# Multi Photon Ionization in Gravity Induced Resonant Emission

Antony Soosaleon  School of Pure & Applied Physics, Mahatma Gandhi University,
Kottayam, Kerala, India-686560

###### keywords:

Multi Photon absorption, Landau Damping, Gravity Induced Resonant Emission,
Lower Hybrid Oscillations, Field Deficit, Electromagnetic Waves, Laser
Ionization

##  1 Introduction

S-Introduction

Damping of electromagnetic waves (_emws_) by cyclotron resonance of particles
in the Lower Hybrid Oscillations (_lhos_) has been proposed as the mechanism
of _gire_. _lhos_ is a coupled oscillations, between ions and electrons in the
cyclotron motion bound by Couloumb force. Gravitational drift of ions induces
an electric field, causes this oscillations in a collisionless plasma where
the magnetic field is controlling the motion of particles. Particles are
mutual accelerated by this oscillations, where the necessary energy is
absorbed from _emws_ by creating a field deficit between the particles. We
have briefly discussed about the role of Landau damping over _gire_ in the
previous papers (Antony & Sunitha, 2017a, b); here we are going to analyze it
on the basis of _mpi_ and through out this study, we are using the same growth
rate and resonant frequency expression from the above 2 papers. This analysis
is done in the following way:

  1. 1.

Initially we are briefing about the required conditions for _mpi_ in Laser

  2. 2.

Describing how these conditions are satisfied in _gire_

  3. 3.

Discussing the effect of various parameters over _mpi_ in _gire_

##  2 Multi Photon Ionization

###  2.1 Photo Ionization

Ionization of atoms is possible with photons of energy greater than required,
but Goeppert-Meyer (1932) theoretically predicted that it is possible with
photons of lesser energy. In 1961, Kaiser experimentally studied double photon
ionization, followed by Abella (1962) and Hall et. al. (1965). High power
laser radiation was necessary for such ionization process and this led to the
development of ultra fast Lasers. Multiple ionization was, first observed by
Voronov & Delone (1965) and Agostini et. al (1987) at low pressure of the
order $10^{16}m^{-3}$. Absorbing a large number of photons more than the
required threshold value, results in multiple ionization. Such absorbtion is
not possible for a free ion, since it violates momentum conservation. But this
is can be made possible when the ion is at bound with some potential of other
ions/electrons. In such condition, the momentum change due to the absorption
of photons will be compensated with reverse momentum of bound particles. This
condition is created in Femto/atto second lasers, the power of a laser is made
intense more than the inter atomic field $10^{19}Wm^{-2}$, so that it can
easily ionizes atoms at initial stage, in such a way that the emitted
electrons stand in potential of the parant ion to give a recoiling momentum
for further absorption of photons. Here the condition is that the power of
laser must be sufficiently high, so that absorption of photons is possible
before emitted electrons leave the potential of parant ion. This means
absorption time is reduced while increasing the power of laser, which is named
as temporal compression of photons.

###  2.2 Temporal Compression

There are more that the temporal Compression is a necessity for higher
ionization; since ionized states are highly uncertain and the time periods are
in the range 100-150 attoseconds. Ionizing atoms in such a short interval of
time is not possible in ordinary situation, unless we reduce the absorption
time of photon. Classically this cannot be less than the interaction time
between electron and photon, whch are in femto seconds. These reasons makes
clear that to achieve emphmpi, the absorption time must be reduced and this is
done by chirpped pulse amplification in laser (Donna & Gerrard, 1985). Here
spatial distribution of photons are reduced to produce high intensity pulse
which gives the effect of temporal compression during absorption. This is
achieved by grating element, which gives a definite phase shift to various
photons and make them to converge at a single point to produce a very high
intensity pulse. With a high intensity pulse greater than the interatomic
field, a large number of photons can be absorbed by ions at the time of single
photon absorption. This is a nonlinear process both temporally and spatially,
but made possible in a high field condition. Multiple ionization was first
observed by (L’Huillier, 1982) and such ionization results to the emission of
UV and X-rays, the intensity of pulsed laser used for multiple ionization was
about $10^{22}Wm^{-2}$, which is much larger than the inter-atomic field
$10^{19}Wm^{-2}$. With these brief description, we shall list the required
conditions for emphmpi.

Four Conditions For Multi Photon Ionization

  1. 1.

A high vacuum of the order $10^{16}m^{-3}$ is required to make collisionless

  2. 2.

Particles must be in bound state with some potential to conserve the momentum

  3. 3.

Intensity of Laser field must be more than the interatomic field
($10^{19}Wm^{-2}$)

  4. 4.

Temporal compression of photons is required to reduce absorption time

All these 4 conditions are satisfied at resonance in _gire_ , we shall analyze
in the following section.

