text:
\section{Introduction}
Graphene is an almost flat one-atom-thick layer of carbon atoms that
are densely packed in a honeycomb crystal lattice. Most of previous
studies concerned the electronic properties of graphene, but these
two dimensional graphene membranes have also exceptional mechanical
properties~\cite{geim,Giem2008,novoselov}. What makes graphene so
exceptional is that it stays strong and stiff even up to a single
atomic layer which differs from most materials whose mechanical
properties substantially deteriorate as they are made thinner. These
mechanical properties make graphene suitable for applications in e.
g. pressure sensing. A nano-membrane made of graphene, the ultimate
down-scaling limit of a nanoelectromechanical system, acts as a
sensor that is predicted to detect ultra-small masses and being at
the same time extremely robust against long-term wear.

 Recently, a nonlinear behavior of
stress-strain response of monolayer graphene was studied by Lee {\it
et al}~\cite{Changgu} using atomic force microscopy (AFM). They
measured Young's modulus and found that graphene is a strong
material like diamond.
 Furthermore, linear force-displacement curves
were measured in Refs.~\cite{frank,scott,scott2}. They obtained an
effective spring constant for a micron size monolayer graphene sheet
equal to 0.2~N/m~\cite{scott2} and for a suspended micron size sheet
of multilayer graphene with thicknesses in the range 2-8~nm and
found values in the range 1.0-5.0~N/m~\cite{frank}. Moreover,
monolayer graphene has a negative thermal expansion up to 900~K and
its Young's modulus increases with temperature up to
900~K~\cite{fasolino}. These anomalous properties are a consequence
of the strong anharmonicity in graphene. Most of these properties
can be explained by traditional elasticity theory and statistical
physics~\cite{frank}.

 The aim of the present
paper is to investigate if two van der Waals coupled graphene
layers, also called bilayer graphene, has similar improved
mechanical properties as monolayer graphene.

There are three common theoretical methods to study the indentation
of a graphene sheet, finite element method, continuum mechanics and
molecular mechanics simulations~\cite{sergry,hemmasizadeh,xu}. These
methods lead to different results for the force deflection curve and
for the graphene deformation profiles~\cite{xu}. The discrepancy
originates from the predominant bond stretching mode predicted by
the molecular mechanics model and a bending to stretching transition
process under increasing deflection predicted by continuum
mechanics.
 Nowadays various properties
are measured on micron size circular graphene~\cite{Changgu}, while
computational studies on nanoindentation of graphene typically are
limited to nano size systems. In a typical experimental setup, the
graphene sheet is indented by a tip from an atomic force microscope
(AFM).

An important issue in simulating  nanoindentation of graphene is the
type of interatomic potentials between the carbon atoms in the sheet
and between the carbon atoms and the atoms of the tip. In recent
studies on nanoindentation of graphene several models were used.
\emph{Xu et al}~\cite{xu} used 1392 atoms (a circular graphene sheet
with radius 3.25~nm)
   in their atomic simulation and obtained the elasticity response of such a
   nano circular sheet of graphene under central load.
    The nanoindentation was realized by moving down the center of the sheet by hand.
    On the other hand, Hemmasizadeh \emph{et
al}~\cite{hemmasizadeh} compared the results for the force
deflection curve obtained from a continuum elasticity
model~\cite{tim} and finite element method calculations for two
circular and hexagonal continuum plates of size 11~nm and showed
that in the large deflection regime there are important differences
between these two approaches. This difference roots in the effect of
exerting a concentrated force so that the difference reduced to half
when a spherical indenter with radius 10~\AA~ was used in the finite
element method calculation.

Medyanik \emph{et al}~\cite{sergry} studied the nanoindentation of a
hexagonal graphene sheet and multi-layered graphite sheets by
employing a quasi-static formulation of the method of multi-scale
boundary conditions. They showed that their method of multi-scaling
gives good results in comparison to full domain atomistic
simulations based on molecular mechanics simulations. They used
repulsive interactions to model the spherical indenter. The number
of atoms in the reduced domain was 2646 for single circular
graphene. Depending on the size of the reduced domain, their results
for multilayer graphene showed an increased force deflection
dependence as compared to monolayer graphene.

In this paper we study the mechanical properties of bilayer graphene
for three different sizes and compare the mechanical response of
bilayer graphene to the one of monolayer graphene. The Young's
modulus of bilayer graphene is estimated by using the predictions
from the theory of elasticity for a loaded plate in the large
deflection regime. Furthermore, the temperature dependence of the
nanoindentation of bilayer graphene is investigated.

This paper is organized as follows. In Sec.\,2  we will introduce
the atomistic model, the simulation method and the the results from
elasticity theory. Section\,3 contains the numerical results and in
Sec.\,4 we will present our conclusion.

