Fix spacing around citations (issue 108)

Author: davidlmobley

paper/basic_training.tex

@@ -244,7 +244,7 @@ \subsubsection{Books}
 Depending on the background, the practitioner can choose one or more of the following books to either learn or refresh their basic knowledge of thermodynamics.
 Here are some works we find particularly helpful:
 \begin{itemize}
-\item Atkins and De Paula's ``Physical Chemistry'' \cite{AtkinsBook}, chapters 1 to 4.
+\item Atkins and De Paula's ``Physical Chemistry'' ~\cite{AtkinsBook}, chapters 1 to 4.
 \item McQuarrie and Simon's extensive work, ``Physical Chemistry: A Molecular Approach''~\cite{McQuarrie:1997:}
 \item Dill's ``Molecular Driving Forces''~\cite{DillBook}
 \item Kittel and Kroemer's ``Thermal Physics''~\cite{Kittel:1980:}
@@ -728,7 +728,7 @@ \subsubsection{Background and How They Work}
 
 Thermostat algorithms work by altering the Newtonian equations of motion that are inherently microcanonical (constant energy).
 Thus, it is preferable that a thermostat not be used if it is desired to calculate dynamical properties such as diffusion coefficients; instead, the thermostat should be turned off after equilibrating the system to the desired temperature.
-However, while all thermostats give non-physical dynamics, some have been found to have little effect on the calculation of particular dynamical properties, and they are commonly used during the production simulation as well\cite{Basconi:2013:JChemTheoryComput}.
+However, while all thermostats give non-physical dynamics, some have been found to have little effect on the calculation of particular dynamical properties, and they are commonly used during the production simulation as well~\cite{Basconi:2013:JChemTheoryComput}.
 
 There are several ways to categorize the many thermostatting algorithms that have been developed.
 For example, thermostats can be either deterministic or stochastic depending on whether they use random numbers to guide the dynamics, and they can be either global or local depending on whether they are coupled to the dynamics of the full system or of a small subset.
@@ -758,32 +758,32 @@ \subsubsection{Popular Thermostats}
         The simple velocity rescaling thermostat is one of the easiest thermostats to implement; however, this thermostat is also one of the most non-physical thermostats.
         This thermostat relies on rescaling the momenta of the particles such that the simulation's instantaneous temperature exactly matches the target temperature~\cite{thermostatAlgorithms2005}.
         Similarly to the Gaussian thermosat, simple velocity rescaling aims to sample the isokinetic ensemble rather than the canonical ensemble.
-        However, it has been shown that the simple velocity rescaling fails to properly sample the isokinetic ensemble except in the limit of extremely small timesteps\cite{Braun:2018}.
-        Its usage can lead to simulation artifacts, so it is not recommended\cite{Harvey:1998:JCompChem,Braun:2018}.
+        However, it has been shown that the simple velocity rescaling fails to properly sample the isokinetic ensemble except in the limit of extremely small timesteps~\cite{Braun:2018}.
+        Its usage can lead to simulation artifacts, so it is not recommended~\cite{Harvey:1998:JCompChem,Braun:2018}.
 
     \item \textbf{Berendsen}
 
-        The Berendsen\cite{berendsen1984molecular} thermostat (also known as the weak coupling thermostat) is similar to the simple velocity rescaling thermostat, but instead of rescaling velocities completely and abruptly to the target kinetic energy, it includes a relaxation term to allow the system to more slowly approach the target.
+        The Berendsen~\cite{berendsen1984molecular} thermostat (also known as the weak coupling thermostat) is similar to the simple velocity rescaling thermostat, but instead of rescaling velocities completely and abruptly to the target kinetic energy, it includes a relaxation term to allow the system to more slowly approach the target.
         Although the Berendsen thermostat allows for temperature fluctuations, it samples neither the canonical distribution nor the isokinetic distribution.
-        Its usage can lead to simulation artifacts, so it is not recommended\cite{Harvey:1998:JCompChem,Braun:2018}.
+        Its usage can lead to simulation artifacts, so it is not recommended~\cite{Harvey:1998:JCompChem,Braun:2018}.
 