Figure 1.: Field Deficit Conditions for Elelctron Ion Landau Damping: Fig. (a)
& (b) shows the sketch of field deficit condition for Ion & Electron Landau
damping. (a) shows the positions of coupled particles where incoming photons
are absorbed by ion; here the field deficit is caused by motion of electrons,
so that the rate of ion damping is at electron cyclotron frequency. (b) shows
the positions particles where electron absorbs photon and here the field
deficit is caused by motion of ions, so that the electron damping is at the
rate of ion cylcotron frequency. Due to this, electron damping is a low energy
(frequncy) prephase one but ion damping is a high energy and post phase one
occurs at resonant condition (intense field)

.

##  3 Conditions of _mpi_ in gire

The first 2 conditions need not much explanations, they are explicit in the
theory of _gire_ , therefore we only marginally mentions these two.

Condition 1: Corona is more vacuum & Collisionless : These are pre-assumed
conditions in developing the theory of _gire_ , where the plasma was considerd
as collisionless. The density used in the _gire_ plot was $10^{15}m^{-3}$,
which is more than the vacuum we have created in the Laboratory for Laser
ionization.

Condition 2: Ions & Electrons are bound by Couloumb Force in _lhos_ :
Particles must be bound state with some potential to conserve the momentum
during photon absorption. In laser ionization, this condition is created with
photo electrons emited from initial ionization. But in _gire_ , this condition
is already exisiting in _lhos_ , here the particles are bound by Couloumb
force and there is more flexibility in reserving momentum since they are
further controlled by magentic force.

Condition 3: High Intensity Field; Particles are at intense electric field in
resonance condition and this happens when Larmour radii of electrons and ions
are same.

Condition 4: Temporal Compression of Photons; this is created by field deficit
due to the loss of electrons at resonance condition

For understanding the last 2 conditions, we need a thorough discussion about
the role of electron and ion Landau damping in _gire_ , after that we will be
analysing these two in the sections 3.4 & 3.5

###  3.1 Role of Electron & ion Landau Damping in _gire_

Landau damping is a categorical phrase used in plasma physics for photon
absorption process, named after Landau, who theoretically predicted this. We
have analyzed this mechanism of energy transfer on the basis of field deficit
in the _lhos_(Antony & Sunitha, 2017b) by Couloumb force. The photon
absorption is a necessity of the particles which are in field deficit
condition; this happens when they mutually cross over in the _lhos_. There are
4 possible positions in the cyclotron orbits, where field deficit situation
can arise, but we can eliminate 2 positions in considering the direction of
photons. In the rest 2, one is prephase, relative to the maximum amplitude
(Electric field of incoming wave ) where the electron damping occurs (see the
fig.2(b)), and the other is postphase, where the ion damping happens
(fig.2(a)). Distinguishing these 2 are necessary to understand the coronal
heating problem and both are equally important. We will be differentiating
them on the basis of their fundemental properties and also compare our
analysis with _gire_.

Figure 2.: Damping of _emws_ in two componant plasma of Fe+ for coronal
condition: This is logarithemic plot of $\omega_{i}$ (Damping/growth of
_emws_) with wave vector (frequency). Already this graph has been analysed in
the paper (Antony & Sunitha, 2017a) but here we doing it again on the basis of
photon absorption. The first part shows growth of _emws_ (+ve slope), this is
due to damping of accoustic waves and the next part shows _emws_ are losing
energy (-ve slope). This is a low frequency region and prephase damping due to
the absorption of photon by electrons. This is a single photon absorption
region since the frequency increases with damping. Next is the last part of
damping before emission, this is due to high field resonance happens when
Larmour radii are same. Here the wave vector is not changing with damping,
i.e., a large number photons of same frequency is absorbed, a huge amount of
energy and last part of damping before the emission must be ion Landau
damping, which is similar to Multi photon Ionization in Laser

.

Table 1.: Comparison of Electron & Ion Landau DampingT-simple Electron Landau damping | Ion Landau Damping
---|---
It is a prephase damping | Postphase damping
It is possble with low energy waves | Only by high energy waves
Damping occurs at a rate of $\Omega_{i}$ | At a rate of $\Omega_{e}$
Acceleration is limited upto 500 KeV | unlimitted
Electrons are lost out during damping | Ionized to high charge state
Electron density decreases | No change in density
Happens at weak field condition | Only at resonance condition
Single photon absorption | Multi photon absorption