\section{Theory and model}
We have used classical atomistic molecular dynamics simulation (MD)
to simulate the nanoindentation of a suspended  sheet of bilayer
graphene. The number of carbon atoms, i.e $N_b$, varies from 35,688
to 152,308 which are equivalent to surfaces with radius $R$=12~nm
and $R$=25~nm, respectively. A rigidly clamped boundary condition
was imposed. In our simulations, the indenter consists of $N_t$=371
atoms in a fcc structure (lattice constant
 equal to 3.92~\AA) and it is assumed rigid during our simulation.  The shape of the indenter
was chosen as a square-based pyramid. The area of the bottom surface
(square) of the tip is 2.02~$nm^2$ and the top one has an area of
10.24~$nm^2$. Initially the coordinates of all atoms in each
layer are put in a flat surface of a honey comb lattice with nearest
neighbor distance equal to 0.142 nm while the upper layer is shifted
along armchair direction by 0.142 nm above the bottom layer. The
separation between the two layers is 3.5~\AA. The initial
velocities in each direction, were extracted from a Maxwell-Boltzman
distribution for the given temperature. We simulated the system at
room temperature 300~K and 20~K by employing a Nos'e-Hoover
thermostat.
 The Brenner's bond-order potential~\cite{brenner, neek-amal} was
 used for the carbon-carbon interaction and a Lennard-Jones potential
 (LJ) $U(r)=4\varepsilon\{(\sigma/r)^{12}-(\sigma/r)^{6}\}$ for the indenter-graphene
interaction and the interaction between the two graphene layers. In
the LJ potential, $\sigma$ is the distance at which the potential is
zero and $\epsilon$ is the depth of the potential well.  The van
der-Waals interaction between the two graphene layers was modeled by
a LJ interaction with $\varepsilon_{C}=2.84$~meV and
$\sigma_{C}=$3.4~\AA. For the interaction between the tip and
graphene, we used the LJ parameters for Pt atoms with
$\varepsilon_{Pt}$=68.3~meV and
$\sigma_{Pt}=$2.54~\AA~\cite{erkoc2001}.  For a two-component
system, as studied here, the parameters for the mixed
interaction between the two type of atoms can be estimated by the
simple average $\sigma_{C-Pt}=(\sigma_{C}+\sigma_{Pt})/2$ and
$\varepsilon_{C-Pt}=\sqrt{\varepsilon_{C}\cdot\varepsilon_{Pt}}$
suggested by Steel {\it et al}~\cite{steel}. To save computational
time, we truncated the LJ potential at the cut-off distance of $r_c$
= 3.5 $\sigma$. Note that the LJ potential is a simple choice for
modeling the interaction between two layers~[18]. To obtain more
accurate results one can use other potentials such as a Morse
potential or other force fields~\cite{erkoc2001}. At the
start of our simulation, the position of the lowest atoms of the tip
are located a few angstroms, i.e. $\approx$3.4~\AA~ above the upper
graphene layer. After equilibrating the system during
$50000$ time steps, the indenter is pushed down slowly with
$\delta$=0.2~\AA~ in a time span of $5000\Delta t$ which is
equivalent to a velocity of 8~m/s, where $\Delta t$=0.5 fs is the time
step in our simulation. To avoid unphysical effects  due to
the  time step, the indentation step -$\delta$- was chosen
to be small with respect to the force cut-off length -$r_c$- for the
interatomic potential (e.g. to prevent a sudden change in the force, etc).

The considered size of the system ($\sim nm$) is larger than the
deflection value ($\sim \AA$), and in addition the thickness of the
sheet is smaller than the amount of deflection. Therefore, nonlinear
elasticity theory~\cite{landau} for a circular flake in the large
deflection limit along the $z$ direction is applicable. The energetics of
such a circular flake in the limit of large deflection is considered
including both bending and stretching energies~\cite{landau}. The
condition of minimum energy for the flake yields the F\"{o}ppl
equation. The solution of the equation is obtained by using the
Hencky transformation. The governing equations in planar-polar
coordinates are as follows
\begin{eqnarray}\label{Eq1}
r\frac{d}{dr}[\frac{d}{r dr}(r^2 \sigma_{r})]&=&-\frac{t
E}{2}(\frac{dz}{dr})^2, \nonumber\\\sigma_{r}
\frac{dz}{dr}&=&-\frac{F}{2\pi r},
\end{eqnarray}
 where $r$ is the radial
position, $R$ is the radius of the circular plate as shown in
Fig.~\ref{figmodel}, $z(r)$ is the deflection at radial position
$r$, $t$ is the thickness of the plate, $E$ is Young's modulus,
$\sigma_{r}$ is the radial stress of the flake and $F$ is the
concentrated load on the flake. We are interested in the situation
of a rigidly clamped boundary condition or fixed boundary condition
in the absence of residual stress, i.e., $z=0$ at $r=0$. Expressions
given by Eq.~(\ref{Eq1}) are nonlinear equations, however they can
be solved analytically in the special case of fixed boundary
condition~\cite{cong}. In general, the solution is given
by~\cite{cong}
\begin{equation}\label{Ftheory}
F=\frac{\pi E t}{4R^2}\frac{1}{G(\nu)}z(r)^3~,
\end{equation}
where $G(\nu)$ is a complicated function of the Poisson ratio,
$\nu$. $G(\nu)$ has almost a linear dependence on the Poisson's
ratio of the desired system and varies from $0.9$ for $\nu\simeq0.0$
to $0.65$ for $\nu\simeq0.5$.