     \item \textbf{Bussi-Donadio-Parrinello (Canonical Sampling through Velocity Rescaling)}
 
-        The Bussi\cite{Bussi:2007:JChemPhys:Canonical} thermostat is similar to the simple velocity rescaling and Berendsen thermostats, but instead of rescaling to a single kinetic energy that corresponds to the target temperature, the rescaling is done to a kinetic energy that is stochastically chosen from the kinetic energy distribution dictated by the canonical ensemble.
+        The Bussi~\cite{Bussi:2007:JChemPhys:Canonical} thermostat is similar to the simple velocity rescaling and Berendsen thermostats, but instead of rescaling to a single kinetic energy that corresponds to the target temperature, the rescaling is done to a kinetic energy that is stochastically chosen from the kinetic energy distribution dictated by the canonical ensemble.
         Thus, this thermostat properly samples the canonical ensemble.
         Similarly to the Berendsen thermostat, a user-specified time coupling parameter can be chosen to vary how abruptly the velocity rescaling takes place
-        The choice of time coupling constant does not affect structural properties, and most dynamical properties are fairly independent of the coupling constant within a broad range\cite{Bussi:2007:JChemPhys:Canonical}.
+        The choice of time coupling constant does not affect structural properties, and most dynamical properties are fairly independent of the coupling constant within a broad range~\cite{Bussi:2007:JChemPhys:Canonical}.
 
     \item \textbf{Andersen}
 
-        The Andersen\cite{andersen1980molecular} thermostat works by selecting particles at random and having them ``collide'' with a heat bath by giving the particle a new velocity sampled from the Maxwell-Boltzmann distribution.
+        The Andersen~\cite{andersen1980molecular} thermostat works by selecting particles at random and having them ``collide'' with a heat bath by giving the particle a new velocity sampled from the Maxwell-Boltzmann distribution.
         The number of particles affected, the time between ``collisions'', and how often it is applied to the system are possible variations of this thermostat.
         The Andersen thermostat does reproduce the canonical ensemble.
         However, it should only be used to sample structural properties, as dynamical properties can be greatly affected by the abrupt collisions.
 
     \item \textbf{Langevin}
 
-        The Langevin\cite{schneider1978molecular} thermostat supplements the microcanonical equations of motion with Brownian dynamics, thus including the viscosity and random collision effects of an implicit solvent.
+        The Langevin~\cite{schneider1978molecular} thermostat supplements the microcanonical equations of motion with Brownian dynamics, thus including the viscosity and random collision effects of an implicit solvent.
         It uses a general equation of the form $F = F_{interaction} + F_{friction} + F_{random}$, where $F_{interaction}$ is the standard interactions calculated during the simulation, $F_{friction}$ is the damping used to tune the ``viscosity'' of the implicit bath, and $F_{random}$ effectively gives random collisions with solvent molecules.
         The frictional and random forces are coupled through a user-specified friction damping parameter. Careful consideration must be taken when choosing this parameter; in the limit of a zero damping parameter, both frictional and random forces go to zero and the dynamics become microcanonical, and in the limit of an infinite damping parameter, the dynamics are purely Brownian.
 
@@ -794,7 +794,7 @@ \subsubsection{Popular Thermostats}
         The choice of ``mass'' of the fictitious particle (which in many simulation packages is instead expressed as a time damping parameter) can be important as it affects the fluctuations that will be observed.
         For many reasonable choices of the mass, dynamics are well-preserved~\cite{Basconi:2013:JChemTheoryComput}.
         This is one of the most widely implemented and used thermostats.
-        However, it should be noted that with small systems, ergodicity can be an issue\cite{martyna1992nose,thermostatAlgorithms2005}.
+        However, it should be noted that with small systems, ergodicity can be an issue~\cite{martyna1992nose,thermostatAlgorithms2005}.
         This can become important even in systems with larger numbers of particles if a portion of the system does not interact strongly with the remainder of the system, such as in alchemical free energy calculations when a solute or ligand is non-interacting.
         Martyna et al.~\cite{martyna1992nose} discovered that by chaining thermostats, ergodicity can be enhanced, and most implementations of this thermostat use Nos\'{e}-Hoover chains.
 
@@ -848,7 +848,7 @@ \subsubsection{Background and How They Work}
 To sample from the isothermal-isobaric ensemble (NPT), a thermostating algorithm like the ones discussed earlier must also be applied.
 
 Much of the background information on barostats is analogous to thermostats.
-The pressure of a molecular dynamics simulation is commonly measured using the virial theorem (an expectation value relating to positions and forces)\cite{ShellNotes, LeachBook}.
+The pressure of a molecular dynamics simulation is commonly measured using the virial theorem (an expectation value relating to positions and forces)~\cite{ShellNotes, LeachBook}.
 When pairwise interactions and periodic boundary conditions are considered, different approaches are often utilized~\cite{allenTildesleyLiquids, tuckermanBook, ShellNotes}.
 Regardless, these formulas give pressure as a time-averaged quantity, similar to the temperature.
 If we use these formulas to calculate the pressure for a single snapshot, this quantity is referred to as the instantaneous pressure.