###  3.2 Electron Landau Damping

This is a prephase damping and the positions of ions and electrons are
depicted in fig.2(b). Here the motion of ions creates the field deficit to
electrons and therefore electron damping is at the rate of ion cyclotron
frequency ($\Omega_{i}$). In the same way, ion damping is a post phase one and
the positions are shown in the fig.2(a). Here the motion of electron creates
field deficit to ions at the rate of its cyclotron frequency ($\Omega_{e}$).
Due to these reasons, ion damping is a high frequency damping but electron is
a low energy one. When the ions and electrons are coupled in _lhos_ , at the
initial stage of coupling, the Larmour radius of electron ($r_{e}$) is smaller
than ion ($r_{i}$); now the particles are at far field positions and the
electrons spiral inside $r_{i}$. In each rotation of ions, it gains energy by
electron damping and $r_{e}$ increases. Here one point is to be noted; the
energy absorbed must be equal to field deficit; when $r_{e}<<r_{i}$, the
particles are at far field positions, so field deficit is small and the rate
of absorption also small. Thus the electron damping is a gradual and low
energy one and this continues till $r_{e}\approx r_{i}$, here the ion Landau
damping starts. These points can be confirmed from the graph of _gire_ shown
in the fig.3 (Antony & Sunitha, 2017a). The first part of plot shows a
positive slope, this is due to the damping of accoustic waves, here _emws_
gain energy. The second part, the slope is negative, now the damping of _emws_
starts. In this region, the damping is gradually increasing with frequency,
starting from a low energy waves. This is exactly reflecting the properties of
electron damping at the initial stage of coupling in the _lhos_ , just as the
particles are at far field positions, the field deficit and energy absorptions
are small. Therefore we can confirm the initial damping is due to the photon
absorption by electrons, since the frequency is unique at every point in the
graph and increases with energy, therefore this is a single photon absorption
process.

Figure 3.: Figure shows the multi photon absorption at resonance condition due
to the Deficit of Electrons. Since $\Omega_{e}>>\Omega_{i}$, electrons meet
ion at every point of its orbit and this gives continuous field deficit. The
resonance condition, $r_{i}=r_{e}$ is satisfied at every point in the
postphase region where ion Landau damping is possible. The resonant wavelength
of photon is proportional to the Larmour radius, since the electrons are
creating the field deficit continuousely in the same orbital length, the ions
absorb several photons of same energy.

###  3.3 Ion Landau Damping

Ions are inertial, a high field is required to accelerate them and this
happens at resonance condition, when $r_{e}=r_{i}$, the particles are much
closer and experiences intense electric field. At this condition, a small
variation in the field causes heavy acceleration to both the particles. The
electrons are already in an accelerated mode by prephase damping and creates a
field deficit at the rate of $\Omega_{e}$. An important point is that these
elelctrons are highly relativistic and at the edge of $r_{i}$, they are easily
lost out from the potential of ions. This makes the field deficit more intense
which gives multiple acceleration to ions in the direction of photons. Thus
the rate of damping extremely high at resonance condition, which can be seen
from the graph (see fig.3). One of the most important point is this; since
$\Omega_{e}>>\Omega_{i}$, electrons meet the ions at every point of its orbit
and gives continuous field deficit in the same orbital length. This situation
is depicted in fig.4, here the resonance condition, $r_{i}=r_{e}$ is satisfied
at every point of the same orbit, therefore the ions continuousely absorb
photons of same amplitude (energy). We find the deficit is starting from the
extreme end of the ion orbit where highly relativistic electrons are scattered
out and then it comes to lower energy electrons too. So this gives a
continuity in the resonance and most of the electrons are lost due to this
high field situation creates the field deficit quite critical to ions which
under go multiple acceleration at the same orbital length (same wavelength) by
absorbing sufficient number of photons. This is can be confirmed from the
graph of _gire_ (see fig.3), in the last pasrt of damping where frequency is
not changing with damping and this is similar to multi photon absorption. Here
the loss of electrons at resonance is compensated by photo-electrons emitted
during _mpi_.
one of the important outcome of prephase Landau damping is, loss in the
electron density. Since they are lighter particles easily get accelerated and
escape from the ion potential. Due to this reason, the electrons cannot be
accelerated to higher energies and maximum possible acceleration must be less
than the free electron energy (511 keV). This is also only at bound state,
i.e., in _lhos_ when $r_{e}\leq r_{i}$. This is one of the most crucial
information regarding acceleration of ions in solar corona. The deficit of
electrons is a continuous phenomenon in _lhos_ and it is further amplified by
coronal loop oscillations (Antony & Sunitha, 2017b).

For giving a clarity, we list the differences between electron and ion Landau
Damping in table form (Table 1)

Figure 4.: Effect of $\mathbf{B}$ over _mpi_ : Logarithemic plot of
damping/emission _emws_ with wave vector at resonance condition. It shows
_mpi_ increasee with $\mathbf{B}$ both in magnitude (number of photons) and
frequency

.