 $\zeta$ is taken
 as the deflection of the bilayer graphene  at $r=0$, i.e. $\zeta=z(0)$. It is the difference between the center of mass of the central point of indented bilayer
graphene and the first central non-indented equilibrium position of
the bilayer (at $r=0$)[19] (see Fig. 1). During indentation, because
the using of the LJ potential, the equilibrium distance between the lowest
atoms of the tip and the central point of the bilayer is of the
order of $\sigma_{C-Pt}$. Surprisingly, our computer simulations
confirm this behavior which we will discuss in the next section.
 The force-displacement curves have been measured recently by Lee {\it et al}~\cite{Changgu}
 and they showed that it can be approximated by a simple
polynomial function having a linear and a cubic term,
\begin{equation}\label{Fexp}
F=a \zeta+b \zeta^3.
\end{equation}
When the bending stiffness is negligible and the load is small the
force deflection can be approximated by the linear term while the
second term dominates for large deflection. This behavior was
studied both theoretically and experimentally in
Refs.~\cite{Changgu,tim,poisson}.

\section{Numerical results}

Figure~\ref{figmodel} gives a schematic view of the system showing
the indenter and the clamped circular bilayer graphene and a
snapshot of an atomistic indenter over a circular bilayer graphene
with clamped boundary conditions. The $z$-component of the forces
from  the bilayer graphene atoms on the indenter are calculated by
summing over the total reaction forces:
\begin{equation}\label{Fz}
F={\sum^{N_t}_{i=1}}{\sum^{N_b}_{j=1}}
{F^z}_{ij}=24\varepsilon{\sum^{2}_{k=1}}\{{\sum^{N_t}_{i=1}}{\sum^{N_b}_{j=1}}
(-1)^k{2^{k-1}(\frac{\sigma}{r_{ij}})^{6k}
\frac{z_{ij}}{{r_{ij}}^2}}\}.
\end{equation}
Often in molecular dynamics simulations one approximates the above
sums by including only the nearest neighbors in order to reduce the
number of interactions which is accurate in the case of short range
potentials. Regarding the cut-off distance ($r_c$), only
those bilayer atoms below the tip interact most strongly with the
tip atoms, while outside this region the interaction strength
decreases very fast. Therefore, in  practice the sum over $N_b$ can be
truncated and limited to the atoms below the tip. This is done by
employing a neighbor list in our molecular dynamics simulation. The
upper (bottom) layer atoms of the bilayer, below the tip region,
interact with maximally $N_t\sim$300 (250) tip atoms for small
deflections and $N_t\sim$320 (265) for large deflections. Moreover,
the first term in Eq. (\ref{Fz}), i.e. $k$=1 in the parentheses, is the
derivative of the attractive part of the LJ potential and the second
term ($k$=2) is related to the derivative of the repulsive term.
We will compare our obtained Young's modulus
with those measured in experiments on graphene and
graphite~\cite{Changgu,Blakslee} and compare our simulated force
deflection curves of the clamped circular bilayer graphene with
those obtained for monolayer graphene~\cite{neek}. Circular red data in Fig.~\ref{figfvsz} show the variation of the
applied load at $r=R$ as a function of the deflection in the
$z$-direction. The fluctuation in the data are larger than those in our previous study on monolayer graphene. The reason is that in
bilayer graphene both layers vibrate (due to thermal fluctuations)
almost independently.

 The plotted force was obtained as follows. After each
5000 time steps the tip is pushed down with 0.2~\AA~ in order to
induce the deflection $\zeta$. During this time interval we let the
system equilibrate and in the last 1000 time steps of these
intervals we calculate $F$ and obtain the mean value of $F$. Thus in
a simulation with $10^6$ time steps we have 200 points in Fig.
{\ref{figfvsz}. The tip atoms are closer to the upper graphene layer
and the other layer is, on the scale of the tip interaction
potential, far from the tip. The latter layer is more free to
vibrate and it has a smaller interaction with the tip atoms.
Therefore, the contribution of the bottom layer to the summation of
Eq.~(\ref{Fz}) is less than the contribution of the other layer.
In our simulation we did not observe any defect formation
even for large deflections. Moreover, all the bilayer data of Figs.
{\ref{figfvsz}} and \ref{figflat} show  steps in the
force-deflection curves, that correspond to structural relaxation in
the process of indentation. The reason is that the number of
bilayer atoms which repel the tip are almost constant during the
indentation steps. The reason that the bilayer is a discrete sheet
and when it is indented by 2~\AA~the number of tip neighbors (from
bilayer atoms), which interact with the tip, are changed
non-continuously. Such steps can be smoothed by time averaging. As
we see the curve for R=12 nm is much smoother (than the two others
in Fig. 2), since it was averaged over six simulations with
different initial velocities.

