- it's where they met and decided to get married so they decided to make the wedding reflect the city where they fell in love. "Beautifully Undone" or funky, fun and relaxed was their approach to personal style- they wanted their guests to fell at home too.
Nicole's said she began collecting old books, silver glassware, cacti & succulents to use as their centerpieces months before hand. Each table also included an & on a silver restaurant stand.
The bride said "It was important to us that the guests felt the love Tim and I had for each other, but also the love that we had for them. We added a lot of touches to help that – every invitation that went out were handmade, we created each centerpiece by hand, the fake place cards with nods to our favorite pop culture pairings (biscuits & gravy, ren & stimpy) and were meant to create conversation and interest. Tim painted all the signs around the grounds.
Their first dance song was " Home is wherever I'm with you-" by Edward Sharpe and the Electric Zeros - which Nicole had engraved engraved inside of his ring.
But, even with all those details, the biggest hit was the photobooth Katherine brought! It added a level of fun and silliness that was just perfect." See their photobooth here!
The couple had hoped to exit in a friend's recently renovated turquoise truck but unfortunately it wasn't ready in time so they used this funky longhorn Cadillac to start off their honeymoon adventure to Marfa.
Cheers to Nicole and Tim and all their future creative adventures in LA!


Bleeding Heart Vine (Clerodendrum thomsoniae) grows as a vine rather than a bush like the other varieties of Clerodendrum. The name comes from the clusters of white or pink heart shaped bracts with red petals beneath each heart. Propagate from cuttings, seeds or runners. The runners are easily controlled. Also known as Scarlet Kiss. It's able to withstand light freezing, although it might die back to the roots, requiring it to start over the following spring. It blooms best in full sun to part shade, with rich soil free from nematodes. It is not salt tolerant. This striking plant comes from west Africa.


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Miami Marlins är en professionell basebollklubb i Miami i Florida i USA som spelar i National League, en av de två ligorna i Major League Baseball (MLB). Klubbens hemmaarena är Loandepot Park.

Historia
Klubben grundades 1993 under namnet Florida Marlins när National League utökades med två nya klubbar (den andra var Colorado Rockies). Klubbens första ägare var entreprenören Wayne Huizenga.

Klubben vann World Series redan 1997, under femte säsongen. Detta var ett nytt rekord för nya klubbar i MLB, ett rekord som sedan slogs av Arizona Diamondbacks som vann World Series under sin fjärde säsong 2001. Marlins vann även World Series 2003. Vid sina två World Series-vinster kom Marlins båda gångerna med till slutspelet som så kallad wild card-klubb, det vill säga man var bästa tvåa i ligan. Klubben har däremot aldrig vunnit sin division.

Inför säsongen 2012 bytte klubben namn till Miami Marlins och bytte samtidigt logotyper och dräkter.

I september 2017 såldes klubben till en grupp investerare ledd av affärsmannen Bruce Sherman. I gruppen ingick även den före detta storspelaren Derek Jeter. Jeter sålde dock sin andel i början av 2022.

Hemmaarena
Hemmaarena är Loandepot Park, tidigare kallad Marlins Park, invigd 2012. För att få ekonomisk hjälp från de lokala myndigheterna med att bygga arenan gick klubben med på att byta namn från Florida Marlins till Miami Marlins. Tidigare spelade klubben i Sun Life Stadium, som man delade med klubben i amerikansk fotboll Miami Dolphins i National Football League (NFL).