###  3.4 High Field at Resonance

We understands from the above discussion, $3^{rd}$ and $4^{th}$ conditions for
_mpi_ are satisfied in _gire_ at resonance condition. But for a comparative
analysis we shall do an average calculation on the rate of energy absorption
in _gire_. Let ${\nu}_{r}$ be the resonant frequency, then the energy absorbed
by an ion in this frquency is $h{\nu}_{r}$. This energy is absorbed at time of
$t=\frac{1}{{\nu}_{r}}$ and since the frequency is not changing during
resonance condition, then energy absorbed per second is given
$Es^{-1}=h{{\nu}_{r}}^{2}$, Inserting the value of resonant frequencyAntony &
Sunitha (2017b),

$Es^{-1}=(\frac{hc^{2}e^{2}}{4{\pi}^{2}mM})(\frac{Z}{\gamma
W})(\frac{n_{i}}{n_{e}}\frac{B^{2}}{gSin\theta})$

Where h, Planck’s constant; e, value of electric charge; c, velocity of light;
m & M are masses of electron and proton; Z, degree of ionization, W, mass
number, $\gamma$, Lorentz factor, $n_{i}$ is the number density ions drifted
per meter; $n_{e}$ is the number density of electrons; $\mathbf{B}$, magnetic
field; $\mathbf{g}$, acceleration due to gravity. There are several varibles
in this formula, since we are comparing it with the maximum power of Laser, we
shall choose conditions of corona, where the hard X-rays are observed.
Keeping, a high $\mathbf{B}$, for lower corona where the coupling starts (we
take $\mathbf{B}=0.1$T, but $\mathbf{B}$ can go upto 0.25T); and field deficit
$\frac{n_{i}}{n_{e}}=10^{7}$ is chosen by assuming all the coupled electrons
are lost out at resonance condition, also considering the elemental abundance.
We keep the angle $30^{o}$ between the $\mathbf{B}$ and g for lower corona.
Using these values subtituting all constants we can calculate the power as
$Es^{-1}=1.16359\times 10^{23}(\frac{Z}{\gamma W})$ eV$s^{-1}$. This value is
very high and sufficient for ionizing any atom, but the rate of absorption
must be analyzed in the atomic time scale. Ionization is a quantum mechanical
process and the energy absorbed is unique for every element, this must be
analyzed on the basis of their ionization time.

Figure 5.: Effect of Electron deficit in _mpi_ : Figure shows the effect of
field deficit in resonant condition. The rate of absorption increases in
frequency with field deficit

.

###  3.5 Temporal Compression by Electron deficit

The fourth condition is satisfied by the deficit of accelerated electrons at
resonant conditions. In laser ionization, time compression is obtained by
compressing photons into high intensity pulse in short duration. This is done
by grating device, which gives definite phase shift to various beams of same
frequency and made to converge at single point. The same effect is produced by
a bunch of highly relativistic electrons in the lower hybrid coupling. Since
$\Omega_{e}>>\Omega_{i}$, electrons meets ion at every point of its orbit
gives a continuos acceleartion to ions which are in phase with photons of same
frequency. Fig.4 shows the situation, since electrons are lighter particles,
easily lost out and this loss creates the field deficit more critical to ions,
starting from the edge of ion orbit, the electrons continuousely creating this
situation at every point in the same orbit of ions. The resonant wavelength of
photon is proportional to Larmour radius, since the electrons creating field
deficit continuousely in the same orbital length of ions, they absorbs the
same energy photons. The degeneracy of electrons also may be helpfull in this
regard for getting a continuous acceleration at resonance condition. Each
electron is unique with its energy and orbits in _lhos_ and the difference
gives a continuity in field deficit at resonance.

Figure 6.: Effect of ionization (Z) over Ion damping: Figure shows the
variation in Damping rate over degree of ionization. We find multi photon
absorption increases with degree of ionization

.

##  4 Effect of various parameters over _mpi_ in _gire_

At resonance, the ions are undergoing _mpi_ and possibly emits all types of
radiations. Unlike in laser, _gire_ has a number parameters are playing very
important role in the resonance condition and we briefly discuss in this
section.

###  4.1 Effect of B, $\frac{n_{i}}{n_{e}}$ & g on Resonance

g: Among these 4 variables, g is a static variable depends on the direction of
$\mathbf{B}$; the effective value depend on where the coupling occurs.
Generally this happens at lower corona or coronal loop where $\theta$ is small
$<30^{\circ}$. For upper corona $\theta\approx 90^{\circ}$ ion damping will be
less comparatively at lower part of the loop. The value of g appears in the
denominator, this reduces the rate of damping and this may be the reason that
why most of hard X-rays are observed in the lower corona where the effective
value is less.