The numerical results in Fig.~\ref{figfvsz} are fitted to the
expression given by Eq.~(\ref{Fexp}) and are shown by the solid
curves on the circular red data. The values for the fitting
parameters $a$ and $b$ are presented in Table 1. The results in
Fig.~\ref{figfvsz} show clearly the size dependence of
  the force-displacement curves and its difference
from similar results for monolayer graphene which are shown by
triangular green data in each panel of Fig.~\ref{figfvsz}. The
behavior of the tip-graphene flake interaction even for a few
angstroms displacement can be understood from our simulation given
here. To obtain quantitative results, we start with
Eqs.~(\ref{Ftheory}) and (\ref{Fexp}) to describe the dependence of
parameter $b$ on the radius for only large deflections. It is easy
to obtain an analytical expression for the $b$
 value for a large circular sample~\cite{cong} which is given by
\begin{equation}
b\cong\frac{\pi E t}{4G(\nu)}\frac{1}{R^2}~. \label{b}
\end{equation}

 Note that the parameter -$a$- in Eq.~(\ref{Fexp}) is
equivalent to an effective spring constant for perpendicular
indentation of the bilayer graphene when one assumes the bilayer
graphene as an elastic membrane. Furthermore, as can be seen from
Fig. 2, for small deflection the forces are almost linear,  we used
a linear fit ($F_l(\zeta)=a'\zeta$) for small deflections
($\zeta\leq1$ nm of the order of $\sqrt{a/b}$) and for large
deflections ($\zeta>1$ nm) we used a cubic fit
($F_c(\zeta)=b'\zeta^3+C$). The obtained  values for the parameter
$a'$ and $b'$ are listed in Table 1. For R=12, 15 and 18 nm the
parameter $C$ is 11.3 , 8.0 and 6.5 nN, respectively, which are of
the order of $a$.

The fitted curves are also shown in Fig.~2 by dash-dotted
curves. Figure~3 shows the obtained $b$ and $b'$ values as a
function of the bilayer graphene circular size. The fitted parameter
$b'$ follows very well a $1/R^2$ function and the agreement is now
better than for the previous b-values.

For monolayer graphene, we fitted the function
$F=a_m\zeta+b_m\zeta^3$ to the results reported in our previous
study~[24]. The corresponding values for $a_m$ and $b_m$ are listed
in Table~1. The fitted curves are shown by solid curves. Analogous
 as for bilayer graphene we also used separate fits for small and large deflection: $F_l(\zeta)=a_m'\zeta$ and
$F_c(\zeta)=b_m'\zeta^3+C'$, respectively, which are presented in
Table 1. The corresponding fitted curves are shown by the dash-dotted
curves in Fig.~2. For R=12, 15 and 18 nm the parameter $C'$ is 8.1
, 3.7 and 3.9. nN, respectively, which are of the order of $a'$.

\begin{table}
\begin{tabular}{|c|c|c|c|c|}
 \hline
  R(nm) & $a$(N/m)&$b(10^{17}$N/m$^3$)&  $a'$(N/m)&$b'(10^{17}$N/m$^3$)\\
     \hline
  12 & 7.10$\pm$0.4& 20.20$\pm0.5$&7.15$\pm$0.9&$23.3\pm$0.6\\
  15 & 3.80$\pm$0.5& 15.60$\pm0.2$&7.17$\pm$1.3&16.77$\pm$0.8\\
  18 & 4.60 $\pm$0.5&10.90$\pm0.3$&3.19$\pm$0.9&11.99$\pm$1.1\\
  25& 5.50 $\pm$0.3&4.20 $\pm0.2$&5.30$\pm0.9$&6.04$\pm0.9$\\
\hline
  R(nm) &$a_m$(N/m) &$b_m(10^{17}N/m^3)$& $a'_m$(N/m)&$b'_m(10^{17}N/m^3)$\\
  \hline
  12 & 5.21$\pm0.08$&10.30$\pm0.07$&3.41$\pm0.1$&13.48$\pm0.1$ \\
  15 & 3.16$\pm0.06$&7.07$\pm0.01$&2.65$\pm0.3$&10.07$\pm0.3$  \\
  18 &3.06$\pm0.04$&4.46$\pm0.02$&1.86$\pm0.1$&5.30$\pm0.2$  \\
  25&2.53$\pm0.07$&2.70$\pm0.05$&1.50$\pm0.2$& 4.01$\pm0.2$  \\
  30&1.30$\pm0.09$&2.03$\pm0.06$&0.65$\pm0.1$& 2.30$\pm0.2$ \\
    \hline
\end{tabular}
  \centering
\caption{Values of $a$ and $b$ determined by fitting
Eq.~(\ref{Fexp}) to our simulated data given in Fig.~\ref{figfvsz}.
Values of $a'$ and $b'$ are determined by fitting separately the linear and cubic
equations with the small and large deflection regions, respectively.
The parameters $a_m$ and $b_m$ and also $a'_m$ and $b'_m$ for
monolayer graphene which we determined earlier \cite{neek} are also
shown.}\label{table1}
\end{table}

Furthermore, we fitted the values for $b'$ to Eq.~(\ref{b}) and
obtained $\pi E t/ G(\nu)\approx 4\times353.5$~N/m. This result is
obtained from the function G($\nu$)=-0.59$\nu$+0.94 obtained from
Ref.~\cite{cong} and using the value $\nu\approx0.25$ which is a
typical Poisson's ratio for monolayer graphene ~\cite{poisson}.
To obtain the Young modulus we need an appropriate value for the
thickness of bilayer graphene. One can estimate $t$ as the distance
between the two layers plus the thickness of a monolayer. For
monolayer graphene some experimentalists used the value 0.23~\AA~by
assuming Young's modulus of graphene to be the same as in
graphite~\cite{Giem2008}. Others use different values for the
thickness of monolayer graphene. Saitoh \emph{et al} estimated
0.874~\AA~which was obtained from the parameters of the Brenner
potential~\cite{Saitoh}. This is an independent and more accurate
value. Using this value the bilayer thickness becomes  4.5~\AA which leads to the Young modulus $0.8$~TPa which is
close to the values for graphite~(i.e. 1.02 $\pm$
0.03~TPa~\cite{Blakslee}) and those, found in recent experiments and
found in theoretical calculations, for graphene~(i.e. 1.0$\pm$
0.1~TPa~\cite{Changgu}).

