[1] Deepark Ojha

# # VSFG of the water liquid-vapor interface from density functional theory-based molecular dynamics simulations

We use an instantaneous definition of the surface, which is more adapted to the study of interfacial phenomena than the Gibbs dividing surface.

How to define instantaneous surface?

What is thickness of the air-water interface?

By calculating the vibrational properties for interfaces of varying thickness, we show that the bulk spectra signatures appear after a thin layer of 2-3 angstrams only.

The thickness of the air-water interface should change along the temperature. What is thickness of the air-water interface at the temperature 0 'C.

The main features include a sharp peak at 3700 cm^-1, readily assigned to the dangling OH bonds protruding into the vapor, and a very broad band for the hydroghen bonded OH groups whose interpretation remains controversial.

[1] Marialore Sulpizi, JPCL, 2012

# # Instantaneous liquid interfaces

A coarse grained density field is constructed, and the interface is defined as a constant density surface for this coarse grained field.

Why they can say their definition is good?

What kind of results can be used to verified the goodness of this definition?

The instantaneous density field at space-time point ($\bold{r}$, t),

$\rho(\mathbf{r}, t)=\sum_{i} \delta\left(\mathbf{r}-\mathbf{r}_{i}(t)\right)$

The sum is over all such particles of interest. We are interested in the water molecules at the interface.

Normal distribution

$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e ^ {-\frac{1}{2} (\frac{x-\mu}{\sigma})^2}$

where $f(x)$ is the probability density function, $\sigma$ is the standard deviation, and $\mu$ is the mean.

$\phi(\mathbf{r} ; \xi)=\left(2 \pi \xi^{2}\right)^{-d / 2} \exp \left(-r^{2} / 2 \xi^{2}\right)$

where $\xi$ is the coarse graining length, and $d$ stands for dimensionality. Applied to $\rho(\mathbf{r}, t)$ we have the coarse grained density field

$\bar{\rho}(\mathbf{r}, t)=\sum_{i} \phi\left(\left|\mathbf{r}-\mathbf{r}_{i}(t)\right| ; \xi\right)$

The choice of $\xi$ will depend upon the physical conditions under considerations. With $\xi$ set, we define interfaces to be the $(d-1)$-dimensional manifold $\mathbf{r} = \mathbf{s}$ for which

$\bar{\rho}(\mathbf{s},t) = c,$

where $c$ is a constant. In other words, we define instantaneous interfaces to be points in space where the coarse grained density field has the value $c$.

How to define the interface of the air-water interface?

In water simulaions, the dimensionality is 3. Hence, the air-water interface is the 2-dimensional manifold. Two-dimensional manifolds are also called surfaces.

For a given molecular configuration, $\{\mathbf{r}_i{t}\}$, the obove equation can be solved quickly through interpolation on a spatial grid. We have taken $\{\mathbf{r}_i(t)\}$ to refer to the positions of all the oxygen atoms in the system, and because the bulk correlation length of liquid water is about one molecular diameter, we have used use $\xi = 2.4$ Å; further, we have used $c = 0.016$ Å$^{-3}$, which is approximately one-half the bulk density. The choice of coarse graining length, $\xi$, is just large enough so that the instantaneous density of bulk water contains few if any voids.

[1] Adam P. Wallard and Divid Chandler

# # CAIR & SKL-IOTSC(UM) Distinguished Lecture Series: Workshop on AU Security and Forensics

To tell real and fake, they look at the shape of eyes.

This was what I have thought before. Use defferent sensors seem like we are going back to the classical way of programming.