B: This is one of the most sensitive variable which affects the resonance
conditions more than any other. If we look into the formula, $\mathbf{B}$
appears in square times magnitude compared with other variables, is
controlling the resonance condition. This is quite meaningful to coronal
conditions, since all the dynamical structures of corona is controlled by
$\mathbf{B}$. The structural variations in the $\mathbf{B}$ has immense effect
on heating corona, which has been observed for the last 75 years. At low
$\beta$, particles are in cyclotron motion and the rate of resonant damping
depend on rotation frequencies. Since they are rotating in opposite direction,
even small variation in $\mathbf{B}$, increases the frequencies for both the
particles in a logarithemic scale which results in the high damping. This
makes the heating more easier in high $\mathbf{B}$ regions and this result is
established in the fig.5., whichfigure shows, both magnitude and frequency
increases with $\mathbf{B}$, here the plot is done with the expression of
growth/damping for _emws_ (Antony & Sunitha, 2017a)

Figure 7.: Effect of mass number over _mpi_ : Resonance plot reflects the
effect of mass number; shows the damping decreases with mass. For heavier
elements, the resonance frequency and damping both are decreasing

.

$\frac{\mathbf{n_{i}}}{\mathbf{n_{e}}}$: We have eloborately discussed the
role of field deficit which makes the multi photon absorption possible. The
density of electron is inversely related to $\mathbf{B}$. In high B, the
$r_{e}$ is small, therefore the loss of electrons are less which makes the
electrons acceleration is possible to maximum energy. This suggests that at
high B, the electron scattering at resonance will be quite high in strong B
region, this supports the observations in coronal emissions of hard X-rays.
For upper corona, the magnetic field is less where the electrons loss is
maximum which gives the deficit is high. Here electrons are lost due to
prephase damping and continues till the resonance condition where it reaches
maximum and this result has been estabilished in the fig.6. We find the
damping date increases in both frequency and magnitude. So combining these two
results we can conclude this, when the B is high the
$\frac{\mathbf{n_{i}}}{\mathbf{n_{e}}}$ is less, and damping rate controlled
by B or if B is low, $\frac{\mathbf{n_{i}}}{\mathbf{n_{e}}}$ is high and the
damping is high. Thus both are reciprocally controlling the damping rate.

Figure 8.:  Effect of Temperature over resonant damping: Figure shows the rate
of damping at resonance condition for difference in Temperatures of ion
($T_{i}$) and electron($T_{e}$). Resonance is maximum when the particles are
closer and this happens when the Larmour radii are same. For this, the
temperatures must differ by an order of their mass ratios, i.e., $\approx
10^{3}$ which is established in this graph.

.

###  4.2 Effect of Z & W

The charge state of ion is continuousely changing during _mpi_ and rate of
damping increases with Z due to higher couloumb force . This result is
established in the fig.7. We find resonant damping enormously increases with Z
and this is helpful for getting continuity in ionization process. Regarding
mass number, we find damping is reduced for heavier elements but one of the
important benefit is the frequency shift. For higher elements, the resonance
condition shifts to low energy region where the maximum intensity is possible
due high solar luminosity. For lighter elements damping is quite high and due
to this reason, these elements will be easily disintegrate. This is reflected
in the fig.8., which shows the ion damping for Fe+ low compared with Na+.

###  4.3 Effect of Temperature

One of the most important parameter that we are interested is temperature but
it is invisible and reflected in the relativistic factor $\gamma$. The
particles resonance is possible only when the larmour radii are same; imposing
this condition we can deduce a relation between electron and ion temperatures
(Antony & Sunitha, 2017b);

$T_{i}=\frac{Z^{2}}{W}\frac{\gamma m}{M}T_{e}$

where $T_{i}$ and $T_{e}$ temperatures, rest al the parameters were mentionede
earlier. $\frac{T_{e}}{T_{i}}\approx\frac{M}{m}$, i.e., $T_{e}$ must be
greater atleast by factor of $10^{3}$ to get maximum resonance and this is
established in the fig.9.

##  5 Conclusion

A comparative study of _mpi_ in Laser and _gire_ is done. Both are same except
prephase electron damping before the resonance condition. In _gire_ , the
whole process is archestrated by a bunch of electrons accelerated by Landau
damping. The temporal compression of photons is obtained by grating element
but in _gire_ it is created by field deficit due to the loss of electrons at
resonant condition. This loss is compensated by the photo electrons emmitted
by _mpi_. In Laser ionization, absorption/emission specrtum is very narrow,
but in _gire_ , it is wide and continuous range of all frequencies. The laser
ionization is solely depend on the intensity (number of photons) but _gire_
has seven variables with more tunability and here the process is controlled by
$\mathbf{B}$ with electrons, hence the high spectral resolution will be high.

Acknowledgment This work is done under UGC Research Award Scheme (2016-2018)
and acknowledges the help of Sunitha Ambrose in programming part.