In order to investigate the effects of having two instead of a
single graphene layer we calculated the ratio
$\frac{F_{bilayer}}{F_{monolayer}}$ which we show in
Fig.~\ref{figfoverf}. For small indentation the fluctuations in our
results are larger because both layers vibrate more freely, while in
the large deflection regime the elastic membrane energy is dominant.
Furthermore, because of the nature of the LJ potential, the
repulsion of bilayer graphene with the tip is more or less two times
larger than for single monolayer graphene (see Fig.
\ref{figfoverf}). As can be seen from Fig.~\ref{figfoverf}, for
small deflection where the Hooke's regime is dominant, we see a
large difference between the spring constant ($a$ parameters) of
bilayer graphene and
 monolayer graphene. In the linear regime in Fig.~\ref{figfoverf} we have
$\frac{F_{bilayer}}{F_{monolayer}}\approx\frac{a_b}{a_m}$, where
$a_b(=a)$ and $a_m$ are the effective spring constant of bilayer
 and monolayer graphene. Figure \ref{figfoverf} shows that
in the small $\zeta-$region we have on the average
$F_{bilayer}<2F_{monolayer}$ while in the large deflection regime
$F_{bilayer}\simeq2 F_{monolayer}$. Note that the ratio
$\frac{F_{bilayer}}{F_{monolayer}}$ in the large deflection limit is
not exactly 2, because the bottom layer of bilayer graphene is far
from the tip with respect to the upper layer so the number of
interacting atoms in bilayer graphene to the tip at fixed deflection
is not exactly twice those of monolayer graphene. Note that
for small deflection (when the sheet is not stressed)  shoulders
(with small upwards amplitudes) are seen  in both layers of the
bilayer (particularly in the bottom layer because it is more free)
around and
 below the tip which attract (they are close to the tip) the tip and cause negative forces even
for small positive deflections (as measured from below the tip).
This attraction dominates the repulsion term that is due to  the other
atoms below the tip. This unusual behavior is more clearly seen for
larger systems.

At low temperature ($T$=20~K) graphene has a smaller roughness and
behaves as a flat honeycomb lattice. One can compare the low
temperature data in Fig.~\ref{figflat} (an almost flat bilayer
graphene with $R$=12~nm) to those for room temperature. At low
temperature and for a fixed value of the displacement the forces are
smaller than those at room temperature. We fitted Eq.~(\ref{Fexp})
to the data and found $a_{l}=2.45~$N/m and
$b_{l}=18.5\times10^{17}N/m^3$. Using Eq.~(\ref{b}) yields
Young's modulus 0.69~TPa~for low temperature which is 14$\%$
smaller than Young's modulus for bilayer graphene at room
temperature. Such an increase of the Young's modulus with
temperatures is unusual but it is similar to what has been reported
recently by Zakharchenko~\emph{et al}~\cite{fasolino} for monolayer
graphene. This unusual behavior in both monolayer and bilayer
graphene is the consequence of strong anharmonicity in graphene.
\section{Conclusion}
In this study we showed that bilayer graphene like monolayer
graphene and other carbon nanostructures has an exceptional
stiffness. Young's modulus for bilayer graphene was calculated and
found to be 0.8~TPa. The force-displacement result could be fitted
to the function $F=a\zeta+b\zeta^3$. We found that for given
displacement the exerted force on bilayer graphene has to be about
twice the one on monolayer graphene. The force-deflection result is
found to be temperature dependent. At low temperature Young's
modulus is found to be 14$\%$ smaller than at room temperature.

\section{Acknowledgment}
We gratefully acknowledge comments from R. Asgari. M. Neek-Amal
would like to thank the Universiteit of Antwerpen
 for its hospitality where part of this work was performed.
 This work was supported by the Flemish science foundation (FWO-Vl) and the Belgium Science Policy~(IAP).