Spelartrupp

Fotogalleri

Referenser

Noter

Webbkällor

Externa länkar

 Sportslogos.net


For anyone who didn't get to see the "Street Outlaws" episode shot here in Kansas City, you missed Justin Price beating Boosted GT. The win gave Price and the twin turbo fox body Mustang the title of fastest small tire car in the nation. "We've been trying to get that race off for so long," Price said, "and we finally got it done." Price added that it felt "Amazing!" While Boosted GT was understandably unhappy with the outcome, Price said he was a cool guy, as are all the guys from the 405. "Everything portrayed on T.V. is what it is. Overall everybody is real cool." Price works in the pharmaceutical automation industry as tech support, but has always been a car guy. "I've been racing for about 15 years now," he said. A long time GM guy, price has built Firebird and an RX7 with an LS motor. "I've had a little bit of everything." He purchased the TT Fox three years and ran low 8s in the quarter at the track with the first set up. "Over the years we've upgraded stuff to make it a little bit better for the street. The Fox currently runs a 408 ci LS motor with twin turbos. "It's pretty basic with off the shelf parts," he said. "You could buy most of the motor out of a Summit catalog." However the fuel system is a bit more complicated. "The car runs two fuel systems. It drives on pump gas and when I get into boost, it switches on the fly to race gas." The Holley EFI controls the switch. When it senses wide open throttle, it automatically switches to the race gas set up. "It's got two fuel pumps, two fuel tanks, two sets of fuel lines, 16 injectors, everything," Price said. This winter, Price will upgrade the car again. The race gas fuel system in the car will be changed to methanol and lose the air-to-water intercooler. He'll change to a six bolt motor that will give it the strength to handle more boost without lifting the heads off the block. He's also going to replace the powerglide transmission for a turbo 400. "You have to keep changing or you'll end up losing," he said. Price uses Maschmeier Performance, a known, local company that builds a lot of high horsepower engines for the Kansas City racing community and Hooken Chassis Racecars in Holt, MO, for his chassis needs. Just to be clear for those readers and racers that don't know, episodes of "Street Outlaws" are filmed with firefighters, ambulances and EMTs on site and ready. All forms of auto racing are dangerous, but street racing is especially dangerous due to the fact that it's often impromptu and done on unprepared, public streets. Not only is it extremely dangerous, but it's also illegal. Kansas City Car Action does not condone street racing in any way. It simply reports on the happenings of the car scene in the area.
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Join us for your choice of a 5K route through Historic Downtown Uxbridge or a quick 1K walk through Elgin Park.
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Wanna stay at G-Dragon's home?
This article is more than 12 months old
PHOTO: ONE PRODUCTION
Aug 20, 2015 08:07 pm
He's a skilled rapper, a fashion icon, part of one of South Korea's biggest boy bands and now, he's Airbnb's newest celebrity host.
K-pop superstar G-Dragon has converted his Dukyang studio crib into an Airbnb staycation spot and he's inviting five lucky fans over for a sleepover.
Making a trip to the 27-year-old's nest in Seoul could almost be considered a pilgrimage for fans. It was in this very studio where he spent the initial years of his career and began his ascent to stardom.
Aside from opening up his iconic studio for two nights, G-Dragon will take his guests on a tour of South Korea's capital, during which he'll show them his favourite spots in the city.
Following that, the Crooked singer will join guests for dinner at the renowned YG Cafeteria.
As a parting, and lasting, gift to his guests, G-Dragon will leave reviews on their Airbnb accounts.
Fans share different views about webtoon featuring BTS
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"I'm thrilled to become a host on Airbnb and I'm excited about welcoming my fans into my second home," said Big Bang's leader.
"I look forward to providing them with a unique local experience by sharing a glimpse into the early years of my career and bringing them around the neighborhood I grew up in."
Mr Patrick Lee, Airbnb's country manager for Korea, said: "We are excited that an icon of popculture like G-Dragon shares our vision of making the world a smaller place. Turning this superstar into a superhost will be a benchmark for Airbnb."
For a chance to score the dream K-pop staycation, fans will have to visit G-Dragon's Airbnb listing and submit a write-up of no more than 300 words or characters (for entries in Japanese, Korean and Mandarin) describing how they would connect with a person from a different cultural background.
The deadline for submissions is before midnight on Aug 29 (Korea time) which is 11pm Singapore time.
One winner each from China, Hong Kong, Japan, Korea and South-east Asia will be notified after the conclusion of the contest.
k-popairbnbSouth KoreaUncategorised


Nishiki Girls' Manitoba 24'' Hybrid Bike is rated 4.6 out of 5 by 5.
The Nishiki® Girls' Manitoba 24'' Hybrid Bike offers the best of both mountain and road bikes all in one. It provides an upright, comfortable and stable riding position with its lightweight alloy frame, youth hybrid frame design, and straight blade fork. She will love its versatility and will feel confident biking thanks to the easy-to-use v-brakes and 7-speed drivetrain.
Rated 4 out of 5 by Anonymous from Lighter than the other bikes I bought the Nishiki Manitoba 24" girls hybrid bike for my daughter. It is not the best bike on the market, but compared to most of the bikes at Dicks, I believe it is above average. My other options were the Nishika Moab (which I also own) and Diamondback Tess mountain bikes. The Manitoba is much lighter than the Moab or Tess, 25 pounds versus 33 pounds. The Manitoba has a 6061 aluminum frame, the others are steel. It has quick release skewers front and rear. THIS IS IMPORTANT! No wrench needed to remove the tires in case of flat or in order to fit the bike into a car. The tires on the Manitoba are 24" x 1.375" wide, which is fine for roads and smooth dirt or gravel trails. Not wide enough for thick mud or rocky terrain, but my daughter is not a serious biker. This bike does not have a suspension front or rear, not a big deal for me either. The brakes and shifters are on par with the other bikes. Shimano Revo shifter and Shimano Tourney derailer. It has 14 speeds. No kickstand. I assembled it myself. I do not recommend this unless you have worked on bikes before. I had to adjust the brakes, install the handle bars and stem, adjust the derailer (it would not shift into cogs 1 or 7), and grease the chain and other components. Vague assembly instructions are online but are not specific to this bike. Have Dicks do the assembly, but double check the function of the brakes and shifters at the store. Overall, the lower weight and quick release tires were reasons enough for me to spend more for this bike. Great for dirt trail riding and cruising around the neighborhood.
Rated 5 out of 5 by WJZR from Right size I just bought this bike. I'm a 5'2" woman with short legs. I like the size, feel, and light weight of this bike. A comfortable and sturdy ride.
Rated 4 out of 5 by RonKM from Great 23 pound bike for short people I bought this for my 10 year old granddaughter and she loves it.
Rated 5 out of 5 by Super J from Great Bike Works great for girls or boys. Easy to use and fun to ride.


Inside São Paulo: Pacaembu Stadium - Sao Paulo: friendly soccer game of Brazil vs Romania and the last participation of Ronaldo. Today!
Pacaembu Stadium - Sao Paulo: friendly soccer game of Brazil vs Romania and the last participation of Ronaldo. Today!
Tonight, at 9h50 pm (GMT -3) the Pacaembu Stadium receives a friendly soccer match: Brazil vs Romania. That will be the last time Ronaldo will be wearing the Brazilian soccer tshirt. After the match, the squad will be unveiled for the Copa America.
Brazil: Vítor, Maicon, Lúcio, David Luiz e André Santos; Sandro, Henrique (Elano) e Elias; Robinho, Fred e Neymar.
Romania: Tatarusanu; Mujdza, Spahic, Papp e Bourceanu; Torje, Sanmartean, Surdu e Zicu; Marica e Tanase.