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# Simulating Vehicle Movement and Multi-Hop Connectivity from Basic Safety
Messages

Noah Carter, Mohammad A. Hoque, Md Salman Ahmed
Department of Computing
East Tennessee State University
{carterns, hoquem<EMAIL_ADDRESS>Noah Carter1, Mohammad A. Hoque1, Md
Salman Ahmed2
1Department of Computing, East Tennessee State University
2Department of Computer Science, Virginia Polytechnic Institute and State
University
1{carterns<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
###### Abstract

The Basic Safety Message (BSM) is a standardized communication packet that is
sent every tenth of a second between connected vehicles using Dedicated Short
Range Communication (DSRC). BSMs contain data about the sending vehicle’s
state, such as speed, location, and the status of the turn signal [1].
Presently, many BSM datasets from various United States locations are
available through the connected vehicle testbeds of U.S. Department of
Transportation. However, without a proper visualization tool, it is not
possible to analyze or obtain a visual overview of the spatio-temporal
distribution of the data. For this purpose, a web application has been
developed which can ingest a raw BSM dataset and display a time-based
simulation of vehicle movement. The simulation also displays multi-hop
vehicular network connectivity for DSRC. This paper gives details about the
application, including an explanation of the multi-hop partitioning algorithm
used to classify the vehicles into separate network partitions. A performance
analysis for the simulation is included, in which it is suggested that
calculating a connectivity matrix with the multi-hop partitioning algorithm is
computationally expensive for a large number of vehicles.

##  I Introduction

Dedicated Short Range Communication (DSRC) offers the potential for a variety
of safety-critical applications that leverage vehicle-to-vehicle (V2V) and
vehicle-to-infrastructure (V2I) communication modes. These applications follow
standard communication protocols defined by SAE J2735 and IEEE 1609.x. One of
the primary requirements for one class of safety applications is the broadcast
of Basic Safety Messages (BSM) every tenth of a second through which the
vehicles share their locations, speed, direction, and mobility information.
When other vehicles and drivers have more information about the world around
them, they can make better and safer decisions. This is the benefit of sending
and receiving BSMs. Such communication is one example of Vehicle-to-Vehicle
(V2V) communication, which has major implications for road safety and
efficiency and is being widely studied.

DSRC is a short-range communication medium over which BSMs can be sent.
However, because the range of DSRC is in many cases less than 1000 meters, it
is necessary and useful to employ ‘multi-hop’ communication. In multi-hop
communication, messages traverse a network of vehicles (that act as message
relays) in order to reach their destinations. Thus, rather than going directly
from the source vehicle to the targets, the messages ‘hop’ along an ad hoc
network of closer vehicles to eventually reach as many targets as possible.

##  II Related Works

###  II-A BSM Data Analysis

Some BSM datasets are publicly available and are interesting subjects for data
analysis. This includes, for example, the Safety Pilot Model Deployment
project, in which tens of Michigan volunteers’ vehicles were mounted with BSM-
broadcasting devices. One aspect of such data analysis is visualization and
simulation. Allowing an analyst to see the data in a helpful and intuitive
format enables the analyst to make more informed and strategic decisions [1,
2]. Our previous research has utilized BSM data for analyzing mobility
patterns and developing various safety-critical applications in connected
vehicle environments [3, 4, 5, 6, 7, 8, 9, 10, 11, 12].

The application described in this paper is intended to assist an analyst in
visualizing location-related aspects of BSM data, specifically vehicle
locations and vehicle connectivity partitions. To display the latter, it is
necessary to calculate the partitions using a multi-hop partitioning
algorithm.

###  II-B Multi-Hop Partitioning Algorithm

Hoque et al. [11] introduced a multi-hop partitioning algorithm based on a
modification of Warshall’s algorithm. The purpose of the algorithm is to
distinguish each vehicular ad hoc network partition–i.e., each connected
component of vehicles that are within multi-hop communication range of each
other. Again, vehicles can communicate directly, but they may also do so
indirectly via one or more intermediate vehicles through which data and
messages can pass (or ‘hop’). All vehicles that can communicate with each
other by one of these two means are grouped together as a partition in the
output of the algorithm. The result is a collection of partitions. The current
work has further extended the algorithm developed by Hoque et. al. [11] to
provide a graphical interface to visualize the connected components within a
metro area using an empirically obtained BSM dataset.

The algorithm begins (see Figure 1) by reading in vehicle locations and
calculating a square, symmetric ‘distance matrix.’ Each element $a_{i,j}$ of
the distance matrix is the calculated distance between the two vehicles that
are represented by row $i$ and column $j$. Each entry of the distance matrix
is then translated into a boolean value by determining whether it is less than
or greater than the predetermined DSRC range (i.e., the maximum distance a
given DSRC device can broadcast communications). Those distances that are less
than the range become $1$; others become $0$. Using boolean algebra, the
newly-formed boolean matrix is then multiplied by a copy of itself. This
multiplication represents the first ‘hop,’ and the result is a ‘connectivity
matrix.’