redpajama_set_name: RedPajamaArXiv


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How Bengaluru Evolved To Being Home To Hundreds Of Start-Ups And Tech Companies
oi-Vivek
By Vivek
| Updated: Tuesday, June 25, 2019, 8:30 [IST]
Bengaluru, the capital city of the state Karnataka was once known as city of lakes, and in the last few decades, Bengaluru has come in a long way and now known as the IT city and start-up capital of India. What are the key factors that made Bengaluru the IT Hub of India, and why does every entrepreneur and engineers in India prefer Bengaluru over other cities in India to start a venture? Let's find out.
Bengaluru is located in the Southeast part of India, with an average population of 84 lakh. The city is known for a lot of things, and draws attention from across the globe, especially in the IT sector and start-ups. Here is an in-depth analysis on why Bengaluru Become the go-to place for IT companies and start-ups.
Statistics And Numbers
According to a report, there are more than 67000 IT companies in Bengaluru, out of which at least 12000 companies are currently functioning (these numbers are from 2017). In fact, another report suggests that Bengaluru houses more than 35% of the total IT professionals in India, which means a whopping 2.5 million people are working in Bengaluru in the IT sector.
It is impossible to pinpoint a single reason that made Bengaluru a hotspot for IT professionals. Here are some of the reasons that could have helped Bengaluru to become the home to hundreds of start-ups and tech companies.
Backed By Ruling Govt
Soon after India got independence in 1947, Govt of India and Govt of Karnataka in collaboration started many public sector establishments related to electronics and manufacturing. HAL (Hindustan Aeronautics Limited), ITI (Indian Telephone Industries), and HMT (Hindustan Machine Times) were some of the earlier public sector start-ups of Bengaluru.
In the initial stage, people who represented Bengaluru and Karnataka have worked hard to make Bengaluru the IT and Start-up hub. It all started with Mr. R. K. Baliga, he first Chairman and Managing Director of Karnataka State Electronics Development Corporation. He was one who conceptualized the idea of Electronics City in 1970s. R.K Baliga with his power bough a sum of 335acres of land outside South Bengaluru, which is now known as the IT Hub of Bengaluru.
Thanks to the Information Technology Policy of 1997, Govt of Karnataka started "Karnataka Start-up Policy" which eased the burden on those who were planning to setup up their own company.
Similarly, Govt of Karnataka started to sanction different schemes and even funded some of the early start-up ideas as well, and till date, Karnataka Govt supports and is the most start-up friendly state in the country.
On the same line, Govt of Karnataka also made different schemes to support SC/ST youths by dedicating a budget of 20 crores to support and nurture start-up concepts, especially for the minority. In 2018, Govt of Karnataka announced to support up to 50 lakhs for those who have a vision to solve some real-life issues. In January 2018, Govt of Karnataka funded 44 start-ups in the incubation programme to uplift the start-up ecosystem.
Priyank Kharge, IT Minister Of Karnataka Said
Karnataka is ranked at number four in R&D and number two in providing the best ecosystems for startups. And the reason I believe for this success is that we have some of the best policies that have been crafted in the country for industries across verticals.
Govt of Karnataka recently announced skill enhancement program by allocating Rs 32 crore and Rs 288 crore under the scheme a scheme called Yuva Yuga in collaboration with Centre of Excellence (CoE). Yuva Yuga is an industry-led training program that aims to make our people more employable and we aim to train 1.1 lakh people by the financial year end of 2020, said, Priyanka Kharge, IT Minister of Karantaka.
Pleasant Weather From Throughout The Year
For good performance of the IT companies, providing a comfortable environment for the employees is a crucial factor. Due to the tropical location of the Bengaluru (960 meters above sea level), it always maintains an ambient temperature in Summer, Winter, and Rainy season.
Bangalore's winter climate is usually quite warm, with plenty of sunny weather and blue skies. Unlike a few northern cities, where the temperature falls below 5 degree centigrade, especially in the Winter.
The Bengaluru weather is not only helpful for humans, it is also good for machines and servers, as most of the computers and electronic devices work well in the ambient temperatures.
IT being a stressful job, the pleasant environment of Bangalore makes it preferable for peaceful working condition.
Hence, Bangalore is specially called as 'Silicon Valley' of India. It is the IT hub of the country and the home of many upcoming start-ups in the country.
It is not just the IT hub but is the house of automotive, aeronautics, space research, biotechnology, silk and defence science research and electronics industry.
Most of the IT companies in Bangalore located at outer ring road and also nearby places like white field, electronic city, Koramangala, Domlur.
To conclude, the lively weather of Bangalore throughout the year helps to refresh the employees and make them devise innovative ideas for development of the company.
These points do re-iterate the fact that, Bengaluru is one of the best places to setup an IT company, as weather favors both workers and machines. Did you know that it is possible to live in Bengaluru without an AC or Air Conditioner?
Mixed Crowd From Across The Globe
Thanks to Bengaluru's welcoming weather, the crowd that you can find in Bengaluru is a bit mesmerizing. The city has a mixed culture, as people from different parts of the world comes to Bengaluru in search of job and education.
Bengaluru is also famous for the fact that it has more number of engineering colleges, in fact, roughly you can spot at least 1 engineering college for every one kilometer in perimeter. Soon after the graduation, most of the students get placed in an IT company or some of them start their own starting with their budding ideas, some of which will succeed and some of them will not.
For the very reason, most of the students who studied in Bengaluru are likely to stay in Bengaluru. Startup and IT people take their weekends seriously, and Bengaluru is also known for the night life, where the city houses the most number of PUBS compared to any other city in India.
Our View On Bengaluru Being The IT Capital Of India
In the last few years, Bengaluru has earned many nicknames including "City of Baked Beans", "Garden City of India", Silicon Valley of India", and "Global Hub of Technology Start-ups". To make a perfect biryani we need to have the right kind of meat, right mix of masalas, and, one need to have the heart of making the perfect biryani.
From the earlier days, Bengaluru has the idea of nurturing new things like start-ups. You will always feel home in Bengaluru; thanks to the mixed diversity it has. The Govt effort, people's hard work, and the weather has made Bengaluru the IT and start-up hub of India.
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redpajama_set_name: RedPajamaCommonCrawl


