star - Standard conditions for a heliacal rising

What I do is compute the limiting magnitude for the position of the object I am interested in, and subtract it from the magnitude of the object (I call this the magnitude contrast). If negative, it should be visible with the naked eye. I use the function limmag_jd() in the Fortran library libTheSky for this.

In order to find the best moment in a given night, I compute the contrast for say every 15 minutes, and find the minimum. You can do this for a number of nights, until the best contrast found is negative, which would be the heliacal rising.

I'm not sure whether there is an easy way using a simple equation - the limiting magnitude will depend on things like the positions of Sun, Moon and the object in question, the phase of the Moon, the magnitude of the object, etc.

gravity - How can a galaxy in-between our view and the galaxy behind it have a 'lensing effect'?

It's called gravitational lensing. Here's a link to the wikipedia article on the subject: http://en.wikipedia.org/wiki/Gravitational_lens.

Gravity affects everything, including light. A massive object such as a star, a galaxy, or in this case, a cluster of galaxies, bends the path of photons that pass very close to the massive object. Bending light is the basis of the lenses in an optical telescope.

The behavior of a gravitational lens is different from that of an optical lens., but the end result is the same: Gravitational lenses enable astronomers to see more distant objects than they would without them. Gravitational lenses create multiple images of the remote objects behind the lens. Oftentimes these multiple images are in the form of streaks. See the below image of gravitational cluster Abell 1689, which is the cluster that let those astronomers see A1689-zD1.

The cluster magnified the remote galaxy A1689-zD1 by a factor of 9.3. Without that magnification, that remote galaxy would be invisible to current technology.

zoology - List of species recently found of economic value

I can only answer for plants. The short answer is no, there is no central source of information of that kind.

You are basically asking about the sub-classifications economic botany and ethnobotany, which cover the economy and human uses of plants respectively. Neither field is particularly fast-paced, so you could simply keep up to date with the latest issues of journals like Economic Botany or Ethnobotany.

One key area of development for new valuable crops is in crop wild relatives, but there is no particular publication you should watch for that. Keep an eye on the Crop Trust as they will shortly be releasing, in collaboration with us (the Millennium Seed Bank) some reports and data about this.

If I wanted to keep up to date with all those things over time, I would set up some saved search alerts on Google Scholar for key search terms like 'emerging crop', 'new crop', 'crop wild relative', etc. Just perform a search on Scholar and then click the envelope button to the right of the search field to create a recurring search alert.

One other potential source of information would be to check FAOSTAT each year. You can examine global and local data about area under cultivation, yield, investment, commodity value, etc. of most crops. If something new were to emerge as a big player, it would appear on there.

Relationship between the Casimir force and dark energy

There are two problems that arise here. One obvious problem is that the Casimir effect is attractive¹, while dark energy is repulsive. The other problem is one of scale.

Casimir (1948) shows that, between two particles (instead of the oft-cited case of two plates)
$$delta E propto R^{-7}$$
That's an enormous drop-off. On large scales, this should be negligible. Dark energy, however, is clearly non-negligible on these scales, while its effects are unobservable on small scales.

The Casimir effect is certainly one manifestation of vacuum energy, which may also be the cause of dark energy (in some theories), but that doesn't mean that dark energy is an example of the Casimir effect, or vice versa.

---

^{1 There are exceptions, as pointed out by Stan Liou, which arise under certain conditions, but they wouldn't play a part here.}

solar system - What Causes the Large Radiation Fields Around Jupiter?

As you stated, we have not been able to simulate the pressure and temperatures required to generate those that are believed to exist in Jupiter's interior other than in short-lived shockwave experiments, according to the NASA webpage A Freaky Fluid inside Jupiter?, observing that

"Liquid metallic hydrogen has low viscosity, like water, and it's a good electrical and thermal conductor," says Caltech's David Stevenson, an expert in planet formation, evolution, and structure. "Like a mirror, it reflects light, so if you were immersed in it [here's hoping you never are], you wouldn't be able to see anything."

Going further, according to the article Jumpin' Jupiter! Metallic Hydrogen (Lawrence Livermore National Laboratory), discuss the shock wave results, finding the level at which hydrogen metallises as being

from 0.9 to 1.4 Mbar, resistivity in the shocked fluid decreases almost four orders of magnitude (i.e., conductivity increases); from 1.4 to 1.8 Mbar, resistivity is essentially constant at a value typical of that of liquid metals. Our data indicate a continuous transition from a semiconducting to metallic diatomic fluid at 1.4 Mbar, nine-fold compression of initial liquid density, and 3,000 K.

The findings from the researchers above are summarised in the diagram below

The source is the Jumping Jupiter link above.

the sun - Do sungrazing comets leave a field of meteoroids near the Sun?

The SOHO image you attached, provides some evidence, that most of the debris continues the trajectory of the original body.
Most of the debris hence won't replenish the Vulcanoid population.
But due to the disruptive event you get an additional delta-v, which may change the orbit a bit, however insufficient to slow down to a Vulcanoid orbit; compare the velocity of the comet near perihelion with the speed of sound as an order of magnitude estimate of the upper limit of the delta-v for debris.
Dust may either be slowed down in this or in future orbits in the solar corona to end up in the Sun, or blown away by solar radiation pressure, again no Vulcanoids.

biochemistry - What happens to colloidal particles in a liquid medium? And how to stabilize it?

"Colloidal particles: What are colloidal systems, give an example,--"

Milk, bear foam, paste, blood, ---

"what happens to colloidal particles in a liquid medium."

I understand the q as solid in liquid so a gel. Examples about gel are "agar, gelatin, jelly and opal" according to my lecture slides. The electrostatic forces are in some sort of middle phase: not enough to repulse into liquid form but not strong enough to form liquid either.

"How to stabilize colloidal systems in a liquid medium."

Wikipedia about stability (here)

"The stability of a colloidal system is the capability of the system
to remain as it is. Stability is hindered by aggregation and by
sedimentation phenomena, that determine phase separation."

Now different things to consider are:

• Electrostatic stabilization

"In a stable colloid, mass of a dispersed phase is so low that its buoyancy or kinetic energy is too weak to overcome the electrostatic
repulsion between charged layers of the dispersing phase."

• steric stabilization

"particles in polymers which prevents the particle to get close in the range of attractive forces."