The algorithm then proceeds with a series of boolean matrix multiplications,
each of which represents a new hop. Every iteration has the possibility of
stringing together and consolidating more vehicles into a partition. Once a
matrix multiplication results in a connectivity matrix identical to the
operands, then the connectivity matrix is considered finalized. Any two
vehicles $i$ and $j$ which have a $1$ at $a_{i,j}$ are said to be connected
together by multi-hop communication. They share the same connectivity
partition.

Figure 1: Flowchart for a multi-hop partitioning algorithm, simplified from
Hoque et al.’s [11] implementation.

##  III Application

###  III-A Concept and Purpose

The purpose of the application is to ingest BSM data and use it to display a
simulation of vehicle activity and connectivity with respect to time. The
simulator takes as input Basic Safety Messages from multiple vehicles.
Ideally, these are BSMs from vehicles that were concurrently producing BSM
output and that therefore have similar timestamps. Once these BSMs are
uploaded as a CSV, for any given timestamp the simulator can display the
position of each vehicle as a pin on a map. The user can progress from one
timestamp to the next, watching the pins move along the roads on the map (see
Figure 5).

In addition to its position, each pin has a color and a character(s). Pins
with matching color-character combinations are in the same connectivity
partition–they are able to send data to each other via multi-hop communication
(see Figure 2). For example, if two pins are within the DSRC range of each
other, they can communicate with a single hop (and will therefore share the
same color and character for each timeframe in which they are within range).
If two pins are not within the DSRC range, then they cannot communicate unless
there exists a middle pin that they can both reach via DSRC. If there is at
least one mutually-reachable middle pin between the two pins, the external
pins can use the middle pin to help broadcast their message, creating an ad-
hoc network and successfully utilizing multi-hop communication.

Figure 2: Vehicle locations represented using markers of different colors

In Figure 2, vehicle locations are represented with pins. The three vehicles
at the bottom left share the same connectivity partition; they have the same
color and character because they can reach each other via multi-hop
communication. With the passing of each timeframe, the colors and characters
on the pins will change. This is because vehicles move in and out of range,
alternately leaving and mingling among connectivity partitions. The range of
DSRC devices–which determines the maximum distance of a single hop–can be
adjusted by the user; the default DSRC range, which is based on prior
research, is 1000 meters.

The simulation was created with C# and ASP.NET; Javascript calls were made to
the Google Maps API.

###  III-B Usage

An example of the expected input format is a large CSV with the structure of
Figure 3. Each row should be an abbreviated form of a BSM; all BSM fields are
removed except the five listed. After uploading, the user must only click ”Run
Simulation” or step through the timestamps one-by-one.

Figure 3: Expected CSV input format for the simulation

##  IV Performance Analysis

A performance analysis of the simulation was conducted. This was done in order
to study the efficiency of both the simulation as a whole and the underlying
multi-hop partitioning algorithm as the number of vehicles increased within a
confined space. The result was a greater understanding of some of the
application’s performance limitations. The multihop partitioning algorithm was
identified as taking the bulk of the computation time. Future performance
analysis should study the effects of keeping vehicle density constant as
vehicle count changes.

Figure 4: Geographical location of the sample dataset used for simulation

###  IV-A Process

The performance testing was done by artificially generating BSM data files and
measuring the simulation’s performance in milliseconds when run on these
files. Each generated file had a different number of vehicles per timestamp
($N$); some had as few as 1 vehicle and others had as many as 200 vehicles per
timestamp. All vehicles’ positions were constrained within a fixed rectangular
area of 348.16 km² in Ann Arbor, Michigan. They would appear at random points
within the green rectangle in Figure 4. Rather than only appearing on road
surfaces, they could appear at random anywhere within this rectangle. Also,
their positions in one timestamp did not influence their positions in the next
timestamp. Whereas vehicles were confined to a given territory in the
generated data, as the number of vehicles increased the density rose quickly.

For test files that contained many vehicles, fewer timestamps were included.
This was done to normalize the test file sizes to less than 5000 KB. It was
observed during the experiment that the application incurred a significant
amount of delay when uploading files larger than about 4500 KB.

The GPS coordinates of the confining rectangle for generated data are as
follows, as seen in Figure 4: (42.356186, -83.522030), (42.356186,
-83.816270), (42.226673, -83.522030), and (42.226673, -83.816270).

Figure 5: Graphical interface of the simulator with sparse distribution of
nodes Figure 6: Graphical interface of the simulator with high density of
nodes

In Figure 5, the graphical interface for the simulator has few vehicles (it
has a sparse distribution). In Figure 6, however, there is a dense
distribution of vehicles and the corresponding partitioning is shown. In
Figure 6, the time to calculate the connectivity matrix has become very
noticeable following the rise in vehicle count. The number of partitions has
increased to its peak and will begin to lower if additional vehicles are
introduced.