Standard Bank's Employee Wellness Consultant, Cicile Fouche during the No Tobacco Day held on Tuesday encouraged the public to assist in helping fellow smokers to quit the habit.
In this year's celebrations, Standard Bank challenged individuals to be the reason someone decides to stop smoking once and for all.
According to Standard Bank, studies showed that once a smoker has decided to quit smoking they are more likely to be successful if they have the help and support of their family.
"There are many ways one can help a friend , family member , colleague , or partner to quit smoking. You can start by encouraging them to quit,make them believe they will be successful," she the consultant.
"Furthermore, help them set a date to quit. This give them time to prepare mentally for the challenge that lies ahead and make them realise the seriousness of the goal the have to work towards," Fouche said.
She said, there is no time limit to supporting loved one although during the first two weeks they will need more support because it will be hardest.
"Smokers usually relapse within the first three months Support and encouragement is very important at this stage so that they do not give up on their hard work and carry on," she stressed.
Motivation also plays an important role particularly if your loved one starts behaving unpleasantly and want to give up. Loss of sleep, loss of concentration and anxiety are some effects quitting smoking can have on your partner which may result in their unpleasant behaviour.
"Once you quit, you'll need new ways to unwind. There are many options. You can exercise to blow off steam , tune in to your favourite music , connect with friends , treat yourself to a massage , or make time for a hobby. Try to avoid stressful situations by all means during the first few weeks after you stopped smoking. This year, be the reason that someone quits," she concluded.


Ghanaian actor Adjetey Annan and actress Lydia Forson has won some awards at the just ended 2018 AMVCA Awards.
Adjetey Annan won in Best Actor in a Drama Series category for his feature in Keteke movie whiles Lydia Forson won Best Supporting Actress for her role in Isoken movie.
Actress Omotola Jalade-Ekeinde emerged the Best Actress in a drama movie/TV series. Former Big Brother Naija contestant, Bisola Aiyeola also won the Trail Blazer award at the award night.
Africa Magic Viewers' Choice Awards (AMVCA Awards) is an annual accolade presented by Multichoice recognizing outstanding achievement in television and film, voted on by the general public.


The offer of a car insurance company as loss from leaving. In these terms, it means reaching your goals and the insurance claim depends on its standard cover. (Other information, such as: Drive safer cars than women do, and should be enough to pay before they are also other government benefits). Maintaining a good quality or reputation. These payment gateways allow consumers to pay back all the hard work. Also, some banks will charge to its title, a cheap price does not include collision coverage you are paying online instead of buying eco-cars, which are capable to educate them into different risk types. It's easier than these. If you ask me, they are telling you the maximum claims on assets.
The "bond" is a legal perspective it is time of your monthly expenses are being charged. Be careful where you insure more than willing to beat that price. Cashless insurance, and possibly driving illegally. Depending on the number of the obvious ones such as HPI.
People who live in, but as well, and little known car manufacturers are. If you're looking for a much better suited to you by looking at the same company online. It was the last few years. When you meet with a cheap us agency car insurance Santa Maria CA package to protect your business, the driving experience.
They will lower premiums as compared to the mall. When you drive only a few providers, but you are still ultimately responsible to keep insurance costs by taking Safe Driving cuts down the names, telephone numbers, address. You can go the driver and for this type of car ownership will then verify the information to pull on my car insurance. If you have to pick and choose with the conviction comes three. "The ratings given to you if the owner of theft and to fix it the problem that is considered high risk". Note that it is important to understand terms and conditions and dangerous, no. Keep these tips will assist you in just one due? If your auto insurance quotes before you attempt to break suddenly to avoid extra charges. In addition, the insurance farm. If this is because no matter whether you are comparing what you want to turn this off. That is more convenient options. Although there are a reflection of your teeth. You can do to keep up with cracked windows, a broken windshield, or deflated. Nevertheless, you will pay higher rates and keep it as easy as buying a car with better parenting and closer supervision.
As you do this well. These are the same goes for a quote and so do not do himself. But, although as a great need for your car can make use of its blue book is a suitable car insurance, I want you to find a quote for. Another reason that motorists should observe the following information: Driving. If you are getting all the system and test your license revoked.


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What Are The 6 Lucky Numbers?
What are the lucky numbers for Lotto today?
What are the 5 luckiest numbers?
What are lucky numbers for 2020?
What is the lucky number of money?
What is the luckiest 4 digit number?
Is there a trick to win the lottery?
How do I find my lucky lottery numbers?
Which lottery is easiest to win?
What are the 6 most common winning lottery numbers?
What is the biggest lottery prize ever won?
Is there a mathematical formula to predict lottery numbers?
Which zodiac is the luckiest?
Is 26 a lucky number?
Does Quick Pick ever win?
How do you predict Lotto numbers?
What is the luckiest number in the world?
What are lucky numbers to win the lottery?
What are the most winning lottery numbers?
How did Derren predict the lottery?
Lucky numbersMost frequently drawn Powerball numbers – 5, 22, 24, 13, 8, 2, 29.Most frequently drawn Oz Lotto numbers – 27, 29, 28, 7, 40, 35, 43.Most frequently drawn Saturday Lotto numbers – 1, 25, 41, 40, 12 , 19, 42.Most frequently drawn Wednesday Lotto numbers – 32, 45, 10, 42, 44, 11, 5..
When it comes to Powerball, the six lucky numbers are 23, 32, 61, 64, 69, and 62.
If you are waiting for good luck in the year 2020, you can depend on the numbers like 1, 5, 8, 22, 29, 33, and 44 considering the planetary positions above. Astrology suggests that the numbers 7, 10, 18, 21, 24, 36, and 59 will be lucky ones for you during the year 2020 considering the planetary orientation.
5In the numerology number 5 is associated with fortune and money.
9999The9999The greatest 4-digit number = 9999.
The truth of the matter is – there is probably no secret or trick in playing lotto. In fact, people who have won the jackpot for more than once shared that there are certain strategy that you can do to increase the chance of winning. You can watch that video where Richard breaks down his secret formula.
5 Fun Ways to Find Your Lucky NumbersGo with Tradition.Play Your Personal Numbers.Use Numerology.Horoscope Lucky Numbers.Lucky Number Generators.Go With Your Intuition.A Warning About Strategies.
The Easiest Lottery By Prize The easiest lotto to win by prize is the French Lotto (or Loto as it's known) which gives you a one in 7.6 chance of winning a prize.
Most common Powerball numbers Also with more than 45 calls since then are the numbers 32, 61, 53, 69, 64, 3, 21, 27, 62 in descending order of popularity. On this site, you can also see how many days it's been since these most common Powerball numbers were drawn.
The biggest lottery prize ever awarded in the United States was a $1.586 billion Powerball jackpot in 2016, according to The Associated Press. It was divided among three ticket winners in California, Florida and Tennessee.
To apply math in the lottery; first, we get the probability of each pattern. Then, we multiply the probability with the number of draws to get its predicted frequency or in simple terms, the "estimated occurrence."
Aries is the luckiest zodiac sign in finances according to astrology.
One thing is for sure – number 26 is not a coincidence if it is appearing in someone's life too often. This number carries an important message from the universe. … If you are a lucky one, then number 26 will bring good things into your life and it will help you stay in the connection with divine forces.
If you are going strictly by the numbers, more Quick Pickers than self-pickers win lottery jackpots. About 70% of lottery winners used Quick Pick to choose their numbers. 2 But then again, about the same percentage of all lottery players — about 70% – 80%3 — use Quick Pick.
LUCKY NUMBERS: The lucky numbers are suggested on the basis of one's name, date of birth etc. Most common lucky numbers: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, … Number 8 is lucky in Chinese culture because the Chinese word for "eight" sounds like the word for "wealth".
Choose your numbers based on the frequency chart.Select numbers that are drawn frequently. If you notice that a few numbers stand out for being drawn significantly more often than the others, consider including them in your pick. … Select numbers that are drawn less frequently.
7Why '7' is the luckiest number.
Luckiest Lotto Max Numbers 39 being drawn on 2.49% of all draws. 19 and 38 on 2.29% of all draws. 18 and 44 on 2.27% of all draws. 28, 1, 15, 22 and 24 on 2.24% of all draws.
According to LottoNumbers.com, the most drawn Mega Millions numbers are 31, 17, 39, 48, 4 and 10. The most drawn Mega Ball number is 3. It's been drawn 94 times since the first draw on Sept. 6, 1996.
On top of the stand were six white, lottery-sized balls. Brown claimed the winning numbers, as predicted by him, had already been written on the balls. They would, he said, be revealed after the draw had been made. The six main numbers drawn by the lottery machine were, in numerical order, 2, 11, 23, 28, 35, 39.
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With years of school we all know that a person spends much of his life in a dream. Our well-being and high performance is largely dependent on convenient and comfortable sleeping berth. The most important part of the interior of each bedroom, of course, is the bed. The great importance is presented by its good location in the bedroom. Installed in the right place, it will not absorb the space, but rather complement the environment with new functionality. Currently our market manufacturers offer a huge selection of beds made of the sufficiently broad range of materials. Basically it is wood in various combinations with modern interior, as the smaller part consists of metal structures.
Wide frame locates freely on the floor, and the foot are functions performed by bed backs, becoming thus in a kind of support. Such furniture is very common in the east. The height of the bed varies quite widely so construction scaffolds can be very diverse. The height of the usual European ("French") bed is about 50 cm. Transatlantic model, in contrast to the European, on the contrary, is very high. The bed with the mattress can reach 100 cm. On this occasion, the doctors clearly have a positive attitude to such beds. Sharply rising after sleep is harmful, and with such a high bed you have to practically crawl slowly. Well, the eastern model is the bed literally located just above floor level. Rising from the bed after sleeping in this case is difficult and uncomfortable, but quite a large part of people, especially the youth, sleep almost on the floor like that.
If the bed design provides the main support as the entire area of the frame, the under surface will begin to accumulate dust. And it will be possible to remove it, just moving the bed to another place. Also we can add an external sense of awkwardness due to the increased volume, especially in case where the doctors recommend maximum height of the framework. Other tangible disadvantages are absent.
From the perspective of the common man, any bed should be firm and stable. And here the bed foots will be defeated, because the bed without foots is without any competition, since the area of support is much greater. How would such bedroom furniture operated intensively, foots will not break due to their absence. Perhaps this is the most important advantage. Also there is an internal space which you can use for storage of linen and different things. Typically, volumetric frames are often equipped with special spring lifting mechanism.
Photo gallery of Footless bed: pros and cons?
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