###  IV-B Results and Conclusions

The completion time was measured in milliseconds and logged for various parts
of the simulation process. Also logged was the number of individual input
vehicles within the BSM timestamp. After numerous runs with different input
CSVs, the log files were combed for the data and patterns were observed; see
Figures 7, 8, 9, and 10.

The time needed to populate the display with pins was insignificant, even when
the population of vehicles was large (see Figure 7). This was important to
verify because it was necessary to determine whether delays were being caused
by the internal multi-hop process or by the display medium.

Note that the simulation began to take considerable time at a certain point
(see Figure 9). This may present a problem for those that wish to use the
current tool to study very large vehicle populations (in excess of 200
vehicles). In the future, an ‘export simulation’ functionality could be
implemented that could allow the user to run the simulation in the background
and output the results to a file, to be displayed later.

Figure 7: Average time to render graphic display

From Figure 7, it appears that time required for rendering the graphic display
would increase linearly as the number of vehicles increases. The display of
each additional vehicle requires only the fetching of the appropriate pin
image from Google’s server and the display of that pin. Ultimately, time to
display was insignificant (relative to the amount of time needed to perform
the consecutive matrix multiplications to form the multi-hop partitions). Note
however that this depends on the strength of Internet connection.

Figure 8: Average time to calculate distances between vehicles

In Figure 8, the distance calculation has become more expensive as the number
of vehicles has increased. A prerequisite to performing the partition
calculations was the calculation of the distance from every vehicle to every
other vehicle. These calculations needed to take place exactly once before the
partitions of any particular timestamp could be determined. Calculating these
distances involved approximately $n^{2}$ amount of work. (The formula for this
is $n(n-1)/2$, which is close to $n^{2}$.) The results were in accordance with
this expectation. Though the calculation of distances would have eventually
become a problem as the number of vehicles increased, it would still be a tiny
fraction of the amount of work needed to perform the partition calculations
(assuming that the vehicle density was allowed to increase).

Figure 9: Time complexity of partitioning algorithm

A series of consecutive matrix multiplications forms the multi-hop partitions.
In Figure 9, we see that as the number of vehicles increased, the multi-hop
algorithm became the most costly part of the simulation. It was concluded that
this algorithm is overall the most work-intensive part of the simulation by
far. At 200 vehicles (0.5 vehicles per km2 ), each timestamp was taking 6
seconds on average.

Figure 10: Average number of partitions

The simulation was run each time assuming that each vehicle had a DSRC range
of 1000 meters (1 km). As the number of vehicles within the rectangle
increased, so did the number of partitions (Figure 10). The number of
partitions increased as vehicle density increased, up to a saturation point.
However, the rate of increase declined as the density grew. It was observed
that at a density of 0.5 vehicles per km2, the number of partitions began to
decrease. If even greater densities had been tested, the number of partitions
would have fallen to 1. It is expected that at a density of 1 vehicle per km2
(where the square root of the inverse of the density equals the transmission
range) there would have been 1 partition on average. Again, however, the
artificial data allowed vehicles to disperse themselves randomly. In real
data, vehicles would limit themselves to the roads, effectively reducing the
space between vehicles. Thus for real data the density at which there would
have been only a single partition would have been considerably less than that
of this artificial data. This is especially true when the roads are less like
a grid and more like a highway, or when the DSRC transmission range is
increased by flat land and few obstacles.

###  IV-C Limitations

The program written to artificially generate BSM data permitted vehicles to be
randomly generated anywhere in the rectangular area. In reality, vehicles stay
on roads and often share the same road. They do not have the freedom of going
everywhere. Thus, in reality, vehicles will be less sparse and less dispersed
than they are in the artificially-generated data. This means that, if real BSM
data had been used for performance analysis, there likely would have been more
partitions than were observed. The number of partitions could have thereby had
an impact on the time to calculate the partitions. There is therefore a
certain degree of uncertainty regarding the extent to which the simulation
will perform similarly for real data. Since this application is intended to
assist transportation researchers and analysts, who generally focus on real
BSM data, in the future we will run the performance analyses with real data.

##  V Conclusion

An intuitive visual simulator has been developed to assist transportation
researchers and analysts to study BSM data. This paper has documented the
application and shared the details of its performance analysis. The
application successfully generates time-ordered displays that represent
vehicle positions and connectivity statuses. The complexity of the
partitioning algorithm has been determined to become the a bottleneck when the
number of vehicles increases within a confined space. In a future build of the
tests, it will be a goal to compare the effects of vehicle population size
with those of vehicle population density. For example, keeping vehicle density
constant while increasing vehicle population may produce interesting results.
In addition, another advancement would be to perform the performance analyses
with real data instead of generated data.

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